A fixed point theorem for Proinov mappings with a contractive iterate

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.

A Proof of Brouwer’s Fixed Point Theorem Using Sperner’s Lemma

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.

ON A FIXED POINT THEOREM IN 2-BANACH SPACES AND SOME OF ITS APPLICATIONS

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.

NEW FIXED POINT THEOREMS OF CONDENSING MAPPINGS SATISFYING THE INTERIOR CONDITION IN BANACH SPACES

In this paper, based on a basic result on condensing mappings satisfying the interior condition, some new fixed point theorems of the condensing mappings of this kind are obtained. As a result, the famous Altman＇s theorem, Roth＇s theorem and Petryshyn＇s theorem are extended to condensing mappings satisfying the interior condition.

NEW FIXED POINT THEOREMS FOR P_1-COMPACT MAPPINGS IN BANACH SPACES

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.

ON NEW APPROXIMATIONS FOR GENERALIZED CAUCHY FUNCTIONAL EQUATIONS USING BRZDȨK AND CIEPLIŃSKI'S FIXED POINT THEOREMS IN 2-BANACH SPACES

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].

A Study of Banach Fixed Point Theorem and It’s Applications

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.

A Generalization of Caristi Fixed Point Theorem

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.

AN EXISTENCE THEOREM OF POSITIVE SOLUTIONS FOR ELASTIC BEAM EQUATION WITH BOTH FIXED END-POINTS

By using the degree theory on cone an existence theorem of positive solution for a class of fourth-order two-point BVP's is obtained. This class of BVP's usually describes the deformation of the elastic beam with both fixed end-points.

SOME NEW EXTENSIONS OF EDELSTEIN-SUZUKI-TYPE FIXED POINT THEOREM TO G-METRIC AND G-CONE METRIC SPACES

In this paper, we prove some fixed point theorems for generalized contractions in the setting of G-metric spaces. Our results extend a result of Edelstein [M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc., 37 （1962）, 74-79] and a result of Suzuki [T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 （2009）, 5313-5317]. We prove, also, a fixed point theorem in the setting of G-cone metric spaces.

FIXED POINTS AND STABILITY FOR QUARTIC MAPPINGS IN β-NORMED LEFT BANACH MODULES ON BANACH ALGEBRAS

The goal of the present paper is to investigate some new HUR-stability results by applying the alternative fixed point of generalized quartic functional equationin β-Banach modules on Banach algebras. The concept of Ulam-Hyers-Rassias stability （briefly, HUR-stability） originated from Th. M. Rassias stability theorem that appeared in his paper： On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 （1978）, 297-300.

Fixed Point Theorems of Mixed Monotone Operators with Applications

In this paper,we get fixed point theorems of mixed monotone operators in much weaker condition and give some applications for nonmonotone operators and differential equations.

Solving Fractional Differential Equations via Fixed Points of Chatterjea Maps

In this paper,we present the existence and uniqueness of fixed points and common fixed points for Reich and Chatterjea pairs of self-maps in complete metric spaces.Furthermore,we study fixed point theorems for Reich and Chatterjea nonexpansive mappings in a Banach space using the Krasnoselskii-Ishikawa iteration method associated withSλand consider some applications of our results to prove the existence of solutions for nonlinear integral and nonlinear fractional differential equations.We also establish certain interesting examples to illustrate the usability of our results.

FIXED POINT THEOREMS FOR MEIR-KEELER CONDENSING OPERATORS VIA MEASURE OF NONCOMPACTNESS

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.

Banach空间中一类泛函方程的Ulam稳定性

结合差分算子的定义,给出二次和四次泛函方程的统一形式,使得这个新的泛函方程涵括Lee、Kayal和玉强等的结论。然后利用经典的不动点法,研究该泛函方程在Banach空间上的Ulam稳定性。最后,应用定理1.1和定理1.2所得结论,改进并推广几类已知二次和四次泛函方程的稳定性结果。

New Fixed Point Results of Generalized g-Quasi-Contractions in Cone b-Metric Spaces Over Banach Algebras

In this paper, we introduce the concept of generalized g-quasi-contractions in the setting of cone b-metric spaces over Banach algebras. By omitting the assump- tion of normality we establish common fixed point theorems for the generalized g- quasi-contractions with the spectral radius r（λ） of the g-quasi-contractive constant vector λ satisfying r（λ） ∈[0,1） in the setting of cone b-metric spaces over Banach al- gebras, where the coefficient s satisfies s ≥ 1. The main results generalize, extend and unify several well-known comparable results in the literature.

GENERALIZED MINIMAX INEQUALITIES AND FIXED POINT THEOREMS

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].

Algorithms for Common Solutions to Generalized Mixed Equilibrium Problems and Fixed Point Problems under Nonlinear Transformations in Banach Spaces

The purpose of this paper is to present a new iterative scheme for finding a common solution of the generalized mixed equilibrium problems with an infinite family of inverse strongly monotone mappings and the fixed point problems of demimetric mappings under nonlinear transformations in Banach spaces. Applications are also included. The results in this paper are the extension and improvement of the recent results in the literature.

FIXED POINT THEOREMS AND BEST APPROXIMATION IN CONVEX METRIC SPACES

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.

More on Fixed Point Theorem of{a,b,c}-Generalized Nonexpansive Mappings in Normed Spaces

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.