Mappings In Convex Metric Spaces Research Articles

Common fixed-point theorems for non-linear non-self contractive mappings in convex metric spaces

Abstract In this article, two pairs of non-self mappings satisfying a collection of non-linear contractive conditions in convex metric space are considered to prove a common fixed-point theorem. An appropriate example is provided to support the results proved herein. In addition, we have proved a theorem as an application of our main result. Our results generalize and extend several existing theorems in the literature.

Stability Results for Enriched Contraction Mappings in Convex Metric Spaces

In this paper, we obtain some stability results of fixed point sets for a sequence of enriched contraction mappings in the setting of convex metric spaces. In particular, two types of convergence of mappings, namely, G -convergence and H -convergence are considered. We also illustrate our results by an application to an initial value problem for an ordinary differential equation.

Common Fixed Points for Hybrid Pair of Maps with CLR-Property in Convex Metric Space

In present work, we prove common fixed point theorem and best proximity point theorem for two pairs of hybrid mappings in convex metric space satisfying \((\psi-\phi)\)-contractive conditions under common limit range property with respect to \(q\). We prove both theorems for two pairs of hybrid mappings which can be utilized to derive common fixed point and best proximity point theorem including any number of finite mappings. We also present an example to support our main result.

Convergence theorems for G-nonexpansive mappings in convex metric spaces with a directed graph

We propose the modified Picard–Mann hybrid iterative process for two G-nonexpansive mappings and prove some interesting theorems in the framework of convex metric space endowed with a directed graph. We prove with some numerical examples that our proposed iterative process converges faster than all of Mann, Ishikawa and Noor iterations. Our results generalize and extend several known results to convex metric space endowed with a directed graph, including the results of Khan (Fixed Point Theory Appl 2013:69, 2013).

Strong and $$\triangle $$-convergence of Moudafi’s iterative algorithm for generalized nonexpansive mappings in convex metric spaces

We study Moudafi’s iterative algorithm for an \(\alpha \)-nonexpansive mapping and a fundamentally nonexpansive mapping in the framework of a convex metric space. We prove \(\triangle \)-convergence and strong convergence results for the algorithm to a common fixed point of the mappings. Our results are new and are also valid in CAT\(\left( 0\right) \) spaces and Banach spaces, simultaneously.

Approximation of Common Fixed Point of Two Quasi-nonexpansive Mappings in Convex Metric Spaces

We use a simple iterative algorithm for two quasi-nonexpansive mappings to approximate their common fixed point through $$ \triangle $$ -convergence and strong convergence of the algorithm. Our results are new in the literature of metrical fixed point theory and are also valid in CAT(0) spaces.

Common fixed point and best approximation results for family of Cq-commuting mappings in convex metric space

Common fixed point and best approximation results for family of Cq-commuting mappings in convex metric space

A new multistep iteration for a finite family of asymptotically quasi-nonexpansive mappings in convex metric spaces

A new multistep iteration for a finite family of asymptotically quasi-nonexpansive mappings in convex metric spaces

Approximating common fixed points for a pair of generalized nonlinear mappings in convex metric space

Approximating common fixed points for a pair of generalized nonlinear mappings in convex metric space

Best proximity pair and fixed point results for noncyclic mappings in convex metric spaces

In this article, we formulate a best proximity pair theorem for noncyclic relatively nonexpansive mappings in convex metrc spaces by using a geometric notion of semi-normal structure. In this way, we generalize a corresponding result in [W. Takahashi, A convexity in metric space and nonexpansive mappings, Kodai Math. Sem. Rep. 22 (1970) 142-149]. We also establish a best proximity pair theorem for pointwise noncyclic contractions in the setting of convex metric spaces. Our result generalizes a result due to Sankara Raju Kosuru and Veeramani [G. Sankara Raju Kosuru and P. Veeramani, A note on existence and convergence of best proximity points for pointwise cyclic contractions, Numer. Funct. Anal. Optim., 82 (2011) 821-830].

Some fixed point results for nonlinear mappings in convex metric spaces

Some fixed point results for nonlinear mappings in convex metric spaces

Convergence to common fixed points of multi-step iteration process for generalized asymptotically quasi-nonexpansive mappings in convex metric spaces

In this paper, we study strong convergence of multi-step iterations with errors for a finite family of generalized asymptotically quasinonexpansive mappings in the framework of convex metric spaces. The new iteration scheme includes modified Mann and Ishikawa iterations with errors, the three-step iteration scheme of Xu and Noor as special cases in Banach spaces. Our results extend and generalize many known results from the current literature.

Cyclic relatively nonexpansive mappings in convex metric spaces

Cyclic relatively nonexpansive mappings in convex metric spaces

Some new results on cyclic relatively nonexpansive mappings in convex metric spaces

In this article, we prove a best proximity point theorem for generalized cyclic contractions in convex metric spaces. Then we investigate the structure of minimal sets of cyclic relatively nonexpansive mappings in the setting of convex metric spaces. In this way, we obtain an extension of the Goebel-Karlovitz lemma, which is a key lemma in fixed point theory.

Some common fixed point and invariant approximation results for nonexpansive mappings in convex metric space

In this work, we introduce a new class of self-maps which satisfy the (E.A.) property with respect to some , where M is q-starshaped subset of a convex metric space and common fixed point results are established for this new class of self-maps. After that we obtain some invariant approximation results as an application. Our results represent a very strong variant of the several recent results existing in the literature. We also provide some illustrative examples in the support of proved results. MSC:46T99, 47H10, 54H25.

Strong convergence theorems of common fixed point for asymptotically quasi-nonexpansive type mappings in convex metric spaces

In this paper, we study a Noor-type iteration process with errors for approximating common fixed point of a finite family ofuniformly $L$-Lipschitzian asymptotically quasi-nonexpansive type mappings in the setting of convex metric spaces. Also, weIn this paper, we study a Noor-type iteration process with errors for approximating common fixed point of a finite family of uniformly \(L\)-Lipschitzian asymptotically quasi-nonexpansive type mappings in the setting of convex metric spaces. Also, we establish some strong convergence theorems for above said mappings and iteration scheme. The results presented in this paper extend, improve and unify some existing results in the previous work.work.

A convergence theorem of common fixed points of a countably infinite family of asymptotically quasi-$f_i$-expansive mappings in convex metric spaces

In this paper, we introduce a countably infinite iterative scheme and consider a sufficient and necessary condition for the existence of common fixed points of a countably infinite family of asymptotically quasi-$f_i$-expansive mappings in convex metric spaces.

Strong convergence of an explicit iteration process for a finite family of asymptotically quasi-nonexpansive mappings in convex metric spaces

Strong convergence of an explicit iteration process for a finite family of asymptotically quasi-nonexpansive mappings in convex metric spaces

New common fixed point theorems and invariant approximation in convex metric spaces

In this paper, we use new concepts of subcompatibility and subsequential continuity contained in (Bouhadjera, Godet-Thobie, Common fixed theorems for pairs of subcompatible maps, 17 June 2009. [math.FA]) to prove common fixed point theorems for a pair of maps in metric as well as convex metric spaces which are essentially patterned after a theorem of Huang and Li (Fixed point theorems of compatible mappings in convex metric spaces, Soochow J. Math. 22(3) (1996), 439--447). We also prove some related fixed point theorems and utilize certain such results to prove theorems on best approximation.

Convergence theorems for common fixed points of asymptotically quasi-nonexpansive mappings in convex metric spaces

In this paper, we consider an implicit iteration process to approximate the common fixed points of two finite families of asymptotically quasi-nonexpansive mappings in convex metric spaces. As a consequence of our result, we obtain some related convergence theorems. Our results generalize some recent results of Khan and Ahmed [4], Khan et al. [6], Sun [12], Wittmann [14] and Xu and Ori [15].