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.

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.

On Some Novel Fixed Point Results for Generalized F-Contractions in b-Metric-Like Spaces with Application

The focusofourwork is on themost recent results infixedpoint theoryrelated tocontractivemappings.Wedescribe variants of(s,q,φ,F)-contractions that expand,supplement and unify an important work widely discussed in the literature,based on existing classes of interpolative and F-contractions.In particular,a large class of contractions in terms of s,q,φand F for both linear and nonlinear contractions are defined in the framework of b-metric-like spaces.The main result in our paper is that(s,q,φ,F)-g-weak contractions have a fixed point in b-metric-like spaces if function F or the specified contraction is continuous.As an application of our results,we have shown the existence and uniqueness of solutions of some classes of nonlinear integral equations.

An Iterative Method for Split Variational Inclusion Problem and Split Fixed Point Problem for Averaged Mappings

In this paper, we use resolvent operator technology to construct a viscosity approximate algorithm to approximate a common solution of split variational inclusion problem and split fixed point problem for an averaged mapping in real Hilbert spaces. Further, we prove that the sequences generated by the proposed iterative method converge strongly to a common solution of split variational inclusion problem and split fixed point problem for averaged mappings which is also the unique solution of the variational inequality problem. The results presented here improve and extend the corresponding results in this area.

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.

Existence of Monotone Positive Solution for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function

This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.

基于ICA Fixed-Point算法的信号图像分析

从ICA算法的基准点出发,探讨了固定点算法中寻找W叠代公式的原理和方法,对分离一个独立成分和分离n个独立成分的运算方法进行了推导和分析;模拟试验表明:逐一分离的效果较好。

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.

UNIQUE COMMON FIXED POINT OF A FAMILY OF SELF-MAPS WITH SAME TYPE CONTRACTIVE CONDITION IN 2-METRIC SPACE

In this paper, we prove that a family of self-maps {Ti,j}i,j∈N in 2-metric space has a unique common fixed point if （i） {Ti,j}i,j∈N satisfies the same type contractive condition for each j ∈ N; （ii） Tm,μ .Tn,v = Tn,v.Tm.μ for all m,n,μ,v ∈ N with μ≠v. Our main result generalizes and improves many known unique common fixed point theorems in 2-metric spaces.

ITERATIVE APPROXIMATION OF FIXED POINTS OF (ASYMPTOTICALLY) NONEXPANSIVE MAPPINGS

Let E be a uniformly convex Banach space which satisfies Opial's condition or has a Frechet differentiable norm,and C be a bounded closed convex subset of E. If T∶C→C is (asymptotically)nonexpansive,then the modified Ishikawa iteration process defined byx n+1 =t nT ns nT nx n+1-s nx n+(1-t n)x n,converges weakly to a fixed point of T ,where {t n} and {s n} are sequences in [0,1] with some restrictions.

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.

COMMON FIXED POINT OF GENERALIZED WEAKLY CONTRACTIVE MAPS IN PARTIAL METRIC SPACES

In this paper, using the context of complete partial metric spaces, some common fixed point results of maps that satisfy the generalized （ψ, Ф）-weak contractive conditions are obtained. Our results generalize, extend, unify, enrich and complement many existing results in the literature. Example are given showing the validaty of our results.

INVOLUTIONS WITH FIXED POINT SET RP(2m)∪P(2m, 2n + 1)

Let （M, T） be a smooth closed manifold with a smooth involution T whose fixed point set is a disjoint union of an even-dimensional real projective space and a Dold manifold. In some cases, the equivariant bordism classes of （M, T） are determined.

AN APPROXIMATE EXPRESSION RELATED WITH RSA FIXED POINTS

Let T=T(n,e,α) be the number of fixed points o f RSA(n,e) that a re co prime with n=pq,and A,B be sets of prime numbers in (1,x) and (1,y) respectively. An estimation on the mean value M(A,B,e,α)=1 (#A)(#B)∑p∈A,q∈B,(p,q)=1logT(pq,e,α) is given.

TOPOLOGICAL DEGREE THEORY AND FIXED POINT THEOREMS IN PROBABILISTIC METRIC SPACES

The Leray-Schauder topological degree theory is established in the probabilistic linearnormed spaces.Based.on this theory,some fixed point theorems for mappings in theprobabilistic linear normed spaces are shown.

Common Fixed Point Theorems for Sequences of φ-type Contraction Set-valued Mappings

在完全的公制的空格，为类型收缩的序列的普通的固定的点定理珍视集合的 mappings 被建立，并且为珍视集合的 mappings 的相应的随机的普通的固定的点定理也被获得。

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 MAPPINGS SATISFYING IMPLICIT RELATION ON TWO COMPLETE AND COMPACT METRIC SPACES

First, the implicit relations were given. A common fixed point theorem was proved for two mappings satisfying implicit relation functions. A further fixed point theorem was proved for mappings satisfying implicit relation functions on two compact metric spaces.

ISHIKAWA ITERATIVE PROCEDURE FOR APPROXIMATING FIXED POINTS OF STRICTLY PSEUDOCONTRACTIVE MAPPINGS

It is shown that any fixed point of a Lipschitzian,strictly pseudocontractive muping T on a closed convex subset K of a Banach space X may be approximated by Ishikawa iterative procedure.The results in this paper provide the new convergence criteria and novel convergence rate estimate for Ishikawa iterative sequence.

A KY FAN MATCHING THEOREM FOR TRANSFER COMPACTLY OPEN COVERS AND THE APPLICATION TO THE FIXED POINT

In this article, a Ky Fan matching theorem for transfer compactly open covers is established. As applications, a Fan-Browder coincidence theorem, a Ky Fan best approximation theorem and a Brouwer-Schauder-Rothe type fixed point theorem are obtained.