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Acta Mathematica Scientia 2018年第2期38卷 377-390页

作者： Janusz BRZDEK Krzysztof CIEPLINSKI Pedagogical University Department of Mathematics AGH University of Science and Technology Faculty of Applied Mathematics

The aim of this article is to prove a fixed point theorem in 2-Banach spaces and show its applications to the Ulam stability of functional equations. The obtained stability re- sults concern both some single variable equations and the most important functional equation in several variables, namely, the Cauchy equation. Moreover, a few corollaries corresponding to some known hyperstability outcomes are presented.

关键词： fixed point theorem 2-normed space Ulam stability hyperstability

Analysis on Krasnoselskii’s fixed point theorem of fuzzy variable fractional differential equation for a novel coronavirus(COVID-19)model with singular operator

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International Journal of Modeling, Simulation, and Scientific Computing 2021年第3期12卷 150-166页

作者： Pratibha Verma Manoj Kumar Anand Shukla Department of Mathematics Motilal Nehru National Institute of Technology Allahabad Prayagraj 211004 Uttar PradeshIndia Department of Mathematics Wollega UniversityEthiopia

The fuzzy variable fractional differential equations(FVFDEs)play a very important role in mathematical modeling of *** scientists are studying and developing several aspects of these COVID-19 *** existence and uniqueness of the solution,stability analysis are the most common and important study *** is no study in the literature to establish the existence,uniqueness,and UH stability for fuzzy variable fractional(FVF)order COVID-19 *** to high demand of this study,we investigate results for the existence,uniqueness,and UH stability for the considered COVID-19 model based on FVFDEs using a fixed point theory approach with the singular ***,discuss the maximal/minimal solution for the FVFDE of the COVID-19 model.

关键词： Novel coronavirus(COVID-19) variable Caputo fractional derivative fixed point theorem existence and uniqueness Ulam-Hyers stability

More on fixed point theorem of{a,b,c}-Generalized Nonexpansive Mappings in Normed Spaces

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Analysis in Theory and Applications 2013年第1期29卷 1-11页

作者： Sahar Mohamed Ali Department of Mathematics Faculty of ScienceAin Shams University Egypt&General Courses Department Riyadh Philanthropic Society for SciencePrince Sultan UniversityCollege for Women

Let X be a weakly Cauchy normed space in which the parallelogram law holds,C be a bounded closed convex subset of X with one contracting point and T be an{a,b,c}-generalized-nonexpansive mapping from C into *** prove that the infimum of the set{‖x-T(x)‖}on C is zero,study some facts concerning the{a,b,c}-generalized-nonexpansive mapping and prove that the asymptotic center of any bounded sequence with respect to C is *** on the fact that the{a,b,0}-generalized-nonexpansive mapping from C into C has fixed points,accord-ingly,another version of the Browder's strong convergence theorem for mappings is given.

关键词： fixed point theorem {a b c}-generalized-nonexp ansive mapping asymptotic center,Browder's strong convergence theorem.

A Generalization of Caristi's fixed point theorem and Its Applications

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Journal of Mathematical Research and Exposition 2006年第2期26卷 199-206页

作者：孙金丽孙经先南京师范大学数学与计算机科学学院江苏南京210097 徐州师范大学数学系江苏徐州221116

The paper generalizes the classical Caristi＇s fixed point theorem. As an application. the classical Ekeland variational principle is generalized. In addition, it is proved that the generalized Caristi＇s fixed point ... 详细信息

关键词： fixed point theorem Zorn's lemma general principle on ordered set variational principle.

A Generalization of Caristi fixed point theorem

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Chinese Quarterly Journal of Mathematics 1992年第1期7卷 72-75页

作者：孙经先山东大学数学系济南250100

Let X be a metric space with an ordering structure,A: X→X is a operator and x≤Ax for any x∈X. In this paper we prove a new fixed point theorem, which generalizes famous caristi fixed point theorem.

关键词： metric space partially ordred set fixed point theorem

ON NEW APPROXIMATIONS FOR GENERALIZED CAUCHY FUNCTIONAL EQUATIONS USING BRZDȨK AND CIEPLIŃSKI'S fixed point theoremS IN 2-BANACH SPACES

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Acta Mathematica Scientia 2020年第3期40卷 824-834页

作者： Laddawan AIEMSOMBOON Wutiphol SINTUNAVARAT Department of Mathematics and Statistics Faculty of Science and TechnologyThammasat University Rangsit CenterPathumthani 12121Thailand

In this work,we apply the Brzdȩk and Ciepliński's fixed point theorem to investigate new stability results for the generalized Cauchy functional equation of the form f(ax+by)=af(x)+bf(y),where a,b∈N and f is a mapping from a commutative group(G,+)to a 2-Banach space(Y,||·,·||).Our results are generalizations of main results of Brzdȩk and Ciepliński[J Brzdȩk,K Ciepliń*** a fixed point theorem in 2-normed spaces and some of its *** Mathematica Scientia,2018,38B(2):377-390].

关键词： fixed point theorem generalized Cauchy functional equation 2-normed space stability

GENERALIZED MINIMAX INEQUALITIES AND fixed point theoremS

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Applied Mathematics and Mechanics(English Edition) 1991年第5期12卷 493-500页

作者：马意海张福保 Department of Mathematics Xuzhou Teacher's College Xuzhou

Recently many authors have generalized the famous Ky Fan's minimax inequality. In this paper, we put forward T-diagonal convexity (concavity) conditions and develop the main results in this respect. Next, we discuss s... 详细信息

关键词： T-diagonal quasi-concave (-convex) minimax inequality fixed point theorem

NEW fixed point theoremS FOR P_1-COMPACT MAPPINGS IN BANACH SPACES

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Analysis in Theory and Applications 2007年第3期23卷 274-282页

作者： Shaoyuan Xu Department of Mathematics Huaibei Colal Industry Teachers College Huaibei 235000 P. R. China and Department of Mathematics Nanjing University Nanjing 210093 P. R. China

E E. Browder and W. V. Petryshyn defined the topological degree for A- proper mappings and then W. V. Petryshyn studied a class of A-proper mappings, namely, P1-compact mappings and obtained a number of important fixed point theorems by virtue of the topological degree theory. In this paper, following W. V. Petryshyn, we continue to study P1-compact mappings and investigate the boundary condition, under which many new fixed point theorems of P1-compact mappings are obtained. On the other hand, this class of A-proper mappings with the boundedness property includes completely continuous operators and so, certain interesting new fixed point theorems for completely continuous operators are obtained immediately. As a result of it, our results generalize several famous theorems such as Leray-Schauder＇s theorem, Rothe＇s theorem, Altman＇s theorem, Petryshyn＇s theorem, etc.

关键词： A-proper mapping P1-compact mapping completely continuous operator,topological degree fixed point theorem

A General Existence Principle for fixed point theorems in One Parameter Case of Soft Da-Metric Space

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Journal of Mathematical Research with Applications 2023年第4期43卷 477-486页

作者： Jeena M S Lovelymol SEBASTIAN Department of Mathematics St.Thomas College

In this paper, we take the case of soft points into consideration and propose a new metric structure called soft Da-metric space for a specific orbit defined with soft points. In order to establish fixed point results... 详细信息

关键词： soft set soft metric D-metric soft D-metric fixed point theorem