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.

Qualitative Properties of Equilibrium Point in a Discrete Predator-Prey Model

In this paper, the dynamic properties of a discrete predator-prey model are discussed. The properties of non-hyperbolic fixed points and hyperbolic fixed points of the model are analyzed. First, by using the classic Shengjin formula, we find the existence conditions for fixed points of the model. Then, by using the qualitative theory of ordinary differential equations and matrix theory we indicate which points are hyperbolic and which are non-hyperbolic and the associated conditions.

Performance Analysis of Fixed-Point Simulations on cdma2000-1x Downlink

Based on the physical layer standard of cdma2000, the performance analysis of fixed point simulations is presented in this paper on cdma2000 1x downlink. The effects of quantization and finite wordlength, which have typically been assumed negligible in floating point simulations, become significant for fixed point simulations. The complete fixed point simulation platform for cdma2000 1x downlink is developed by EDA tool - COSSAP. The structure and performance of the key component in cdma2000 systems, the RAKE receiver, are discussed in details. Comparisons of results between floating point and fixed point simulations lead to some important conclusions, which provide certain references for the implementation of practical systems.

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.

Fixed points on complete metric spaces

Two new fixed point theorems on two complete metric spaces are proved by using the concept of w -distance. One of the results is: let (X,d) and (Y,ρ) be two complete metric spaces,let p 1 be a w -distance on X and p 2 be a w -distance on Y . If T is a continuous mapping of X into Y and S is a mapping of Y into X ,satisfying the inequalities: p 1(STx,STx′)≤c max ｛p 1(x,x′),p 1(x,STx),p 1(x′,STx′),p 1(x,STx′)/2,p 2(Tx,Tx′)｝ and p 2(TSy,TSy′)≤c max ｛p 2(y,y′),p 2(y,TSy),p 2(y′,TSy′),p 2(y,TSy′)/2,p 1(Sy,Sy′)｝ for all x,x′ in X and y,y′ in Y ,where 0≤ c<1. We have proved that ST has a unique fixed point z in X and TS has a unique fixed point w in Y . The two theorems have improved the fixed point theorems of Fisher and Namdeo,et al.

Common Fixed Point Theorems for Commuting Maps on a Complete Metric Space

The concept of w distance on a metric space is introduced and three common fixed points theorems for commuting maps on a complete metric space are proved. These results extended fixed point theorems of Jungck and Ciric.

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.

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

In complete metric spaces, the common fixed point theorems for sequences of φ-type contraction set-valued mappings are established, and the corresponding random com- mon fixed point theorems for set-valued mappings are also obtained.

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.

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.