scholarly journals Fixed Point Approximation of Nonexpansive Mappings on a Nonlinear Domain

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Safeer Hussain Khan
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Hyperbolic Space ◽  
Iterative Process ◽  
Nonexpansive Mappings ◽  
Hyperbolic Spaces ◽  
Uniformly Convex ◽  
Convergence Results ◽  
Uniformly Convex Banach Spaces ◽  
Uniformly Convex Hyperbolic Space

We use a three-step iterative process to prove some strong andΔ-convergence results for nonexpansive mappings in a uniformly convex hyperbolic space, a nonlinear domain. Three-step iterative processes have numerous applications and hyperbolic spaces contain Banach spaces (linear domains) as well as CAT(0) spaces. Thus our results can be viewed as extension and generalization of several known results in uniformly convex Banach spaces as well as CAT(0) spaces.

Some convergence results for nonexpansive mappings in uniformly convex hyperbolic spaces

2017 ◽  
Vol 26 (3) ◽  
pp. 331-338
Author(s):  
AYNUR SAHIN ◽  
◽  
METIN BASARIR ◽  
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Hyperbolic Space ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Hyperbolic Spaces ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Convergence Results ◽  
Uniformly Convex Hyperbolic Space

In this paper, we establish some strong and 4-convergence theorems of an iteration process for approximating a common fixed point of three nonexpansive mappings in a uniformly convex hyperbolic space. The results presented here extend and improve various results in the existing literature.

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.

scholarly journals Approximating Fixed Points of Reich–Suzuki Type Nonexpansive Mappings in Hyperbolic Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Kifayat Ullah ◽  
Junaid Ahmad ◽  
Manuel De La Sen ◽  
Muhammad Naveed Khan
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Iterative Process ◽  
Fixed Point Theory ◽  
Nonexpansive Mappings ◽  
Point Theory ◽  
Hyperbolic Spaces ◽  
Uniformly Convex ◽  
Convergence Results ◽  
Hyperbolic Metric Space

In this work, we prove some strong and Δ convergence results for Reich-Suzuki type nonexpansive mappings through M iterative process. A uniformly convex hyperbolic metric space is used as underlying setting for our approach. We also provide an illustrate numerical example. Our results improve and extend some recently announced results of the metric fixed-point theory.

scholarly journals Fixed Point Approximation for Asymptotically Nonexpansive Type Mappings in Uniformly Convex Hyperbolic Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Shin Min Kang ◽  
Samir Dashputre ◽  
Bhuwan Lal Malagar ◽  
Young Chel Kwun
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Iterative Process ◽  
Hyperbolic Spaces ◽  
Uniformly Convex ◽  
Point Approximation ◽  
Convergence Results ◽  
Asymptotically Nonexpansive

We use a modifiedS-iterative process to prove some strong andΔ-convergence results for asymptotically nonexpansive type mappings in uniformly convex hyperbolic spaces, which includes Banach spaces and CAT(0) spaces. Thus, our results can be viewed as extension and generalization of several known results in Banach spaces and CAT(0) spaces (see, e.g., Abbas et al. (2012), Abbas et al. (2013), Bruck et al. (1993), and Xin and Cui (2011)) and improve many results in the literature.

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 Common fixed point iterations for a class of multi-valued mappings in $$\mathbf {CAT}(0)$$ spaces

2020 ◽  
Vol 9 (3) ◽  
pp. 681-690
Author(s):  
Khairul Saleh ◽  
Hafiz Fukhar-ud-din
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Hilbert Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Finite Family ◽  
Uniformly Convex ◽  
Uniformly Convex Banach Spaces ◽  
Fixed Point Iterations

Abstract In this work, we propose an iterative scheme to approach common fixed point(s) of a finite family of generalized multi-valued nonexpansive mappings in a CAT(0) space. We establish and prove convergence theorems for the algorithm. The results are new and interesting in the theory of $$CAT\left( 0\right) $$ C A T 0 spaces and are the analogues of corresponding ones in uniformly convex Banach spaces and Hilbert spaces.

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.

scholarly journals Fixed point approximation of Presic nonexpansive mappings in product of CAT (0) spaces

2016 ◽  
Vol 32 (3) ◽  
pp. 315-322
Author(s):  
HAFIZ FUKHAR-UD-DIN ◽  
◽  
VASILE BERINDE ◽  
ABDUL RAHIM KHAN ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Banach Spaces ◽  
Point Theorem ◽  
Nonexpansive Mappings ◽  
Iterative Algorithms ◽  
Control Parameters ◽  
Uniformly Convex ◽  
Uniformly Convex Banach Spaces

We obtain a fixed point theorem for Presiˇ c nonexpansive mappings on the product of ´ CAT (0) spaces and approximate this fixed points through Ishikawa type iterative algorithms under relaxed conditions on the control parameters. Our results are new in the literature and are valid in uniformly convex Banach spaces.

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