Nonexpansive iterations in uniformly convex 𝑊-hyperbolic spaces

2010 ◽  
pp. 193-210 ◽  
Author(s):  
Laurenţiu Leuştean
Keyword(s):  
Hyperbolic Spaces ◽  
Uniformly Convex

Convergence theorems for total asymptotically nonexpansive single-valued and quasi nonexpansive multi-valued mappings in hyperbolic spaces

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Preeyalak Chuadchawna ◽  
Ali Farajzadeh ◽  
Anchalee Kaewcharoen
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Hyperbolic Space ◽  
Hyperbolic Spaces ◽  
Iterative Sequence ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive ◽  
Uniformly Convex Hyperbolic Space

Abstract In this paper, we discuss the Δ-convergence and strong convergence for the iterative sequence generated by the proposed scheme to approximate a common fixed point of a total asymptotically nonexpansive single-valued mapping and a quasi nonexpansive multi-valued mapping in a complete uniformly convex hyperbolic space. Finally, by giving an example, we illustrate our result.

scholarly journals Approximating Stationary Points of Multivalued Generalized Nonexpansive Mappings in Metric Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-6 ◽  
Author(s):  
Kifayat Ullah ◽  
Junaid Ahmad ◽  
Muhammad Arshad ◽  
Manuel de la Sen ◽  
Muhammad Safi Ullah Khan
Keyword(s):  
Current Literature ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Hyperbolic Spaces ◽  
Stationary Points ◽  
Uniformly Convex ◽  
Numerical Example

In this research, under some appropriate conditions, we approximate stationary points of multivalued Suzuki mappings through the modified Agarwal-O’Regan-Sahu iteration process in the setting of 2-uniformly convex hyperbolic spaces. We also provide an illustrative numerical example. Our results improve and extend some recently announced results of the current literature.

scholarly journals Mixed Type Algorithms for Asymptotically Nonexpansive Mappings in Hyperbolic Spaces

2021 ◽  
Vol 14 (3) ◽  
pp. 650-665
Author(s):  
Tanakit Thianwan
Keyword(s):  
Fixed Point ◽  
Mixed Type ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Hyperbolic Spaces ◽  
Strong Convergence Theorem ◽  
Uniformly Convex ◽  
Mild Conditions ◽  
Asymptotically Nonexpansive ◽  
Uniformly Convex Hyperbolic Space

In this paper, a new mixed type iteration process for approximating a common fixed point of two asymptotically nonexpansive self-mappings and two asymptotically nonexpansive nonself-mappings is constructed. We then establish a strong convergence theorem under mild conditions in a uniformly convex hyperbolic space. The results presented here extend and improve some related results in the literature.

scholarly journals A one-step-two-mappings iterative scheme for multi-valued maps in W-hyperbolic spaces

Filomat ◽  
2018 ◽  
Vol 32 (4) ◽  
pp. 1403-1411 ◽  
Author(s):  
Birol Gunduz ◽  
Sezgin Akbulut
Keyword(s):  
Banach Spaces ◽  
Hyperbolic Space ◽  
Iterative Scheme ◽  
Hyperbolic Spaces ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Nonexpansive Maps ◽  
Uniformly Convex Banach Spaces ◽  
One Step ◽  
Geodesic Spaces

In this paper, we study a one-step iterative scheme for two multi-valued nonexpansive maps in W-hyperbolic spaces. We establish strong and ?-convergence theorems for the proposed algorithm in a uniformly convex W-hyperbolic space which improve and extend the corresponding known results in uniformly convex Banach spaces as well as CAT(0) spaces. Our new results are also valid in geodesic spaces.

Iteration schema for common fixed points of nonlinear mappings in spaces of nonpositive curvature

2014 ◽  
Vol 5 (2) ◽  
Author(s):  
Muhammad Aqeel Ahmad Khan
Keyword(s):  
Fixed Points ◽  
Nonexpansive Mappings ◽  
Nonpositive Curvature ◽  
Common Fixed Points ◽  
Hyperbolic Spaces ◽  
Uniformly Convex ◽  
Convergence Results ◽  
One Step ◽  
Uniformly Continuous ◽  
Nonlinear Mappings

Abstract.In this paper, we propose a one-step iteration for the approximation of common fixed points of two uniformly continuous total asymptotically quasi-nonexpansive mappings in uniformly convex hyperbolic spaces. We establish strong convergence and Δ-convergence results of the proposed iteration in this setting. As a consequence, our convergence results improve and generalize various results announced in the current literature.

The implicit midpoint rule for nonexpansive mappings in 2-uniformly convex hyperbolic spaces

2019 ◽  
Vol 26 (1/2) ◽  
pp. 95-105
Author(s):  
H. Fukhar-ud-din ◽  
A.R. Khan
Keyword(s):  
Banach Spaces ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Hyperbolic Spaces ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Implicit Midpoint Rule ◽  
Midpoint Rule ◽  
Uniformly Convex Banach Spaces ◽  
Special Cases

The purpose of this paper is to introduce the implicit midpoint rule (IMR) of nonexpansive mappings in 2- uniformly convex hyperbolic spaces and study its convergence. Strong and △-convergence theorems based on this algorithm are proved in this new setting. The results obtained hold concurrently in uniformly convex Banach spaces, CAT(0) spaces and Hilbert spaces as special cases.

THE EXISTENCE OF A SOLUTION OF THE NONLINEAR INTEGRAL EQUATION VIA THE FIXED POINT APPROACH

2021 ◽  
Vol 10 (7) ◽  
pp. 2977-2998
Author(s):  
T.A. Adeyemi ◽  
F. Akusah ◽  
A.A. Mebawondu ◽  
M.O. Adewole ◽  
O.K. Narain
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Nonlinear Integral Equation ◽  
Nonexpansive Mappings ◽  
Iterative Algorithms ◽  
Hyperbolic Spaces ◽  
Uniformly Convex ◽  
Existence Of A Solution ◽  
Uniformly Convex Banach Spaces ◽  
Uniformly Convex Hyperbolic Space

In this paper, we present some fixed point results for a generalized class of nonexpansive mappings in the framework of uniformly convex hyperbolic space and also propose a new iterative scheme for approximating the fixed point of this class of mappings in the framework of uniformly convex hyperbolic spaces. Furthermore, we establish some basic properties and some strong and $\triangle$-convergence theorems for these mappings in uniformly convex hyperbolic spaces. Finally, we present an application to the nonlinear integral equation and also, a numerical example to illustrate our main result and then display the efficiency of the proposed algorithm compared to different iterative algorithms in the literature with different choices of parameters and initial guesses. The results obtained in this paper extends and generalizes corresponding results in uniformly convex Banach spaces, CAT(0) spaces and other related results in literature.

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