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

2014 ◽  
Vol 2014 (1) ◽  
Author(s):  
Moosa Gabeleh ◽  
Naseer Shahzad
Keyword(s):  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Relatively Nonexpansive Mappings ◽  
Convex Metric Spaces ◽  
Relatively Nonexpansive

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

Filomat ◽  
2016 ◽  
Vol 30 (12) ◽  
pp. 3149-3158 ◽  
Author(s):  
Moosa Gabeleh ◽  
Naseer Shahzad
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Normal Structure ◽  
Relatively Nonexpansive Mappings ◽  
Convex Metric Spaces ◽  
Relatively Nonexpansive ◽  
Cyclic Contractions ◽  
Funct Anal ◽  
Best Proximity Pair

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].

scholarly journals Best Approximation Results in Various Frameworks

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 67
Author(s):  
Taoufik Sabar ◽  
Abdelhafid Bassou ◽  
Mohamed Aamri
Keyword(s):  
Best Approximation ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Nonexpansive Mappings ◽  
Partial Metric ◽  
Relatively Nonexpansive Mappings ◽  
Partial Metric Spaces ◽  
Relatively Nonexpansive ◽  
Cyclic Mapping

We first provide a best proximity point result for quasi-noncyclic relatively nonexpansive mappings in the setting of dualistic partial metric spaces. Then, those spaces will be endowed with convexity and a result for a cyclic mapping will be obtained. Afterwards, we prove a best proximity point result for tricyclic mappings in the framework of the newly introduced extended partial S b -metric spaces. In this way, we obtain extensions of some results in the literature.

scholarly journals On convergence theorems for single-valued and multi-valued mappings in p-uniformly convex metric spaces

2021 ◽  
Vol 37 (3) ◽  
pp. 513-527
Author(s):  
JENJIRA PUIWONG ◽  
◽  
SATIT SAEJUNG ◽  
◽  
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Iterative Sequence ◽  
Uniformly Convex ◽  
Fixed Point Set ◽  
Convergence Theorems ◽  
Convex Metric Spaces ◽  
Strict Fixed Point ◽  
Point Set

We prove ∆-convergence and strong convergence theorems of an iterative sequence generated by the Ishikawa’s method to a fixed point of a single-valued quasi-nonexpansive mappings in p-uniformly convex metric spaces without assuming the metric convexity assumption. As a consequence of our single-valued version, we obtain a result for multi-valued mappings by showing that every multi-valued quasi-nonexpansive mapping taking compact values admits a quasi-nonexpansive selection whose fixed-point set of the selection is equal to the strict fixed-point set of the multi-valued mapping. In particular, we immediately obtain all of the convergence theorems of Laokul and Panyanak [Laokul, T.; Panyanak, B. A generalization of the (CN) inequality and its applications. Carpathian J. Math. 36 (2020), no. 1, 81–90] and we show that some of their assumptions are superfluous.

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