scholarly journals Convergence of SP-iteration for generalized nonexpansive mapping in Hadamard spaces

2017 ◽  
Vol 48 (2) ◽  
Author(s):  
Izhar Uddin ◽  
Mohammad Imdad
Keyword(s):  
Nonexpansive Mapping ◽  
Generalized Nonexpansive Mapping

Convergence Theorems for Suzuki Generalized Nonexpansive Mapping in Banach Spaces

2021 ◽  
Vol 54 ◽  
Author(s):  
Abdulhamit Ekinci ◽  
Seyit Temir
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Convergence Theorems ◽  
Approximate Fixed Point ◽  
Strong Theorems ◽  
Numerical Example ◽  
Generalized Nonexpansive Mapping

In this paper, we study a new iterative scheme to approximate fixed point of Suzuki nonexpansive type mappings in Banach space. We also provesome weak and strong theorems for Suzuki nonexpansive typemappings. Numerical example is given to show the efficiency of newiteration process. The results obtained in this paper improve therecent ones announced by B. S. Thakur et al. \cite{Thakur}, Ullahand Arschad \cite{UA}.

scholarly journals On a Class of Generalized Nonexpansive Mappings

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1085 ◽  
Author(s):  
Simeon Reich ◽  
Alexander J. Zaslavski
Keyword(s):  
Hilbert Space ◽  
Nonexpansive Mapping ◽  
Fixed Points ◽  
Convex Set ◽  
Nonexpansive Mappings ◽  
General Function ◽  
New Class ◽  
Generalized Nonexpansive Mapping ◽  
Closed And Convex Set ◽  
Definition Of

In our recent work we have introduced and studied a notion of a generalized nonexpansive mapping. In the definition of this notion the norm has been replaced by a general function satisfying certain conditions. For this new class of mappings, we have established the existence of unique fixed points and the convergence of iterates. In the present paper we construct an example of a generalized nonexpansive self-mapping of a bounded, closed and convex set in a Hilbert space, which is not nonexpansive in the classical sense.

On $\alpha$-nonexpansive mapping and fixed-points in Banach spaces

2018 ◽  
Vol 2018 (-) ◽  
Author(s):  
Prondanai Kaskasem ◽  
Chakkrid Klin-eam ◽  
Suthep Suantai
Keyword(s):  
Nonexpansive Mapping ◽  
Fixed Points ◽  
Banach Spaces

scholarly journals On Mann’s Method with Viscosity for Nonexpansive and Nonspreading Mappings in Hilbert Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Nawab Hussain ◽  
Giuseppe Marino ◽  
Afrah A. N. Abdou
Keyword(s):  
Nonexpansive Mapping ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Common Fixed Points ◽  
Nonspreading Mapping ◽  
Type Mapping ◽  
Nonspreading Mappings

In the setting of Hilbert spaces, inspired by Iemoto and Takahashi (2009), we study a Mann’s method with viscosity to approximate strongly (common) fixed points of a nonexpansive mapping and a nonspreading mapping. A crucial tool in our results is the nonspreading-average type mapping.

scholarly journals Strong convergence for nonexpansive mappings by viscosity approximation methods in Hadamard manifolds

2015 ◽  
Vol 4 (2) ◽  
pp. 299
Author(s):  
Mandeep Kumari ◽  
Renu Chugh
Keyword(s):  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Approximation Method ◽  
Nonexpansive Mappings ◽  
Approximation Methods ◽  
Hadamard Manifolds ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Viscosity Approximation Methods

<p>In 2010, Victoria Martin Marquez studied a nonexpansive mapping in Hadamard manifolds using Viscosity approximation method. Our goal in this paper is to study the strong convergence of the Viscosity approximation method in Hadamard manifolds. Our results improve and extend the recent research in the framework of Hadamard manifolds.</p>

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