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.

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.

New Necessary Conditions for a Fixed-Point of Maps in Non-Metric Spaces

Our purpose is to introduce new necessary conditions for a fixed point of maps on non-metric spaces. We use a contraction map on a metric topological space and a lately published definition of limit of a function between the metric topological space and the non-metric topological space. Then we show that we can create a function h on the non-metric space Y, h :Y →Y and present necessary conditions for a fixed point of this map on this map on Y. Therefore, this gives an opportunity to take a best conclusion in some sense, when non-metrizable matter is under consideration.

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.

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.

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.

高阶非线性分数阶微分方程三点边值问题正解的存在性(英文)

In this paper,we consider the positive solutions of fractional three-point boundary value problem of the form D_0~α+u(t) + f(t,u(t),u'(t),…,u^((n-3))(t),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-l<a≤n,n≥2,ξ,β∈(0,1),βξ^(α-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.

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.

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.

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）.

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.

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.

Asymptotic Stability of Singular Solution for Camassa-Holm Equation

The aim of this paper is to study singular dynamics of solutions of Camassa-Holm equation. Based on the semigroup theory of linear operators and Banach contraction mapping principle, we prove the asymptotic stability of the explicit singular solution of Camassa-Holm equation.

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.

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.

Some Notes on G-cone Metric Spaces

In this paper, we introduce a G metric on the G-cone metric space and then prove that a complete G-cone metric space is always a complete G metric space and verify that a contractive mapping on the G-cone metric space is a contractive mapping on the G metric space. At last, we also give a new way to obtain the unique fixed point on G-cone metric space.