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Corrigendum to the paper “Equivalence of the existence of best proximity points and best proximity pairs for cyclic and noncyclic nonexpansive mappings”

Gabeleh Moosa

Demonstratio Mathematica

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2021

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Vol. 54, nr 1

9--10

EN

The purpose of this short note is to present a correction of the proof of the main result given in the paper “Equivalence of the existence of best proximity points and best proximity pairs for cyclic and noncyclic nonexpansive mappings, ”Demonstr. Math. 53 (2020), 38-43.

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Convergence theorems for generalized hemicontractive mapping in p-uniformly convex metric space

Ugwunnadi Godwin C., Izuchukwu Chinedu, Mewomo Oluwatosin T.

Journal of Applied Analysis

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2020

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Vol. 26, nr 2

221--229

EN

In this paper, we introduce and study an Ishikawa-type iteration process for the class of generalized hemicontractive mappings in p-uniformly convex metric spaces, and prove both Delta-convergence and strong convergence theorems for approximating a fixed point of generalized hemicontractive mapping in complete p-uniformly convex metric spaces. We give a surprising example of this class of mapping that is not a hemicontractive mapping. Our results complement, extend and generalize numerous other recent results in CAT(0) spaces.

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Equivalence of the existence of best proximity points and best proximity pairs for cyclic and noncyclic nonexpansive mappings

Gabeleh Moosa, Künzi Hans-Peter A.

Demonstratio Mathematica

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2020

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Vol. 53, nr 1

38--43

EN

In this study, at first we prove that the existence of best proximity points for cyclic nonexpansive mappings is equivalent to the existence of best proximity pairs for noncyclic nonexpansive mappings in the setting of strictly convex Banach spaces by using the projection operator. In this way, we conclude that the main result of the paper [Proximal normal structure and nonexpansive mappings, Studia Math. 171 (2005), 283–293] immediately follows. We then discuss the convergence of best proximity pairs for noncyclic contractions by applying the convergence of iterative sequences for cyclic contractions and show that the convergence method of a recent paper [Convergence of Picard's iteration using projection algorithm for noncyclic contractions, Indag. Math. 30 (2019), no. 1, 227–239] is obtained exactly from Picard’s iteration sequence.

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Noncyclic Meir-Keeler contractions and best proximity pair theorems

Gabeleh M., Markin J.

Demonstratio Mathematica

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2018

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Vol. 51, nr 1

171--181

EN

In this article, we consider the class of noncyclic Meir-Keeler contractions and study the existence and convergence of best proximity pairs for such mappings in the setting of complete CAT(0) spaces. We also discuss asymptotic pointwise noncyclic Meir-Keeler contractions in the framework of uniformly convex Banach spaces and generalize a main result of Chen [Chen C. M., A note on asymptotic pointwise weaker Meir-Keeler type contractions, Appl. Math. Lett., 2012, 25, 1267-1269]. Examples are given to support our main results.

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Noor iterations associated with Zamfirescu mappings in uniformly convex Banach spaces

Bosede A. O.

Fasciculi Mathematici

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2009

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Nr 42

29-38

EN

In this paper, we establish some fixed point theorems for Noor iterations associated with Zamfirescu mappings in uniformly convex Banach spaces and deduce similar other results on Mann and Ishikawa iterations as special cases. Our results improve a multitude of recent results in the fixed point theory especially the result of Ciric [5].

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A basic fixed point theorem

Pasicki L.

Bulletin of the Polish Academy of Sciences. Mathematics

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2006

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Vol. 54, no 1

85-88

EN

The paper contains a fixed point theorem for stable mappings in metric discus spaces (Theorem 10). A consequence is Theorem 11 which is a far-reaching extension of the fundamental result of Browder, Göhde and Kirk for non-expansive mappings.