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Some properties of geodesic $(\alpha,E)$-preinvex functions on a Riemannian manifold

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Absos Ali Shaikh Chandan Kumar Mondal, Ravi P Agarwal

Differential Geometry · Submitted 20 May 2019

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We have also established an important relation between geodesic $(\alpha,E)$-preinvex function and geodesic $(\alpha,E)$-invex function in a complete Riemannian manifold.

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arXiv ID1905.08182 (version 2)
Pith IDXIKTZKJJ, Pith's permanent record of this paper and its review
CitationAbsos Ali Shaikh Chandan Kumar Mondal, Ravi P Agarwal. "Some properties of geodesic $(\alpha,E)$-preinvex functions on a Riemannian manifold." arXiv:1905.08182 (2019). https://pith.science/paper/XIKTZKJJ
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,725 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.05 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.04 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

In this article, we have introduced the concept of \textit{geodesic $(\alpha,E)$-invex set} and by using this concept the notion of \textit{geodesic $(\alpha,E)$-preinvex functions} and \textit{geodesic $(\alpha,E)$-invex functions} are developed on a Riemannian manifold. Moreover, several properties and results are deduced within aforesaid functions. An example is also constructed to illustrate the definition of geodesic $(\alpha,E)$-invex set. We have also established an important relation between geodesic $(\alpha,E)$-preinvex function and geodesic $(\alpha,E)$-invex function in a complete Riemannian manifold.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this article, we have introduced the concept of \textit{geodesic $(\alpha,E)$-invex set} and by using this concept the notion of \textit{geodesic $(\alpha,E)$-preinvex functions} and \textit{geodesic $(\alpha,E)$-invex functions} are developed on a Riemannian manifold. contribution 1.00 0.96 0.18 asserted 1.00
s1 Moreover, several properties and results are deduced within aforesaid functions. contribution 0.53 0.94 0.12 asserted 0.99
s2 An example is also constructed to illustrate the definition of geodesic $(\alpha,E)$-invex set. contribution 0.64 0.95 0.03 asserted 1.00
s3 We have also established an important relation between geodesic $(\alpha,E)$-preinvex function and geodesic $(\alpha,E)$-invex function in a complete Riemannian manifold. result 0.91 0.96 0.44 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

In this article, we have introduced the concept of \textit{geodesic $(\alpha,E)$-invex set} and by using this concept the notion of \textit{geodesic $(\alpha,E)$-preinvex functions} and \textit{geodesic $(\alpha,E)$-invex functions} are developed on a Riemannian manifold. Moreover, several properties and results are deduced within aforesaid functions. An example is also constructed to illustrate the definition of geodesic $(\alpha,E)$-invex set. We have also established an important relation between geodesic $(\alpha,E)$-preinvex function and geodesic $(\alpha,E)$-invex function in a complete Riemannian manifold.

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