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.

Traversable Wormholes and the Brouwer Fixed-Point Theorem

The Brouwer fixed-point theorem in topology states that for any continuous mapping f on a compact convex set into itself admits a fixed point, i.e., a point x0 such that f(x0) = x0. Under suitable conditions, this fixed point corresponds to the throat of a traversable wormhole, i.e., b(r0) = r0 for the shape function b = b(r). The possible existence of wormholes can therefore be deduced from purely mathematical considerations without going beyond the existing physical requirements.

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.

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.

NONSMOOTH CRITICAL POINT THEOREMS AND ITS APPLICATIONS TO QUASILINEAR SCHRDINGER EQUATIONS

In this paper, the existence and nonexistence of solutions to a class of quasilinear elliptic equations with nonsmooth functionals are discussed, and the results obtained are applied to quasilinear SchrSdinger equations with negative parameter which arose from the study of self-channeling of high-power ultrashort laser in matter.

EXISTENCE THEOREMS FOR A SECOND ORDER THREE-POINT BOUNDARY VALUE PROBLEM WITH IMPULSES

In this paper,two existence theorems are given concerning the following 3-point boundary value problem of second order differential systems with impulses[HL(2:1,1Z;2,1Z]x″(t)=f(t,x(t),x′(t)),t∈(0,1),t≠t_k,k=1,2,...,m, Δx|_~t=t_k =I_k(x(t_k)),k=1,2,...,m, Δx′|_~t=t_k =J_k(x(t_k),x′(t_k)),k=1,2,...,m, x(0)=0,x(1)=αx(η).

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 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.

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].

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.

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.

Common Fixed Point Theorems of Single-valued and Set-valued Mappings in Complete,Convex Metric Spaces

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.

MINIMAX THEOREMS FOR SUBCONVEXLIKEFUNCTIONS WITH APPLICATIONS TO SADDLEPOINT PROBLEMS

In this paper some minimax theorems are presented for subconvexlike functions. These are then applied to obtain saddle point theorems.

CARISTI TYPE HYBRID FIXED POINT THEOREMS IN MENGERPROBABILISTIC METRIC SPACE

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.

MINIMAX THEOREM AND SADDLE POINT THEOREM WITHOUT LINEAR STRUCTURE

In this paper, a new kind of concavity of a function defined on a set without linear structure is introduced and a generalization of Fam Ky inequality is given. Minimax theorem in a general topological space is obtained. Moreover, a saddle point theorem on a topological space without any linear structure is established.

NEW COLLECTIVELY FIXED POINT THEOREMS AND APPLICATIONS IN G-CONVEX SPACES

By applying the technique of continuous partition of unity and Tychonoff's fixed point theorem,. some new collectively fixed point theorems for a family of set-valued, mappings defined on the product space of noncompact G-convex spaces are proved. As applications, some nonempty intersetion theorems of Ky Fan type for a family of subsets of the product space of G convex spaces are proved; An existence theorem of solutions for a system of nonlinear inequalities is given in G-convex spaces and some equilibrium existence of abstract economies are also obtained in G convex spaces. Our theorems theorems of improve, unify and generalized many important known results in recent literature.

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.

Common Fixed Point Theorem in Intuitionistic Fuzzy Metric Space Using <i>R</i>-Weakly Commuting Mappings

In this paper, we prove a common fixed point theorem in Intuitionistic fuzzy metric space by using pointwise R-weak commutativity and reciprocal continuity of mappings satisfying contractive conditions.