Continuous selections for pseudo-lower semicontinuous set-valued mappings on convex structure spaces and hyperspace contractibility

SINCE 1956, Michael’s continuous selection theory has been applied to functional analysis,topology, approximation theory and other mathematical fields. In this letter, the concept ofthe pseudo-lower semicontinuity is introduced, and a convex structure of metric space is de-fined. A continuous selection theorem for pseudo-lower semicontinuity is given. This

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.

Topological degree for 1-set-contractive fields in M-PN spaces and its applications

In this paper, we define the topological degree for 1-set-contractive fields in PN spaces. Based on this, we obtain some new fixed point theorems for 1-set-contractive operators. As an application, we study the existence of solutions for a kind of nonlinear Volterra integral equations in Z-M-PN space.

Fixed Point Theorems of Hegedus Contraction Mapping in Some Types of Distance Spaces

In the present paper, we prove some fixed point theorems of Hegedus contraction in some types of distance spaces, dislocated metric space, left dislocated metric space, right dislocated metric space and dislocated quasi-metric metric space which are generalized metrics spaces where self-distances are not necessarily zero.

Common Fixed Point Results for Quasi-contractions Involving Altering Distance Functions in Ordered Cone Metric Spaces

Some common fixed point results for mappings satisfying a quasi-contractive condition which involves altering distance functions are obtained in partially ordered complete cone metric spaces. A sufficient condition for the uniqueness of common fixed point is proved. Also, an example is given to support our results.

Unique Common Fixed Points for Two Weakly C~*-contractive Mappings on Partially Ordered 2-metric Spaces

In this paper, we give existence theorems of common fixed points for two mappings with a weakly C*-contractive condition on partially ordered 2-metric spaces and give a sufficient condition under which there exists a unique common fixed point.

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.

A GENERALIZED CONTRACTION PRINCIPLE IN MENGER SPACES USING A CONTROL FUNCTION

In the present paper we use a control function to define a generalized contraction in Menger spaces and obtain a unique fixed point theorem. The work is in line with the research for developing probabilistic contractions with the help of control functions and related fixed point results. We have given an example to which our theorem is applicable. Some corollaries are also discussed.

Some New Fixed Point Theorems for Fuzzy Iterated Contraction Maps in Fuzzy Metric Spaces

The purpose of this paper is to introduce the notion of fuzzy iterated contraction maps in fuzzy metric spaces and establish some new fixed point theorems for fuzzy iterated contraction maps in fuzzy metric spaces.

B-Implicit Contractive Conditions and Unique（Common） Fixed Points on Complex Valued Metric Spaces

A class B of complex functions is introduced and several existence theorems of unique(common) fixed points for mappings satisfying a B-implicit contraction are presented.Moreover, the existence results of common fixed points for two mappings on a nonempty set with two complex valued metrics are provided. Our outcomes generalize and improve some known results, especially, for instance, Banach contraction principle, Chatterjea-type fixed point theorem and the corresponding fixed point theorems.

APPROXIMATION OF FIXED POINTS AND VARIATIONAL SOLUTIONS FOR PSEUDO-CONTRACTIVE MAPPINGS IN BANACH SPACES

Let K be a nonempty, closed and convex subset of a real reflexive Banach space E which has a uniformly Gateaux differentiable norm. Assume that every nonempty closed con- vex and bounded subset of K has the fixed point property for nonexpansive mappings. Strong convergence theorems for approximation of a fixed point of Lipschitz pseudo-contractive map- pings which is also a unique solution to variational inequality problem involving φ-strongly pseudo-contractive mappings are proved. The results presented in this article can be applied to the study of fixed points of nonexpansive mappings, variational inequality problems, con- vex optimization problems, and split feasibility problems. Our result extends many recent important results.

Uniqueness of Common Fixed Points for a Family of Mappings with <i>Φ</i>-Contractive Condition in 2-Metric Spaces

In this paper, we will introduce a class of 5-dimensional functions Φ and prove that a family of self-mappings {Ti,j} iεN in 2-metric space have an unique common fixed point if 1) {Ti,j} iεN satisfies Φj-contractive condition, where ΦjεΦ, for each jεN;2) Tm,μ n,v for all m,n,μ,vεN with μ ≠ v . Our main result generalizes and unifies many known unique common fixed point theorems in 2-metric spaces.

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.

THE CONTRACTION LINEAR METRIC PROJECTIONS IN L_p SPACES

In this paper, we study the contraction linearity for metric projection in L p spaces. A geometrical property of a subspace Y of L p is given on which P Y is a contraction projection.

A Family of Non-Self Maps Satisfying <i>Φ</i>_i-Contractive Condition and Having Unique Common Fixed Point in Metrically Convex Spaces

Class of 5-dimensional functions Φ was introduced and a convergent sequence determined by non-self mappings satisfying certain Φi-contractive condition was constructed, and then that the limit of the sequence is the unique com-mon fixed point of the mappings was proved. Finally, several more general forms were given. Our main results gener-alize and unify many same type fixed point theorems in references.

Fixed Point and Common Fixed Point Theorems for Cyclic Quasi-Contractions in Metric and Ultrametric Spaces

In this paper, we prove introduce some fixed point theorems for quasi-contraction under the cyclical conditions. Then, we point out that a common fixed point extension is also applicable via our earlier results equipped together with a weaker cyclical properties, namely a co-cyclic representation. Examples are as well provided along this paper.

Some Fixed Point Theorems for Fuzzy Iterated Contraction Maps in Fuzzy Metric Spaces

In 1975, Kramosil and Michalek [1] first introduced the concept of a fuzzy metric space. In 1994, George and Veeramani [2] slightly modified the concept of fuzzy metric space introduced by Kramosil and Michalek, defined a Hausdorff topology and proved some known results. In 1969, Rheinboldt [3] initiated the study of iterated contraction. The concept of iterated contraction proves to be very useful in the study of certain iterative process and has wide applicability in metric spaces. In this paper we introduce the notion of fuzzy iterated contraction maps in fuzzy metric spaces and establish some fixed point theorems for fuzzy iterated contraction maps in fuzzy metric spaces.

Common Fixed Points for Two Mappings with Implicit-linear Contractions on Partially Ordered 2-metric Spaces

In this paper, we introduce a new class U of 3-dimensional real functions, use U and a 2-dimensional real function ? to construct a new implicit-linear contractive condition and obtain some existence theorems of common fixed points for two mappings on partially ordered 2-metric spaces and give a sufficient condition under which there exists a unique common fixed point. The obtained results goodly generalize and improve the corresponding conclusions in references.

Common Fixed Points for Two Contractive Mappings of Integral Type in Metric Spaces

In this paper, we obtain unique common fixed point theorems for two mappings satisfying the variable coefficient linear contraction of integral type and the implicit contraction of integral type respectively in metric spaces.