A new implicit algorithm of asymptotically quasi-nonexpansive maps in uniformly convex Banach spaces

H. Fukhar-Ud-Din; A. R. Khan; M. A.A. Khan

A new implicit algorithm of asymptotically quasi-nonexpansive maps in uniformly convex Banach spaces

H. Fukhar-Ud-Din^*
, A. R. Khan
, M. A.A. Khan

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

In this paper, we introduce and study weak and strong convergence of a two-step implicit algorithm for a finite family of asymptotically quasi-nonexpansive maps in a uniformly convex Banach space. The results are proved for a more general implicit algorithm under weaker assumptions on the control sequences of parameters. Our results are generalizations of several well-known results in the current literature.

Original language	English
Pages (from-to)	171-175
Number of pages	5
Journal	IAENG International Journal of Applied Mathematics
Volume	42
Issue number	3
State	Published - Sep 2012

Keywords

Asymptotically nonexpansive map
Asymptotically quasi-nonexpansive map
Common fixed point
Condition (A)
Demi-compactness

ASJC Scopus subject areas

Applied Mathematics

Cite this

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title = "A new implicit algorithm of asymptotically quasi-nonexpansive maps in uniformly convex Banach spaces",

abstract = "In this paper, we introduce and study weak and strong convergence of a two-step implicit algorithm for a finite family of asymptotically quasi-nonexpansive maps in a uniformly convex Banach space. The results are proved for a more general implicit algorithm under weaker assumptions on the control sequences of parameters. Our results are generalizations of several well-known results in the current literature.",

keywords = "Asymptotically nonexpansive map, Asymptotically quasi-nonexpansive map, Common fixed point, Condition (A), Demi-compactness",

author = "H. Fukhar-Ud-Din and Khan, \{A. R.\} and Khan, \{M. A.A.\}",

year = "2012",

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language = "English",

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journal = "IAENG International Journal of Applied Mathematics",

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AU - Fukhar-Ud-Din, H.

AU - Khan, A. R.

AU - Khan, M. A.A.

PY - 2012/9

Y1 - 2012/9

N2 - In this paper, we introduce and study weak and strong convergence of a two-step implicit algorithm for a finite family of asymptotically quasi-nonexpansive maps in a uniformly convex Banach space. The results are proved for a more general implicit algorithm under weaker assumptions on the control sequences of parameters. Our results are generalizations of several well-known results in the current literature.

AB - In this paper, we introduce and study weak and strong convergence of a two-step implicit algorithm for a finite family of asymptotically quasi-nonexpansive maps in a uniformly convex Banach space. The results are proved for a more general implicit algorithm under weaker assumptions on the control sequences of parameters. Our results are generalizations of several well-known results in the current literature.

KW - Asymptotically nonexpansive map

KW - Asymptotically quasi-nonexpansive map

KW - Common fixed point

KW - Condition (A)

KW - Demi-compactness

UR - https://www.scopus.com/pages/publications/84868689377

M3 - Article

AN - SCOPUS:84868689377

SN - 1992-9978

VL - 42

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EP - 175

JO - IAENG International Journal of Applied Mathematics

JF - IAENG International Journal of Applied Mathematics

IS - 3

ER -

A new implicit algorithm of asymptotically quasi-nonexpansive maps in uniformly convex Banach spaces

Abstract

Keywords

ASJC Scopus subject areas

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