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arxiv: 2607.00101 · v1 · pith:JZUSJXYXnew · submitted 2026-06-30 · 💻 cs.GT

From Welfare to Utility: Generalized Objectives in Budget-Feasible Procurement

Alon Eden , Eldar Kerner , Kira Goldner , Thodoris Tsilivis This is my paper

Pith reviewed 2026-07-02 17:12 UTC · model grok-4.3

classification 💻 cs.GT
keywords budget-feasible procurementmechanism designwelfare maximizationutility maximizationprior-free approximationBayesian mechanismex-post budget constraint
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The pith

In budget-feasible procurement, a simple mechanism achieves constant-factor welfare approximation without priors while Bayesian mechanisms optimize utility and can be adjusted for exact budget satisfaction.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops mechanisms for a buyer who wants to buy services from strategic sellers under a fixed budget, shifting focus from maximizing the buyer's value alone to maximizing welfare (value minus sellers' production costs) and utility (value minus payments to sellers). It presents a simple mechanism that guarantees a constant-factor approximation to optimal welfare even in the worst case over all possible seller costs. When the buyer knows the probability distribution of those costs, the paper gives an optimal mechanism for utility that meets the budget on average and then shows how to modify it so the budget holds for every realized set of costs while keeping utility nearly optimal. The same techniques extend to objectives that blend welfare and utility. A reader would care because many real procurement settings, such as hiring contractors or buying cloud services, impose hard budgets and sellers keep their costs private.

Core claim

For the welfare objective, a simple mechanism obtains a constant-factor approximation in the prior-free setting. For the utility objective, an optimal mechanism is provided that satisfies the budget constraint in expectation, which can then be modified to satisfy the budget ex-post while retaining near-optimal utility guarantees. The mechanisms are further generalized to other objectives.

What carries the argument

Budget-feasible mechanisms for welfare (value minus production costs) and utility (value minus payments), with a modification step that moves from expected-budget to ex-post-budget satisfaction.

If this is right

  • Constant-factor welfare approximation holds without any distributional knowledge of seller costs.
  • Utility can be maximized optimally when cost distributions are known, subject only to an expected budget constraint.
  • The utility mechanism can be altered to enforce the budget for every cost realization with only small loss in performance.
  • The same design approach extends directly to other linear combinations of value, costs, and payments.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Platforms could use the prior-free welfare mechanism when historical cost data is unavailable or unreliable.
  • The Bayesian-to-ex-post adjustment technique might transfer to procurement settings with additional constraints such as quality thresholds.
  • Testing the mechanisms on repeated procurement rounds could show whether the constant factors remain stable across changing seller populations.

Load-bearing premise

The buyer knows the exact probability distribution over sellers' private costs.

What would settle it

A single-seller instance in which every mechanism that always respects the budget yields zero utility, or a worst-case cost profile in which the welfare mechanism's guarantee falls below any fixed constant.

Figures

Figures reproduced from arXiv: 2607.00101 by Alon Eden, Eldar Kerner, Kira Goldner, Thodoris Tsilivis.

Figure 1
Figure 1. Figure 1: Allocation functions ˜xi(q) and x ∗ i (q). We rewrite agent i’s contribution to the (ironed) objective in quantile space: Z 1 0 [PITH_FULL_IMAGE:figures/full_fig_p031_1.png] view at source ↗
read the original abstract

We study mechanism design for the budget-feasible procurement problem, a natural problem that arises when a buyer wants to procure goods or services from multiple strategic sellers who each have a cost to provide that service, the buyer has a value for each service procured, but is constrained by a budget. In contrast to prior work, which has focused on buyer value maximization for this problem, we solve for optimal and approximately-optimal mechanisms for the objectives of buyer utility (value of procured services minus payments), welfare (value minus production costs), and generalizations of the two. For welfare, we design a simple mechanism that obtains a constant-factor approximation for the prior-free (worst-case) setting. As prior-free mechanisms fail to provide any guarantee for utility, even for a single seller, we consider Bayesian settings, where the buyer has distributional knowledge over sellers' costs. We first provide a utility-optimal mechanism that satisfies the buyer's budget constraint in expectation, then we show how to modify the mechanism to satisfy the budget constraint ex-post, for every realization of seller costs, while still obtaining near-optimal utility guarantees. Finally, we generalize our mechanisms to other objectives.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The manuscript studies mechanism design for budget-feasible procurement, where a buyer procures from strategic sellers under a budget constraint. Unlike prior work focused on value maximization, it addresses buyer utility (value minus payments), welfare (value minus production costs), and generalizations of these objectives. For welfare, a simple mechanism is designed that achieves a constant-factor approximation in the prior-free (worst-case) setting. For utility, in Bayesian settings where the buyer knows the distribution over sellers' costs, an optimal mechanism is first given that satisfies the budget constraint in expectation; this is then modified to satisfy the budget ex-post for every cost realization while retaining near-optimal utility guarantees. The mechanisms are extended to other objectives.

Significance. If the claims hold, the work meaningfully extends budget-feasible mechanism design by shifting attention from value maximization to utility and welfare, with an explicit separation of prior-free and Bayesian regimes. The paper correctly flags that prior-free utility mechanisms fail even for a single seller, and the expectation-to-ex-post conversion follows standard technique while preserving near-optimality under distributional knowledge. These distinctions and the generalization step are useful contributions when rigorously established.

minor comments (3)
  1. [Abstract] The abstract states a 'constant-factor approximation' for welfare but does not name the factor; if the factor is derived in the body (e.g., §3 or Theorem 1), a parenthetical mention would improve readability.
  2. The transition from the expectation-budget mechanism to the ex-post version (described in the abstract) would benefit from an explicit statement of the approximation loss incurred by the modification, even if only a high-level bound.
  3. Notation for the generalized objectives is introduced late; defining the family of objectives (e.g., via a parameter α interpolating between welfare and utility) in §2 would clarify the scope of the final results.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the supportive review and recommendation of minor revision. The assessment correctly identifies the paper's focus on extending budget-feasible mechanism design beyond value maximization to utility and welfare objectives, along with the prior-free versus Bayesian distinction and the generalization step.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's central results distinguish prior-free welfare approximation (constant-factor mechanism) from Bayesian utility optimization (expectation-budget mechanism followed by ex-post modification). These rely on standard mechanism-design techniques for budget constraints rather than any self-definitional equations, fitted parameters renamed as predictions, or load-bearing self-citations. The abstract explicitly flags that prior-free utility guarantees fail even for one seller, confirming the results do not reduce to internal constructions. No load-bearing steps match the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; the distributional-knowledge assumption for the Bayesian case is the only visible modeling choice.

pith-pipeline@v0.9.1-grok · 5736 in / 1024 out tokens · 21957 ms · 2026-07-02T17:12:04.324243+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

233 extracted references · 64 canonical work pages · 2 internal anchors

  1. [1]

    Greenwade

    George D. Greenwade. The C omprehensive T ex A rchive N etwork ( CTAN ). TUGBoat. 1993

    1993

  2. [2]

    2010 , volume =

    Papadimitriou, Christos and Singer, Yaron , title =. 2010 , volume =

    2010

  3. [3]

    2010 , isbn =

    Singer, Yaron , title =. 2010 , isbn =. doi:10.1109/FOCS.2010.78 , booktitle =

    work page doi:10.1109/focs.2010.78 2010

  4. [4]

    2024 , month =

    Liu, Xiang and Chan, Hau and Li, Minming and Wu, Weiwei , booktitle =. 2024 , month =. doi:10.24963/ijcai.2024/899 , url =

    work page doi:10.24963/ijcai.2024/899 2024

  5. [5]

    European Journal of Operational Research , volume =

    Ludwig Ensthaler and Thomas Giebe , keywords =. European Journal of Operational Research , volume =. 2014 , issn =. doi:https://doi.org/10.1016/j.ejor.2013.09.031 , url =

    work page doi:10.1016/j.ejor.2013.09.031 2014

  6. [6]

    Economic Theory , number =

    B. Economic Theory , number =. 2009 , bdsk-url-1 =. doi:10.1007/s00199-008-0347-7 , id =

    work page doi:10.1007/s00199-008-0347-7 2009

  7. [7]

    , journal =

    Myerson, Roger B. , journal =. 1981 , publisher =

    1981

  8. [8]

    , title =

    Balkanski, Eric and Hartline, Jason D. , title =. 2016 , isbn =. doi:10.1145/2872427.2883032 , booktitle =

    work page doi:10.1145/2872427.2883032 2016

  9. [9]

    2014 , organization=

    Anari, Nima and Goel, Gagan and Nikzad, Afshin , booktitle=. 2014 , organization=

    2014

  10. [10]

    Yan, Qiqi , booktitle=

  11. [11]

    Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms , pages =

    Chen, Ning and Gravin, Nick and Lu, Pinyan , title =. Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms , pages =. 2011 , publisher =

    2011

  12. [12]

    2017 , publisher =

    Jarman, Felix and Meisner, Vincent , journal =. 2017 , publisher =

    2017

  13. [13]

    2025 , isbn =

    Bhawalkar, Kshipra and Dean, Jeff and Liaw, Christopher and Mehta, Aranyak and Patel, Neel , title =. 2025 , isbn =. doi:10.1145/3736252.3742683 , booktitle =

    work page doi:10.1145/3736252.3742683 2025

  14. [14]

    2025 , editor =

    Deng, Yuan and Karbasi, Amin and Mirrokni, Vahab and Paes Leme, Renato and Velegkas, Grigoris and Zuo, Song , booktitle =. 2025 , editor =

    2025

  15. [15]

    Proceedings of the 26th ACM Conference on Economics and Computation , pages =

    Charalampopoulos, Andreas and Fotakis, Dimitris and Patsilinakos, Panagiotis and Tolias, Thanos , title =. Proceedings of the 26th ACM Conference on Economics and Computation , pages =. 2025 , isbn =

    2025

  16. [16]

    2020 , publisher=

    Gravin, Nick and Jin, Yaonan and Lu, Pinyan and Zhang, Chenhao , journal=. 2020 , publisher=

    2020

  17. [17]

    2018 , publisher=

    Anari, Nima and Goel, Gagan and Nikzad, Afshin , journal=. 2018 , publisher=

    2018

  18. [18]

    2010 , organization=

    Kempe, David and Salek, Mahyar and Moore, Cristopher , booktitle=. 2010 , organization=

    2010

  19. [19]

    Flaxman and Jason D

    Matthew Cary and Abraham D. Flaxman and Jason D. Hartline and Anna R. Karlin , editor =. Proceedings of the Nineteenth Annual. 2008 , url =

    2008

  20. [20]

    Proceedings of the 42nd

    Sayan Bhattacharya and Gagan Goel and Sreenivas Gollapudi and Kamesh Munagala , editor =. Proceedings of the 42nd. 2010 , url =. doi:10.1145/1806689.1806743 , timestamp =

    work page doi:10.1145/1806689.1806743 2010

  21. [21]

    49th Annual

    Shahar Dobzinski and Ron Lavi and Noam Nisan , title =. 49th Annual. 2008 , url =. doi:10.1109/FOCS.2008.39 , timestamp =

    work page doi:10.1109/focs.2008.39 2008

  22. [22]

    Chayes and Nicole Immorlica and Mohammad Mahdian and Amin Saberi , editor =

    Christian Borgs and Jennifer T. Chayes and Nicole Immorlica and Mohammad Mahdian and Amin Saberi , editor =. Proceedings 6th. 2005 , url =. doi:10.1145/1064009.1064014 , timestamp =

    work page doi:10.1145/1064009.1064014 2005

  23. [23]

    2021 , isbn =

    Zhang, Jingwen and Wu, Yuezhou and Pan, Rong , title =. 2021 , isbn =. doi:10.1145/3442381.3449888 , booktitle =

    work page doi:10.1145/3442381.3449888 2021

  24. [24]

    22nd International World Wide Web Conference,

    Yaron Singer and Manas Mittal , editor =. 22nd International World Wide Web Conference,. 2013 , url =. doi:10.1145/2488388.2488489 , timestamp =

    work page doi:10.1145/2488388.2488489 2013

  25. [25]

    22nd International World Wide Web Conference,

    Adish Singla and Andreas Krause , editor =. 22nd International World Wide Web Conference,. 2013 , url =. doi:10.1145/2488388.2488490 , timestamp =

    work page doi:10.1145/2488388.2488490 2013

  26. [26]

    Nima Anari and Gagan Goel and Afshin Nikzad , title =. 55th. 2014 , url =. doi:10.1109/FOCS.2014.36 , timestamp =

    work page doi:10.1109/focs.2014.36 2014

  27. [27]

    2018 , publisher=

    Abebe, Rediet and Goldner, Kira , journal=. 2018 , publisher=

    2018

  28. [28]

    Abraham, Ittai and Babaioff, Moshe and Dughmi, Shaddin and Roughgarden, Tim , Booktitle =

  29. [29]

    1991 , url =

    Aharoni, Ron , journal =. 1991 , url =

    1991

  30. [30]

    , booktitle=

    Alaei, S. , booktitle=. 2011 , pages=. doi:10.1109/FOCS.2011.90 , ISSN=

    work page doi:10.1109/focs.2011.90 2011

  31. [31]

    1953 , publisher=

    Allais, Maurice , journal=. 1953 , publisher=

    1953

  32. [32]

    International Symposium on Algorithmic Game Theory , pages=

    Amanatidis, Georgios and Markakis, Evangelos and Santorinaios, Christodoulos and Sch. International Symposium on Algorithmic Game Theory , pages=. 2025 , organization=

    2025

  33. [33]

    2021 , organization=

    Amer, Ameer and Talgam-Cohen, Inbal , booktitle=. 2021 , organization=

    2021

  34. [34]

    Anderson, Edward J and Nash, Peter , year=

  35. [35]

    Econometrica , keywords =

    Armstrong, Mark , doi =. Econometrica , keywords =

  36. [36]

    Ausubel, Lawrence M and others , journal=

  37. [37]

    Ausubel, Lawrence M , journal=

  38. [38]

    Matthew , Booktitle =

    Azar, Pablo and Daskalakis, Constantinos and Micali, Silvio and Weinberg, S. Matthew , Booktitle =

  39. [39]

    2022 , isbn =

    Agrawal, Priyank and Balkanski, Eric and Gkatzelis, Vasilis and Ou, Tingting and Tan, Xizhi , title =. 2022 , isbn =. doi:10.1145/3490486.3538306 , booktitle =

    work page doi:10.1145/3490486.3538306 2022

  40. [40]

    Gonczarowski , editor =

    Moshe Babaioff and Kira Goldner and Yannai A. Gonczarowski , editor =. Proceedings of the 2020. 2020 , url =. doi:10.1137/1.9781611975994.150 , timestamp =

    work page doi:10.1137/1.9781611975994.150 2020

  41. [41]

    and Nisan, Noam , title =

    Babaioff, Moshe and Gonczarowski, Yannai A. and Nisan, Noam , title =. Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing , series =. 2017 , isbn =. doi:10.1145/3055399.3055426 , acmid =

    work page doi:10.1145/3055399.3055426 2017

  42. [42]

    Matthew , Booktitle =

    Babaioff, Moshe and Immorlica, Nicole and Lucier, Brendan and Weinberg, S. Matthew , Booktitle =

  43. [43]

    2310.02879 , archivePrefix=

    Eric Balkanski and Vasilis Gkatzelis and Xizhi Tan and Cherlin Zhu , year=. 2310.02879 , archivePrefix=

    work page arXiv

  44. [44]

    1997 , publisher=

    Banerjee, Abhijit V , journal=. 1997 , publisher=

    1997

  45. [45]

    2012 , isbn =

    Bei, Xiaohui and Chen, Ning and Gravin, Nick and Lu, Pinyan , title =. 2012 , isbn =. doi:10.1145/2213977.2214020 , booktitle =

    work page doi:10.1145/2213977.2214020 2012

  46. [46]

    American Economic Review , month =

    Bergemann, Dirk and Brooks, Benjamin and Morris, Stephen , doi =. American Economic Review , month =

  47. [47]

    Bhawalkar, Kshipra and Mertzanidis, Marios and Mohan, Divyarthi and Psomas, Alexandros , booktitle =

  48. [48]

    Birmpas, Georgios and Ezra, Tomer and Leonardi, Stefano and Russo, Matteo , journal=

  49. [49]

    2016 , publisher=

    Braverman, Mark and Chen, Jing and Kannan, Sampath , journal=. 2016 , publisher=

    2016

  50. [50]

    Matthew , journal=

    Briest, Patrick and Chawla, Shuchi and Kleinberg, Robert and Weinberg, S. Matthew , journal=. 2015 , publisher=

    2015

  51. [51]

    Proceedings of the 2017

    Johannes Brustle and Yang Cai and Fa Wu and Mingfei Zhao , Bibsource =. Proceedings of the 2017. 2017 , Bdsk-Url-1 =. doi:10.1145/3033274.3085148 , Pages =

    work page doi:10.1145/3033274.3085148 2017

  52. [52]

    1989 , publisher=

    Bulow, Jeremy and Roberts, John , journal=. 1989 , publisher=

    1989

  53. [53]

    , booktitle=

    Yang Cai and Daskalakis, C. , booktitle=. 2011 , pages=. doi:10.1109/FOCS.2011.76 , ISSN=

    work page doi:10.1109/focs.2011.76 2011

  54. [54]

    Matthew , title =

    Cai, Yang and Daskalakis, Constantinos and Weinberg, S. Matthew , title =. SIGecom Exch. , issue_date =. 2011 , issn =. doi:10.1145/1998549.1998555 , acmid =

    work page doi:10.1145/1998549.1998555 2011

  55. [55]

    Matthew Weinberg , booktitle =

    Yang Cai and Constantinos Daskalakis and S. Matthew Weinberg , booktitle =. 2012 , crossref =. doi:10.1109/FOCS.2012.88 , timestamp =

    work page doi:10.1109/focs.2012.88 2012

  56. [56]

    Matthew Weinberg , title =

    Yang Cai and Constantinos Daskalakis and S. Matthew Weinberg , title =. CoRR , volume =. 2013 , url =

    2013

  57. [57]

    Matthew , title =

    Cai, Yang and Daskalakis, Constantinos and Weinberg, S. Matthew , title =. Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms , series =. 2013 , isbn =

    2013

  58. [58]

    and Goldner, Kira and McAfee, R

    Cai, Yang and Devanur, Nikhil R. and Goldner, Kira and McAfee, R. Preston , title =. Proceedings of the 2019 ACM Conference on Economics and Computation , series =. 2019 , isbn =. doi:10.1145/3328526.3329562 , publisher =

    work page doi:10.1145/3328526.3329562 2019

  59. [59]

    and Weinberg, S

    Cai, Yang and Devanur, Nikhil R. and Weinberg, S. Matthew , title =. Proceedings of the Forty-eighth Annual ACM Symposium on Theory of Computing , series =. 2016 , isbn =. doi:10.1145/2897518.2897645 , acmid =

    work page doi:10.1145/2897518.2897645 2016

  60. [60]

    2013 , url =

    Cai, Yang and Huang, Zhiyi , booktitle =. 2013 , url =

    2013

  61. [61]

    Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing , series =

    Cai, Yang and Zhao, Mingfei , title =. Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing , series =. 2017 , isbn =. doi:10.1145/3055399.3055465 , acmid =

    work page doi:10.1145/3055399.3055465 2017

  62. [62]

    2019 , isbn =

    Cai, Yang and Zhao, Mingfei , title =. 2019 , isbn =. doi:10.1145/3328526.3329616 , booktitle =

    work page doi:10.1145/3328526.3329616 2019

  63. [63]

    2007.07990 , archivePrefix=

    Shuchi Chawla and Nikhil Devanur and Thodoris Lykouris , year=. 2007.07990 , archivePrefix=

    work page arXiv 2007

  64. [64]

    Proceedings of the Fifteenth ACM Conference on Economics and Computation , year =

    Chawla, Shuchi and Fu, Hu and Karlin, Anna , title =. Proceedings of the Fifteenth ACM Conference on Economics and Computation , year =

  65. [65]

    and Miller, J

    Chawla, Shuchi and Goldner, Kira and Karlin, Anna R. and Miller, J. Benjamin , title =. Proceedings of the 17th International Symposium on Algorithmic Game Theory (SAGT) , editor="Sch

  66. [66]

    Benjamin and Pountourakis, Emmanouil , title =

    Chawla, Shuchi and Goldner, Kira and Miller, J. Benjamin and Pountourakis, Emmanouil , title =. Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms , pages =. 2018 , isbn =

    2018

  67. [67]

    2021 , organization=

    Cai, Yang and Goldner, Kira and Ma, Steven and Zhao, Mingfei , booktitle=. 2021 , organization=

    2021

  68. [68]

    and Kleinberg, Robert , booktitle =

    Chawla, Shuchi and Hartline, Jason D. and Kleinberg, Robert , booktitle =. 2007 , url =

    2007

  69. [69]

    Chawla, Shuchi and Hartline, Jason D and Malec, David L and Sivan, Balasubramanian , Booktitle =

  70. [70]

    Games and Economic Behavior , volume =

    Shuchi Chawla and David Malec and Balasubramanian Sivan , keywords =. Games and Economic Behavior , volume =. 2015 , note =. doi:http://dx.doi.org/10.1016/j.geb.2012.08.010 , url =

    work page doi:10.1016/j.geb.2012.08.010 2015

  71. [71]

    Benjamin , Booktitle =

    Chawla, Shuchi and Miller, J. Benjamin , Booktitle =. 2016 , Bdsk-Url-1 =. doi:10.1145/2940716.2940756 , Isbn =

    work page doi:10.1145/2940716.2940756 2016

  72. [72]

    2022 , isbn =

    Chawla, Shuchi and Rezvan, Rojin and Teng, Yifeng and Tzamos, Christos , title =. 2022 , isbn =. doi:10.1145/3519935.3520065 , booktitle =

    work page doi:10.1145/3519935.3520065 2022

  73. [73]

    2023 , organization=

    Chawla, Shuchi and Rezvan, Rojin and Teng, Yifeng and Tzamos, Christos , booktitle=. 2023 , organization=

    2023

  74. [74]

    SIGecom Exch

    Chawla, Shuchi and Sivan, Balasubramanian , title =. SIGecom Exch. , issue_date =. 2014 , issn =. doi:10.1145/2692375.2692378 , acmid =

    work page doi:10.1145/2692375.2692378 2014

  75. [75]

    2000 , volume =

    Che, Yeon-Koo and Gale, Ian , journal=. 2000 , volume =

    2000

  76. [76]

    Chen, Yiling and Eden, Alon and Wang, Juntao , journal=

  77. [77]

    1971 , publisher=

    Clarke, Edward H , journal=. 1971 , publisher=

    1971

  78. [78]

    2023 , organization=

    Cohen, Avi and Feldman, Michal and Mohan, Divyarthi and Talgam-Cohen, Inbal , booktitle=. 2023 , organization=

    2023

  79. [79]

    2015 , publisher=

    Collinson, Robert and Ellen, Ingrid Gould and Ludwig, Jens , booktitle=. 2015 , publisher=

    2015

  80. [80]

    On the rate of convergence of Krasnosel'ski

    Cominetti, Roberto and Soto, Jos. On the rate of convergence of Krasnosel'ski. Israel Journal of Mathematics , volume=. 2014 , publisher=

    2014

Showing first 80 references.