Iterative Construction of Common Fixed Points in Convex Metric Spaces

2014 ◽  
pp. 3-43
Author(s):  
Abdul Khan ◽  
Hafiz Fukhar-ud-din
Keyword(s):  
Fixed Points ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Convex Metric Spaces ◽  
Iterative Construction

scholarly journals Viscosity Approximation Methods for * −Nonexpansive Multi-Valued Mappings in Convex Metric Spaces

Axioms ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 10
Author(s):  
Azadeh Ghanifard ◽  
Hashem Parvaneh Masiha ◽  
Manuel De La Sen ◽  
Maryam Ramezani
Keyword(s):  
Fixed Points ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Approximation Methods ◽  
Viscosity Approximation ◽  
Convergence Theorems ◽  
Convex Metric Spaces ◽  
Viscosity Approximation Methods

In this paper, we prove convergence theorems for viscosity approximation processes involving * −nonexpansive multi-valued mappings in complete convex metric spaces. We also consider finite and infinite families of such mappings and prove convergence of the proposed iteration schemes to common fixed points of them. Our results improve and extend some corresponding results.

scholarly journals Existence of common fixed points via modified mann iteration in convex metric spaces and an invariant approximation result

2010 ◽  
Vol 41 (4) ◽  
pp. 335-348
Author(s):  
G.V.R. Babu ◽  
G.N. Alemayehu
Keyword(s):  
Fixed Points ◽  
Metric Space ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Convex Metric Space ◽  
Approximation Result ◽  
Mann Iteration ◽  
Invariant Approximation ◽  
Convex Metric Spaces ◽  
Weakly Contractive

We prove the existence of common fixed points for two selfmaps $T$ and $f$ of a convex metric space $X$ via the convergence of modified Mann iteration where $T$ is a nonlinear $f$-weakly contractive selfmap of $X$ and range of $f$ is complete. An invariant approximation result is also proved.

scholarly journals On two pairs of non-self hybrid mappings

2007 ◽  
Vol 83 (1) ◽  
pp. 17-30 ◽  
Author(s):  
Ljubomir B. Ćirić ◽  
Jeong Sheok Ume ◽  
Nebqjša T. Nikolić
Keyword(s):  
Fixed Points ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Convex Metric Spaces

AbstractAbstrac In this paper we obtain some results on coincidence and common fixed points for two pairs of multi-valued and single-valued non-self mappings in complete convex metric spaces. We improve on previously used methods of proof and obtain results for mappings which are not necessarily compatible and not necessarily continuous, generalizing some known results. In particular, a theorem by Rhoades [19] and a theorem by Ahmed and Rhoades [2] are generalized and improved.

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