Mappings In Metric Spaces Research Articles

Fixed point theorems for \alpha-\psi-contractive type mappings in metric spaces

Fixed point theorems for \alpha-\psi-contractive type mappings in metric spaces

Cascade search for preimages and coincidences: Global and local versions

In previous papers of the author, the cascade search principle was proposed, which makes it possible to construct a set-valued self-map of a metric spaceX from a set-valued functional or a collection of set-valued maps of X so that the new map generates a multicascade, i.e., a set-valued discrete dynamical system whose limit set coincides with the zero set of the given functional, with the coincidence set of the given collection, or with the common preimage of a closed subspace under the maps from this collection. Stability issues of cascade search were studied. This paper is devoted to a generalization and local modifications of the cascade search principle and their applications to problems concerning local search and approximation of common preimages of subspaces and coincidence sets for finite collections of set-valued maps of metric spaces.

A Note on the Fixed Point of Generalized Eventual Cyclic Gross Contractive Mappings

Based on the work of Agarwal et al., in press, we introduce a concept of generalized eventual cyclic gross contractive mapping in metric spaces, which is a generalization of the eventual cyclic gross contractions. Furthermore, we analyze the existence of a fixed point for this type of contractive mapping, and present a new and general fixed point theorem.

New Existence Results and Generalizations for Coincidence Points and Fixed Points without Global Completeness

Some new existence theorems concerning approximate coincidence point property and approximate fixed point property for nonlinear maps in metric spaces without global completeness are established in this paper. By exploiting these results, we prove some new coincidence point and fixed point theorems which generalize and improve Berinde-Berinde's fixed point theorem, Mizoguchi-Takahashi's fixed point theorem, Kikkawa-Suzuki's fixed point theorem, and some well known results in the literature. Moreover, some applications of our results to the existence of coupled coincidence point and coupled fixed point are also presented.

Modified ψ-contractive mappings in ordered metric spaces and applications

Abstract We set up two new variants of ψ-contractive mappings designed for two and three maps in metric spaces and originate common fixed point theorems for T -strictly weakly isotone increasing mappings and relatively weakly increasing mappings in complete ordered metric spaces. To demonstrate our results, we give some examples throughout the paper. At the same time, as applications of the presented theorems, we get hold of common fixed point results for generalized contractions of integral type and we prove an existence theorem for solutions of a system of integral equations. MSC:47H10, 45F05.

Notes on the paper “Fixed point theory for set-valued quasi-contraction maps in metric spaces” by A. Amini-Harandi

Notes on the paper “Fixed point theory for set-valued quasi-contraction maps in metric spaces” by A. Amini-Harandi

Mann iteration process for asymptotic pointwise nonexpansive mappings in metric spaces

Let (M,d) be a complete 2-uniformly convex metric space. Let C be a nonempty, bounded, closed, and convex subset of M, and let T:C→C be an asymptotic pointwise nonexpansive mapping. In this paper, we prove that the modified Mann iteration process defined by xn+1=tnTn(xn)⊕(1−tn)xn converges in a weaker sense to a fixed point of T.

Fixed point theorems for expanding mappings in partial metric spaces

AbstractIn this paper, we define expanding mappings in the setting of partial metric spaces analogous to expanding mappings in metric spaces. We also obtain some results for two mappings to the setting of partial metric spaces

Coupled coincidence points for two mappings in metric spaces and cone metric spaces

This article is concerned with coupled coincidence points and common fixed points for two mappings in metric spaces and cone metric spaces. We first establish a coupled coincidence point theorem for two mappings and a common fixed point theorem for two w-compatible mappings in metric spaces. Then, by using a scalarization method, we extend our main theorems to cone metric spaces. Our results generalize and complement several earlier results in the literature. Especially, our main results complement a very recent result due to Abbas et al.

Coupled Common Fixed Points of Contractive Mappings in Metric Spaces

Coupled Common Fixed Points of Contractive Mappings in Metric Spaces

On the Jackson theorem for periodic functions in metric spaces with integral metric. II

In the spaces L ψ (T m ) of periodic functions with metric $$ \uprho {\left( {f,0} \right)_\uppsi } = \int\limits_{{{\text{T}}^m}} {\uppsi \left( {\left| {f(x)} \right|} \right)dx}, $$ where ψ is a function of the type of modulus of continuity, we study the direct Jackson theorem in the case of approximation by trigonometric polynomials. It is proved that the direct Jackson theorem is true if and only if the lower dilation index of the function ψ is not equal to zero.

A convergence result on random products of mappings in metric spaces

Let X be a metric space and {T1, ..., TN} be a finite family of mappings defined on D ⊂ X. Let r : ℕ → {1,..., N} be a map that assumes every value infinitely often. The purpose of this article is to establish the convergence of the sequence (xn) defined by

The Existence of Fixed Points for Nonlinear Contractive Maps in Metric Spaces with w‐Distances

Some fixed point theorems for (φ, ψ, p)‐contractive maps and (φ, k, p)‐contractive maps on a complete metric space are proved. Presented fixed point theorems generalize many results existing in the literature.

Some Fixed and Periodic Points in Abstract Metric Spaces

We generalize in this paper some results on common fixed points of two, respectively four, contractive‐type mappings in abstract metric spaces by removing condition of normality of the cone in their formulations. Further, some results about periodic points of self‐maps are extended to the setting of abstract metric spaces.

A Unique Common Triple Fixed Point Theorem for Hybrid Pair of Maps

We obtain a unique common triple fixed point theorem for hybrid pair of mappings in metric spaces. Our result extends the recent results of B. Samet and C. Vetro (2011). We also introduced a suitable example supporting our result.

Global Optimal Solutions of Noncyclic Mappings in Metric Spaces

We study some minimization problems for noncyclic mappings in metric spaces. We then apply the solution to obtain some results in the theory of analytic functions.

On fixed points of quasi-contraction type multifunctions

In 2009, Ilić and Rakoc˘ević proved that quasi-contraction maps on normal cone metric spaces have a unique fixed point (Ilić and Rakoc˘ević, 2009 [6] ). Then, Kadelburg, Radenović and Rakoc˘ević generalized their results by considering an additional assumption (Kadelburg et al., 2009 [7] ). Also, they proved that quasi-contraction maps on cone metric spaces have the property (P) whenever λ ∈ ( 0 , 1 2 ) . Later, Haghi, Rezapour and Shahzad proved same results without the additional assumption and for λ ∈ ( 0 , 1 ) by providing a new technical proof (Rezapour et al., 2010 [4] ). In 2011, Wardowski published a paper (Wardowski, 2011 [8] ) and tried to test fixed point results for multifunctions on normal cone metric spaces. Of course, he used a special view in his results. Recently, Amini-Harandi proved a result on the existence of fixed points of set-valued quasi-contraction maps in metric spaces by using the technique of Rezapour et al. (2010) [4] . But, like Kadelburg et al. (2009) [7] , he could prove it only for λ ∈ ( 0 , 1 2 ) (Amini-Harandi (2011) [3] ). In this work, we prove again the main result of Amini-Harandi (2011) [3] by using a simple method. Also, we introduce quasi-contraction type multifunctions and show that the main result of Amini-Harandi (2011) [3] holds for quasi-contraction type multifunctions.

Fixed point theorems for nonlinear weakly [formula omitted]-contractive mappings in metric spaces

The purpose of this paper is to present some fixed point and coupled fixed point theorems for a nonlinear weakly C -contraction type mapping in metric and ordered metric spaces. Also, an example is given to support our results. Our results generalize several well-known results from the current literature.

Fixed point theory for set-valued quasi-contraction maps in metric spaces

In this paper, we give a fixed point theorem for set-valued quasi-contraction maps in metric spaces. Our main result improves some well-known results from the literature.

Approximation of common fixed points of weakly compatible pairs using the Jungck iteration

We show that the Jungck iteration scheme can be used to approximate the common fixed points of some weakly compatible pairs of generalized quasicontractive operators defined on metric spaces. The existence of coincidence points are also discussed for those pair of maps. The results are generalizations of well known results of the convergence of Picard iterations for single self maps of Banach spaces. In particular, the results improve, generalize and extend the recent results of Berinde [V. Berinde, A common fixed point theorem for compatible quasi contractive self mappings in metric spaces, Applied Mathematics and Computation 213 (2009) 348–354] and answers the open question posed in the paper.