Convergence Theorems of φ-pseudo Contractive Type Mappings in Normed Linear Spaces

In this paper, by virtue of an inequality and sane analysis techniques, we prove sane convergence theorems cm the iterative process for nonlinear mappings of-pseudo contractive type in named linear spaces, which extend and improve the corresponding results obtained by others recently.

Viscosity approximation methods with weakly contractive mappings for nonexpansive mappings

Let K be a closed convex subset of a real reflexive Banach space E, T：K→K be a nonexpansive mapping, and f：K→K be a fixed weakly contractive （may not be contractive） mapping. Then for any t∈（0, 1）, let x1∈K be the unique fixed point of the weak contraction x1→tf（x）＋（1-t）Tx. If T has a fixed point and E admits a weakly sequentially continuous duality mapping from E to E^＊, then it is shown that {xt} converges to a fixed point of T as t→0. The results presented here improve and generalize the corresponding results in （Xu, 2004）.

ON THE CONVERGENCE PROBLEMS OF ISHIKAWA AND MANN ITERATIVE PROCESSES WITH ERROR FOR Φ-PSEUDO CONTRACTIVE TYPE MAPPINGS

The purpose of this paper is to introduce the concept of Φ_pseudo contractive type mapping and to study the convergence problem of Ishikawa and Mann iterative processes with error for this kind of mappings. The results presented in this paper improve and extend many authors'recent results.

SOME NEW ITERATED FUNCTION SYSTEMS CONSISTING OF GENERALIZED CONTRACTIVE MAPPINGS

Iterated function systems （IFS） were introduced by Hutchinson in 1981 as a natural generalization of the well-known Banach contraction principle. In 2010, D. R. Sahu and A. Chakraborty introduced K-Iterated Function System using Kannan mapping which would cover a larger range of mappings. In this paper, following Hutchinson, D. R. Sahu and A. Chakraborty, we present some new iterated function systems by using the so-called generalized contractive mappings, which will also cover a large range of mappings. Our purpose is to prove the existence and uniqueness of attractors for such class of iterated function systems by virtue of a Banach-like fixed point theorem concerning generalized contractive mappings.

Generalized contraction mapping principle in intuitionistic Menger spaces and application to differential equations

Using the idea of Atanassov, we define the notion of intuitionistic Menger spaces as a netural generalizations of Menger spaces due to Menger. We also obtain a new generalized contraction mapping and utilize this contraction mapping to prove the existance theorems of solutions to differential equations in intuitionistic Menger spaces.

FIXED POINT THEOREMS OF LOCAL CONTRACTION MAPPINGS ON MENGER SPACES

In this paper,we introduce the concept ofε-chainable PM-space,and give severalfixed point theorems of one-valued and multivalued local contraction mapping on the kindof spaces.

ORDERING CONTRACTION MAPPING PRINCIPLE AND APPLICATIONS

This paper establishes an ordering contraction mapping principle for increasing mapping in partial ordering metric spaces, and applies it to prove the existence and uniqueness of fixed point for some nonlinear operators controlled by a linear operator and phi-concave operator in a partial ordering Banach space. Therefore, this two results are unified.

THE EXISTENCE AND UNIQUENESS OF SOLUTION FOR A CLASS OF STOCHASTIC FUNCTIONAL EQUAFIONS ON S.P.SPACE

This paper is concerned with the existence and uniqueness of solution for a class of stochastic functional equation: X =φ(X), where φ: B → B and B is a Banach space consisted of all left-continuous, (■_t)-adapted processes. Also, the main result is applied to some S.D.E (or S.I.E.). And the authors adopted some of the results in current research in the models of stochastic control recently. This paper proves the ekistence and uniquence and uniqueness of solution for stochastic functional equation. A series of corollaries are deduced from the special examples of the theorems in this paper.

Existence of Positive Solutions of Three-point Boundary Value Problem for Higher Order Nonlinear Fractional Differential Equations

In this paper, we consider the positive solutions of fractional three-point boundary value problem of the form Dο^α＋u（t）＋f（t,u（t）,u＇（t）,…,u^（n-3）（5）,u^（n-2）（t））=0,u^（i）（0）=0,0≤i≤n-2,u^（n-2）（1）-βu^（n-2）（ξ）=0,where 0〈t〈1,n-1〈α≤n,n≥2,ξ Е（0,1）,βξ^a-n〈1. We first transform it into another equivalent boundary value problem. Then, we derive the Green＇s function for the equivalent boundary value problem and show that it satisfies certain properties. At last, by using some fixed-point theorems, we obtain the existence of positive solution for this problem. Example is given to illustrate the effectiveness of our result.

BOUNDARY VALUE PROBLEM FOR DEGENERATE AND SINGULAR p-LAPLACIAN SYSTEMS

In this article, using the contraction mapping principle and the shooting method, the authors obtain the existence and uniqueness of the local solution and the global solution to a class of quasilinear elliptic systems with p-Laplacian as its principal. They also obtain the continuous dependence of the solutions on the boundary data.

GENERALIZATIONS OF THE SUZUKI AND KANNAN FIXED POINT THEOREMS IN G-CONE METRIC SPACES

In this paper we develop the Banach contraction principle and Kannan fixed point theorem on generalized cone metric spaces. We prove a version of Suzuki and Kannan type generalizations of fixed point theorems in generalized cone metric spaces.

A GENERALIZATION OF CLARKE'S FIXED POINT THEOREM

This paper proposes a formally stronger set-valued Clarke's fixed point theorem. By this theorem we can improve a fixed point theorem for weakly inward contraction set-valued mapping of D. Dowing and W.A. Kirk.

FRACTAL PROPERTIES OF STATISTICALLY SELF-SIMILAR SETS

In this paper, authors compute the Packing dimension of statistically selfsimilar sets and obtaine the dimension and dimension distribution of statistically self-similar measure.

On Dynamics of Infinitely Generated Contractive Mapping Systems on pZ_p

Let p≥2 be a prime number and Zp be the ring of p-adic intergers.Let G be a semigroup generated by infinitely many contractive maps on p Zp.It is shown that if G satisfies the open tiling conditions,then there exists a shift transformation on the limit set of G and the shift transformation is ergodic with respect to the Haar measure on p Zp.As an application,we can generalize p-adic Khinchin’s Theorem and p-adic Lochs’Theorem to any infinitely generated semigroup by use of the ergodicity of the shift transformation.

ON A NONLINEAR VOLTERRA-HAMMERSTEIN INTEGRAL EQUATION IN TWO VARIABLES

Using a fixed point theorem of Krasnosel＇skii type, this article proves the exis- tence of asymptotically stable solutions for a Volterra-Hammerstein integral equation in two variables.

Viscosity approximation with weak contractions for fixed point problem,equilibrium problem,and variational inequality problem

This paper proposes a modified iterative algorithm using a viscosity approximation method with a weak contraction.The purpose is to find a common element of the set of common fixed points of an infinite family of nonexpansive mappings and the set of a finite family of equilibrium problems that is also a solution to a variational inequality.Under suitable conditions,some strong convergence theorems are established in the framework of Hilbert spaces.The results presented in the paper improve and extend the corresponding results of Colao et al.（Colao,V.,Acedo,G.L.,and Marino,G.An implicit method for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of infinite family of nonexpansive mappings.Nonlinear Anal.71,2708–2715（2009））,Plubtieng and Punpaeng（Plubtieng,S.and Punpaeng,R.A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces.J.Math.Anal.Appl.336,455–469（2007））,Colao et al.（Colao,V.,Marino,G.,and Xu,H.K.An iterative method for finding common solutions of equilibrium problem and fixed point problems.J.Math.Anal.Appl.344,340–352（2008））,Yao et al.（Yao,Y.,Liou,Y.C.,and Yao,J.C.Convergence theorem for equilibrium problems and fixed point problems of infinite family of nonexpansive mappings.Fixed Point Theory Application 2007,Article ID 64363（2007）DOI 10.1155/2007/64363）,and others.

Better Hausdorff Dimension Estimations of Quadratic and Cubic Functions' Julia Sets

More accurate Hausdorff dimension estimations of Julia sets for two simple functions are given by the methods of composition mapping and invariant set of contraction mapping. For quadratic function fc （ z ） = z^2 ＋ c（c ∈^C）, the range of parameter c is expanded largely and a result on the Hausdorff dimension of its Julia set is gained. Similarly, a better result is obtained for cubic function fc（z） = z^3 ＋ c（c ∈ ^C）.

HAUSDORFF DIMENSION OF GENERALIZED STATISTICALLY SELF-AFFINE FRACTALS

The authors consider generalized statistically self-affine recursive fractals K with random numbers of subsets on each level. They obtain the Hausdorff dimensions of K without considering whether the subsets on each level are non-overlapping or not. They also give some examples to show that many important sets are the special cases of their models.

A Kind of Boundary Value Problems for Stochastic Differential Equations

In this paper we discuss stochastic differential equations with a kind of periodic boundary value conditions（in sense of mean value）. Appealing to the decomposition of equations, the existence of solutions is obtained by using the contraction mapping principle and Leray-Schauder fixed point theorem, respectively.

Fixed Point Theorems for Weakly Contractive Mappings in Ordered Metric Spaces with an Application

In this paper,we prove fixed point theorem for weakly contractive mappings using locally T-transitivity of binary relation and presenting an analogous version of Harjani and Sadarangani theorem involving more general relation theoretic metrical notions.Our fixed point results under universal relation reduces to Harjani and Sadarangani[Nonlinear Anal.,71(2009),3403-3410]fixed point theorems.In this way we also generalize some of the recent fixed point theorems for weak contraction in the existing literature.