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.

A Note on the Paper “Generalized -Contraction for a Pair of Mappings on Cone Metric Spaces”

We note that Theorem 2.3 [1] is a consequence of the same theorem for one map.

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.

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.

Coupled Fixed Point for (<i>&alpha;</i>, <i>&Psi;</i>)-Contractive in Partially Ordered Metric Spaces Using Compatible Mappings

In this paper, first we introduce notions of (α, Ψ)-contractive and (α)-admissible for a pair of map and prove a coupled coincidence point theorem for compatible mappings using these notions. Our work extends and generalizes the results of Mursaleen et al. [1]. At the end, we will provide an example in support of our result.

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.

Fixed Point Theorems of the Iterated Function Systems

In this paper, we present some fixed point theorems of iterated function systems consisting of α-ψ-contractive type mappings in Fractal space constituted by the compact subset of metric space and iterated function systems consisting of Banach contractive mappings in Fractal space constituted by the compact subset of generalized metric space, which is Mso extensively applied in topological dynamic system.

ON(η,d)-CONTRACTIBLE ORBITS OF VECTOR FIELDS

Let ■ be the linear space of all C1 vector fields X on a compact n-dimensionalC∞ Riemann manifold（n≥2）,endowed with the C1 norm ‖X‖1.Write θ（X）for the numberof contractible periodic orbits of X∈（?）,which may be finite or infinite.Let （?）* be the set ofall X∈（?） possessing the property that X has a neighbourhood （?） such that every Y∈（?） hasonly a finite number of singularities and at most a countable number of periodic orbits.Inthis paper,it is shown that any given S∈（?） has a neighbourhood （?） in （?） together with anumber λ=λ（?）】0 such that θ（X）≤λfor all X∈（?）.

A New Contraction Principle in Menger Spaces

In the present work we introduce a new type of contraction mapping by using a specific function and obtain certain fixed point results in Menger spaces. The work is in line with the research for generalizing the Banach＇s contraction principle. We extend the notion of altering distance function to Menger Spaces and obtain fixed point results.