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A fixed point theorem for Proinov mappings with a contractive iterate
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作者 Erdal Karapnar Andreea Fulga 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2023年第3期403-412,共10页
In this paper,we consider the fixed point theorem for Proinov mappings with a contractive iterate at a point.In other words,we combine and unify the basic approaches of Proinov and Sehgal in the framework of the compl... In this paper,we consider the fixed point theorem for Proinov mappings with a contractive iterate at a point.In other words,we combine and unify the basic approaches of Proinov and Sehgal in the framework of the complete metric spaces.We consider examples to illustrate the validity of the obtained result. 展开更多
关键词 contractive iterate at a point Proinov mappings fixed point theorems
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A Proof of Brouwer’s Fixed Point Theorem Using Sperner’s Lemma
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作者 Cassie Lu 《数学计算(中英文版)》 2023年第2期1-6,共6页
This article offers a simple but rigorous proof of Brouwer’s fixed point theorem using Sperner’s Lemma.The general method I have used so far in the proof is mainly to convert the n-dimensional shapes to the correspo... This article offers a simple but rigorous proof of Brouwer’s fixed point theorem using Sperner’s Lemma.The general method I have used so far in the proof is mainly to convert the n-dimensional shapes to the corresponding case under the Sperner’s Labeling and apply the Sperner’s Lemma to solve the question. 展开更多
关键词 Brouwer’s fixed point theorem Sperner’s Lemma PROOF
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A Generalization of Caristi Fixed Point Theorem 被引量:5
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作者 孙经先 《Chinese Quarterly Journal of Mathematics》 CSCD 1992年第1期72-75,共4页
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
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ON A FIXED POINT THEOREM IN 2-BANACH SPACES AND SOME OF ITS APPLICATIONS 被引量:5
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作者 Janusz BRZDEK Krzysztof CIEPLINSKI 《Acta Mathematica Scientia》 SCIE CSCD 2018年第2期377-390,共14页
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 ... 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. 展开更多
关键词 fixed point theorem 2-normed space Ulam stability HYPERSTABILITY
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FIXED POINT THEOREMS FOR MEIR-KEELER CONDENSING OPERATORS VIA MEASURE OF NONCOMPACTNESS 被引量:1
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作者 A.AGHAJANI M.MURSALEEN A.SHOLE HAGHIGHI 《Acta Mathematica Scientia》 SCIE CSCD 2015年第3期552-566,共15页
In this article, we introduce the notion of Meir-Keleer condensing operator in a Banach space, a characterization using L-functions and provide a few generalization of Darbo fixed point theorem. Also, we introduce the... In this article, we introduce the notion of Meir-Keleer condensing operator in a Banach space, a characterization using L-functions and provide a few generalization of Darbo fixed point theorem. Also, we introduce the concept of a bivariate Meir-Keleer condensing operator and prove some coupled fixed point theorems. As an application, we prove the existence of solutions for a large class of functional integral equations of Volterra type in two variables. 展开更多
关键词 Measure of noncompactness Darbo fixed point theorem couple fixed point Meir-Keeler condensing operator Volterra integral equation
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FIXED POINT THEOREMS AND BEST APPROXIMATION IN CONVEX METRIC SPACES 被引量:2
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作者 I.Beg N.Shahzad M.Iqbal 《Analysis in Theory and Applications》 1992年第4期97-105,共9页
Results regarding best approximation and best Simultaneous approximation on convex metric spaces are Obtained.Existence of fixed points for an ultimately nonexpansive semigroup of mappings is also shown.
关键词 CIG fixed point theoremS AND BEST APPROXIMATION IN CONVEX METRIC SPACES
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More on Fixed Point Theorem of{a,b,c}-Generalized Nonexpansive Mappings in Normed Spaces 被引量:1
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作者 Sahar Mohamed Ali 《Analysis in Theory and Applications》 2013年第1期1-11,共11页
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 C.We prove... 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 C.We 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 singleton.Depending 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. 展开更多
关键词 fixed point theorem {a b c}-generalized-nonexp ansive mapping asymptotic center Browder's strong convergence theorem.
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GENERALIZED MINIMAX INEQUALITIES AND FIXED POINT THEOREMS 被引量:1
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作者 马意海 张福保 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1991年第5期493-500,共8页
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 discu... 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 some fixed point problems, and generalize the Fan-Glicksberg's fixed point theorem[14]. 展开更多
关键词 T-diagonal quasi-concave (-convex) minimax inequality fixed point theorem
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Common Fixed Point Theorems of Single-valued and Set-valued Mappings in Complete,Convex Metric Spaces 被引量:1
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作者 LIANGJun-qi ZHANGZhi-hong ZHAOLing 《Chinese Quarterly Journal of Mathematics》 CSCD 2003年第3期264-270,共7页
Under the conditions of compatility or sub -c ompatility between a sigle-valued mapping and set-valued mapping, this paper d iscusses the existence of common fixed points for two set-valued mappings and a single-value... Under the conditions of compatility or sub -c ompatility between a sigle-valued mapping and set-valued mapping, this paper d iscusses the existence of common fixed points for two set-valued mappings and a single-valued mapping in complete, convex matric spaces. We extend and develop the main results. 展开更多
关键词 complete convex metric spaces compatible mappings s ub-compatible mappings common fixed point theorems
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CARISTI TYPE HYBRID FIXED POINT THEOREMS IN MENGERPROBABILISTIC METRIC SPACE
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作者 石川 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1997年第2期201-209,共9页
This paper brings forward the concept of Caristi type hybrid fixed point in M-PM-space, by giving two hybrid fixed point theorems and two common hybrid fixed point theorems of sequences of set-valued mappings, the the... This paper brings forward the concept of Caristi type hybrid fixed point in M-PM-space, by giving two hybrid fixed point theorems and two common hybrid fixed point theorems of sequences of set-valued mappings, the theorems improve and generalize the Caristi's fixed point and correspond to recent important results. 展开更多
关键词 probabilistic metric space Menger space Caristi's fixed point theorem hybrid fixed point common hybrid fixed point
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ON NEW APPROXIMATIONS FOR GENERALIZED CAUCHY FUNCTIONAL EQUATIONS USING BRZDȨK AND CIEPLIŃSKI'S FIXED POINT THEOREMS IN 2-BANACH SPACES
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作者 Laddawan AIEMSOMBOON Wutiphol SINTUNAVARAT 《Acta Mathematica Scientia》 SCIE CSCD 2020年第3期824-834,共11页
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 m... 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 Ciepliński.On a fixed point theorem in 2-normed spaces and some of its applications.Acta Mathematica Scientia,2018,38B(2):377-390]. 展开更多
关键词 fixed point theorem generalized Cauchy functional equation 2-normed space stability
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SET-VALUED CARISTI’S FIXED POINT THEOREM AND EEELAND’S VARIATIONAL PRINCIPLE
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作者 张石生 罗群 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1989年第2期119-121,共3页
This paper proposes a formally stronger set-valued Caristi’s fixed point theorem and by using a simple method we give a direct proof for the equivalence between Ekeland’s variational principle and this set-valued Ca... This paper proposes a formally stronger set-valued Caristi’s fixed point theorem and by using a simple method we give a direct proof for the equivalence between Ekeland’s variational principle and this set-valued Caristi’s fixed point theorem.The results stated in this paper improve and strengthen the corresponding results in[4]. 展开更多
关键词 S fixed point theorem AND EEELAND S VARIATIONAL PRINCIPLE SET-VALUED CARISTI
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NEW FIXED POINT THEOREMS FOR P_1-COMPACT MAPPINGS IN BANACH SPACES
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作者 Shaoyuan Xu 《Analysis in Theory and Applications》 2007年第3期274-282,共9页
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 fixe... 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. 展开更多
关键词 A-proper mapping P1-compact mapping completely continuous operator topological degree fixed point theorem
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DEGREE THEORY FOR MULTIVALUED (S) TYPE MAPPINGS AND FIXED POINT THEOREMS
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作者 张石生 陈玉清 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1990年第5期441-454,共14页
The main purpose of this paper is devoted to generalizing the results of Browder[1,2]This paper consists of four parts. In the first part, we introduce the concepts of multivalued (S) and (S), type mappings and the co... The main purpose of this paper is devoted to generalizing the results of Browder[1,2]This paper consists of four parts. In the first part, we introduce the concepts of multivalued (S) and (S), type mappings and the concepts of the limits of multivalued (S) and (S) + type mappings. These kinds of mappings contain many monotone type mappings, such as maximal monotone mapping, bounded pseudo-monotone mapping and bounded generalized pseudo-monotone mapping, as its special cases. In the second part we define the pseudo-degree for (S) type mapping and the degree for (S)+ type mapping. These two kinds of degrees are all the generalizations of the degree defined by Browder[1,2] As applications, we utilize the degree theory presented in part 2 to study the existence of solutions for the multivalued operator equations (see part 3) and to obtain some new fixed point theorems in part 4. 展开更多
关键词 TYPE MAPPINGS AND fixed point theoremS DEGREE THEORY FOR MULTIVALUED
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AN APPLICATION OF SCHAUDER’S FIXED POINT THEOREM TO THE EXISTENCE OF SOLUTlONS OF IMPULSIVELY DIFFERENTIAL EQUATIONS
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作者 董玉君 邹尔新 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1995年第4期377-381,共5页
In this paper the existence of solutions of a boundary value problem forimpulsively differential equations that is difficult to solve by the upper and lowersolution method will be proved by means of Schauder’s fixed ... In this paper the existence of solutions of a boundary value problem forimpulsively differential equations that is difficult to solve by the upper and lowersolution method will be proved by means of Schauder’s fixed point theorem,whichimproves some existing results. 展开更多
关键词 Schaudcr’s fixed point theorem boundary value problem existence of solutions
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A Study of Caristi’s Fixed Point Theorem on Normed Space and Its Applications
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作者 Md. Abdul Mannan Moqbul Hossain +1 位作者 Halima Akter Samiran Mondal 《Advances in Pure Mathematics》 2021年第3期169-179,共11页
In this work, we will discuss Caristi’s fixed point theorem for mapping results introduced in the setting of normed spaces. This work is a generalization of the classical Caristi’s fixed point theorem. Also, Caristi... In this work, we will discuss Caristi’s fixed point theorem for mapping results introduced in the setting of normed spaces. This work is a generalization of the classical Caristi’s fixed point theorem. Also, Caristi’s type of fixed points theorem was partial discussed in Reich, Mizoguchi and Takahashi’s and Amini-Harandi’s results, we developed ideas that many known fixed point theorems can easily be derived from the Caristi theorem. 展开更多
关键词 NORM UNIFORMITY Mizoguchi and Takahashi’s Rich’s Problem Caristi’s fixed point theorem Strong and Weak Contraction SEMI-CONTINUOUS
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Rothe’s Fixed Point Theorem and the Controllability of the Benjamin-Bona-Mahony Equation with Impulses and Delay
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作者 Hugo Leiva Jose L. Sanchez 《Applied Mathematics》 2016年第15期1748-1764,共18页
For many control systems in real life, impulses and delays are intrinsic phenomena that do not modify their controllability. So we conjecture that under certain conditions the abrupt changes and delays as perturbation... For many control systems in real life, impulses and delays are intrinsic phenomena that do not modify their controllability. So we conjecture that under certain conditions the abrupt changes and delays as perturbations of a system do not destroy its controllability. There are many practical examples of impulsive control systems with delays, such as a chemical reactor system, a financial system with two state variables, the amount of money in a market and the savings rate of a central bank, and the growth of a population diffusing throughout its habitat modeled by a reaction-diffusion equation. In this paper we apply the Rothe’s Fixed Point Theorem to prove the interior approximate controllability of the following Benjamin Bona-Mohany(BBM) type equation with impulses and delay where and are constants, Ω is a domain in , ω is an open non-empty subset of Ω , denotes the characteristic function of the set ω , the distributed control , are continuous functions and the nonlinear functions are smooth enough functions satisfying some additional conditions. 展开更多
关键词 Interior Approximate Controllability Benjamin Bona-Mohany Equation with Impulses and Delay Strongly Continuous Semigroup Rothe’s fixed point theorem
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FIXED POINT THEOREM OF NONEXPANSIVE MAPPINGS IN CONVEX METRIC SPACES
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作者 李秉友 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1989年第2期183-188,共6页
Let X be a convex metric space with the property that every decreasing sequence of nonenply dosed subsets of X with diameters tending to has menemptyintersection. This paper proved that if T is a mapping of a elosed c... Let X be a convex metric space with the property that every decreasing sequence of nonenply dosed subsets of X with diameters tending to has menemptyintersection. This paper proved that if T is a mapping of a elosed conver nonempty subset K of X into itself satisfying the inequality:for all x,y in K,where then T has a unique fixed point in K. 展开更多
关键词 fixed point theorem OF NONEXPANSIVE MAPPINGS IN CONVEX METRIC SPACES
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A Study of Banach Fixed Point Theorem and It’s Applications
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作者 Md. Abdul Mannan Md. R. Rahman +2 位作者 Halima Akter Nazmun Nahar Samiran Mondal 《American Journal of Computational Mathematics》 2021年第2期157-174,共18页
This paper aims at treating a study of Banach fixed point theorem for mapping results that introduced in the setting of normed space. The classical Banach fixed point theorem is a generalization of this work. A fixed ... This paper aims at treating a study of Banach fixed point theorem for mapping results that introduced in the setting of normed space. The classical Banach fixed point theorem is a generalization of this work. A fixed point theory is a beautiful mixture of Mathematical analysis to explain some conditions in which maps give excellent solutions. Here later many mathematicians used this fixed point theory to establish their results, see for instance, Picard-Lindel of Theorem, The Picard theorem, Implicit function theorem etc. Also, we developed ideas that many of known fixed point theorems can easily be derived from the Banach theorem. It extends some recent works on the extension of Banach contraction principle to metric space with norm spaces. 展开更多
关键词 Metric Space Norm Space Complete Norm Space Operator Banach fixed point theorem UNIFORMITY Strong and Weak contraction SEMI-CONTINUOUS
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AN APPLICATION OF A FIXED POINT THEOREM TO BEST SIMULTANEOUS APPROXIMATION
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作者 Isinat Beg Naseer Shahzad 《Analysis in Theory and Applications》 1994年第3期1-4,共4页
Using a recent result regarding the fixed points of multivalued mappings, the existence of invariant best simultaneous approximation in chainable metric space is proved.
关键词 AN APPLICATION OF A fixed point theorem TO BEST SIMULTANEOUS APPROXIMATION
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