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On multidimensional fixed-point theorems and their applications

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H. Akhadkulov, S. Akhatkulov, T. Y. Ying, R. Tilavov

Functional Analysis · Submitted 23 Jul 2021

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

The authors' main claim For this, we provide a multidimensional fixed point theorem and then using this theorem we prove the existence and uniqueness of a solution of a nonlinear Hammerstein integral equation.

how it is stated · asserted 1.00 read the record →

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arXiv ID2107.12904 (version 1)
Pith IDUI7SRKPD, Pith's permanent record of this paper and its review
CitationH. Akhadkulov, R. Tilavov, S. Akhatkulov, T. Y. Ying. "On multidimensional fixed-point theorems and their applications." arXiv:2107.12904 (2021). https://pith.science/paper/UI7SRKPD
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,887 input tokens.

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

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

The purpose of this paper is to present some multidimensional fixed-point theorems and their applications. For this, we provide a multidimensional fixed point theorem and then using this theorem we prove the existence and uniqueness of a solution of a nonlinear Hammerstein integral equation. Moreover, we provide an example to illustrate the hypotheses and the abstract result of this paper.

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 The purpose of this paper is to present some multidimensional fixed-point theorems and their applications. contribution 0.91 0.49 0.13 asserted 0.83
s1 For this, we provide a multidimensional fixed point theorem and then using this theorem we prove the existence and uniqueness of a solution of a nonlinear Hammerstein integral equation. contribution 0.89 0.95 0.47 asserted 1.00
s2 Moreover, we provide an example to illustrate the hypotheses and the abstract result of this paper. contribution 0.79 0.95 0.05 asserted 0.99

What kind of paper the classifier reports this is: theoretical result 1.00 · 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

The purpose of this paper is to present some multidimensional fixed-point theorems and their applications. For this, we provide a multidimensional fixed point theorem and then using this theorem we prove the existence and uniqueness of a solution of a nonlinear Hammerstein integral equation. Moreover, we provide an example to illustrate the hypotheses and the abstract result of this paper.

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