Viscosity approximation method for generalized asymptotically quasi-nonexpansive mappings in a convex metric space

Abdul Rahim Khan; Nusrat Yasmin; Hafiz Fukhar-ud-din; Sami Atif Shukri

doi:10.1186/s13663-015-0447-6

Viscosity approximation method for generalized asymptotically quasi-nonexpansive mappings in a convex metric space

Abdul Rahim Khan
, Nusrat Yasmin^*
, Hafiz Fukhar-ud-din
, Sami Atif Shukri

^*Corresponding author for this work

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

1 Scopus citations

Abstract

A general viscosity iterative method for a finite family of generalized asymptotically quasi-nonexpansive mappings in a convex metric space is introduced. Special cases of the new iterative method are the viscosity iterative method of Chang et al. (Appl. Math. Comput. 212:51-59, 2009), an analogue of the viscosity iterative method of Fukhar-ud-din et al. (J. Nonlinear Convex Anal. 16:47-58, 2015) and an extension of the multistep iterative method of Yildirim and Özdemir (Arab. J. Sci. Eng. 36:393-403, 2011). Our results generalize and extend the corresponding known results in uniformly convex Banach spaces and CAT(0)$\operatorname{CAT}(0)$ spaces simultaneously.

Original language	English
Article number	196
Journal	Fixed Point Theory and Algorithms for Sciences and Engineering
Volume	2015
Issue number	1
DOIs	https://doi.org/10.1186/s13663-015-0447-6
State	Published - 1 Dec 2015

Bibliographical note

Publisher Copyright:
© 2015, Khan et al.

Keywords

common fixed point
convex metric space
generalized asymptotically quasi-nonexpansive mapping
strong convergence
uniformly Hölder continuous function
viscosity iterative method
△-convergence

ASJC Scopus subject areas

Geometry and Topology
Applied Mathematics

Access to Document

10.1186/s13663-015-0447-6

Cite this

@article{e00c91d1c2324de1911a3f292db56cac,

title = "Viscosity approximation method for generalized asymptotically quasi-nonexpansive mappings in a convex metric space",

abstract = "A general viscosity iterative method for a finite family of generalized asymptotically quasi-nonexpansive mappings in a convex metric space is introduced. Special cases of the new iterative method are the viscosity iterative method of Chang et al. (Appl. Math. Comput. 212:51-59, 2009), an analogue of the viscosity iterative method of Fukhar-ud-din et al. (J. Nonlinear Convex Anal. 16:47-58, 2015) and an extension of the multistep iterative method of Yildirim and {\"O}zdemir (Arab. J. Sci. Eng. 36:393-403, 2011). Our results generalize and extend the corresponding known results in uniformly convex Banach spaces and CAT(0)\$\textbackslash{}operatorname\{CAT\}(0)\$ spaces simultaneously.",

keywords = "common fixed point, convex metric space, generalized asymptotically quasi-nonexpansive mapping, strong convergence, uniformly H{\"o}lder continuous function, viscosity iterative method, △-convergence",

author = "Khan, \{Abdul Rahim\} and Nusrat Yasmin and Hafiz Fukhar-ud-din and Shukri, \{Sami Atif\}",

note = "Publisher Copyright: {\textcopyright} 2015, Khan et al.",

year = "2015",

month = dec,

day = "1",

doi = "10.1186/s13663-015-0447-6",

language = "English",

volume = "2015",

journal = "Fixed Point Theory and Algorithms for Sciences and Engineering",

issn = "1687-1820",

publisher = "SpringerOpen",

number = "1",

}

TY - JOUR

T1 - Viscosity approximation method for generalized asymptotically quasi-nonexpansive mappings in a convex metric space

AU - Khan, Abdul Rahim

AU - Yasmin, Nusrat

AU - Fukhar-ud-din, Hafiz

AU - Shukri, Sami Atif

PY - 2015/12/1

Y1 - 2015/12/1

N2 - A general viscosity iterative method for a finite family of generalized asymptotically quasi-nonexpansive mappings in a convex metric space is introduced. Special cases of the new iterative method are the viscosity iterative method of Chang et al. (Appl. Math. Comput. 212:51-59, 2009), an analogue of the viscosity iterative method of Fukhar-ud-din et al. (J. Nonlinear Convex Anal. 16:47-58, 2015) and an extension of the multistep iterative method of Yildirim and Özdemir (Arab. J. Sci. Eng. 36:393-403, 2011). Our results generalize and extend the corresponding known results in uniformly convex Banach spaces and CAT(0)$\operatorname{CAT}(0)$ spaces simultaneously.

AB - A general viscosity iterative method for a finite family of generalized asymptotically quasi-nonexpansive mappings in a convex metric space is introduced. Special cases of the new iterative method are the viscosity iterative method of Chang et al. (Appl. Math. Comput. 212:51-59, 2009), an analogue of the viscosity iterative method of Fukhar-ud-din et al. (J. Nonlinear Convex Anal. 16:47-58, 2015) and an extension of the multistep iterative method of Yildirim and Özdemir (Arab. J. Sci. Eng. 36:393-403, 2011). Our results generalize and extend the corresponding known results in uniformly convex Banach spaces and CAT(0)$\operatorname{CAT}(0)$ spaces simultaneously.

KW - common fixed point

KW - convex metric space

KW - generalized asymptotically quasi-nonexpansive mapping

KW - strong convergence

KW - uniformly Hölder continuous function

KW - viscosity iterative method

KW - △-convergence

UR - https://www.scopus.com/pages/publications/84945966133

U2 - 10.1186/s13663-015-0447-6

DO - 10.1186/s13663-015-0447-6

M3 - Article

AN - SCOPUS:84945966133

SN - 1687-1820

VL - 2015

JO - Fixed Point Theory and Algorithms for Sciences and Engineering

JF - Fixed Point Theory and Algorithms for Sciences and Engineering

IS - 1

M1 - 196

ER -

Viscosity approximation method for generalized asymptotically quasi-nonexpansive mappings in a convex metric space

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Fingerprint

Cite this