Strong Convergence Theorems for Strict Pseudocontractions in Uniformly Convex Banach Spaces

Weak and strong convergence theorems are established for hybrid implicit iteration for a finite family of non-self-nonexpansive mappings in uniformly convex Banach spaces. The results presented in this paper extend and improve some recent results.

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Common fixed points of two finite families of nonexpansive mappings by iterations

Carpathian Journal of Mathematics ◽

10.37193/cjm.2015.03.08 ◽

2015 ◽

Vol 31 (3) ◽

pp. 325-331

Author(s):

HAFIZ FUKHAR-UD-DIN ◽

◽

Keyword(s):

Strong Convergence ◽

Fixed Points ◽

Banach Spaces ◽

Iterative Scheme ◽

Nonexpansive Mappings ◽

Common Fixed Points ◽

Uniformly Convex ◽

Convergence Theorems ◽

Uniformly Convex Banach Spaces

We study a Mann type iterative scheme for two finite families of nonexpansive mappings and establish 4− convergence and strong convergence theorems. The obtained results are applicable in uniformly convex Banach spaces (linear domain) and CAT (0) spaces (nonlinear domain) simultaneously.

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Existence and Convergence Theorems of Best Proximity Points

Journal of Applied Mathematics ◽

10.1155/2013/101439 ◽

2013 ◽

Vol 2013 ◽

pp. 1-6 ◽

Cited By ~ 6

Author(s):

Moosa Gabeleh ◽

Naseer Shahzad

Keyword(s):

Banach Spaces ◽

Convergence Theorem ◽

Best Proximity Point ◽

Nonexpansive Mappings ◽

Uniformly Convex ◽

Convergence Theorems ◽

Best Proximity Points ◽

Relatively Nonexpansive Mappings ◽

Uniformly Convex Banach Spaces ◽

Relatively Nonexpansive

The aim of this paper is to prove some best proximity point theorems for new classes of cyclic mappings, called pointwise cyclic orbital contractions and asymptotic pointwise cyclic orbital contractions. We also prove a convergence theorem of best proximity point for relatively nonexpansive mappings in uniformly convex Banach spaces.

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Convergence Theorems for Finite Family of Multivalued Maps in Uniformly Convex Banach Spaces

ISRN Mathematical Analysis ◽

10.5402/2011/576108 ◽

2011 ◽

Vol 2011 ◽

pp. 1-13 ◽

Cited By ~ 1

Author(s):

Yekini Shehu

Keyword(s):

Banach Space ◽

Fixed Point ◽

Strong Convergence ◽

Iterative Process ◽

Real Banach Space ◽

Finite Family ◽

Uniformly Convex ◽

Multivalued Maps ◽

Convergence Theorems ◽

Uniformly Convex Banach Spaces

We introduce a new iterative process to approximate a common fixed point of a finite family of multivalued maps in a uniformly convex real Banach space and establish strong convergence theorems for the proposed process. Furthermore, strong convergence theorems for finite family of quasi-nonexpansive multivalued maps are obtained. Our results extend important recent results.

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

Filomat ◽

10.2298/fil1804403g ◽

2018 ◽

Vol 32 (4) ◽

pp. 1403-1411 ◽

Cited By ~ 1

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.

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

Arab Journal of Mathematical Sciences ◽

10.1016/j.ajmsc.2019.02.002 ◽

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.

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Nonexpansive Mappings and Iterative Methods in Uniformly Convex Banach Spaces

Georgian Mathematical Journal ◽

10.1515/gmj.2002.591 ◽

2002 ◽

Vol 9 (3) ◽

pp. 591-600

Author(s):

Haiyun Zhou ◽

Ravi P. Agarwal ◽

Yeol Je Cho ◽

Yong Soo Kim

Keyword(s):

Banach Spaces ◽

Iterative Methods ◽

Nonexpansive Mappings ◽

Uniformly Convex ◽

Convergence Theorems ◽

Iterative Schemes ◽

Uniformly Convex Banach Spaces

Abstract In this paper, most of classical and modern convergence theorems of iterative schemes for nonexpansive mappings are presented and the main results in the paper generalize and improve the corresponding results given by many authors.

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A New Faster Iterative Scheme for Numerical Fixed Points Estimation of Suzuki’s Generalized Nonexpansive Mappings

Mathematical Problems in Engineering ◽

10.1155/2020/3863819 ◽

2020 ◽

Vol 2020 ◽

pp. 1-9 ◽

Cited By ~ 5

Author(s):

Shanza Hassan ◽

Manuel De la Sen ◽

Praveen Agarwal ◽

Qasim Ali ◽

Azhar Hussain

Keyword(s):

Fixed Point ◽

Strong Convergence ◽

Banach Spaces ◽

Iterative Scheme ◽

Nonexpansive Mappings ◽

Iteration Scheme ◽

Uniformly Convex ◽

Weak And Strong Convergence ◽

Uniformly Convex Banach Spaces ◽

The Stability

The purpose of this paper is to introduce a new four-step iteration scheme for approximation of fixed point of the nonexpansive mappings named as S∗-iteration scheme which is faster than Picard, Mann, Ishikawa, Noor, Agarwal, Abbas, Thakur, and Ullah iteration schemes. We show the stability of our proposed scheme. We present a numerical example to show that our iteration scheme is faster than the aforementioned schemes. Moreover, we present some weak and strong convergence theorems for Suzuki’s generalized nonexpansive mappings in the framework of uniformly convex Banach spaces. Our results extend, improve, and unify many existing results in the literature.

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Approximation of Fixed Points for Suzuki’s Generalized Non-Expansive Mappings

Mathematics ◽

10.3390/math7060522 ◽

2019 ◽

Vol 7 (6) ◽

pp. 522 ◽

Cited By ~ 2

Author(s):

Javid Ali ◽

Faeem Ali ◽

Puneet Kumar

Keyword(s):

Strong Convergence ◽

Fixed Points ◽

Banach Spaces ◽

Iterative Scheme ◽

Uniformly Convex ◽

Weak And Strong Convergence ◽

Numerical Example ◽

Matlab Program ◽

Convergence Results ◽

Uniformly Convex Banach Spaces

In this paper, we study a three step iterative scheme to approximate fixed points of Suzuki’s generalized non-expansive mappings. We establish some weak and strong convergence results for such mappings in uniformly convex Banach spaces. Further, we show numerically that the considered iterative scheme converges faster than some other known iterations for Suzuki’s generalized non-expansive mappings. To support our claim, we give an illustrative numerical example and approximate fixed points of such mappings using Matlab program. Our results are new and generalize several relevant results in the literature.

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