Common Fixed Point Iterations of Non-Lipschitzian Mappings in a Convex Metric Space

Hafiz Fukhar-ud-din; Juan J. Nieto; Abdul Rahim Khan

doi:10.1007/s00009-015-0619-y

Common Fixed Point Iterations of Non-Lipschitzian Mappings in a Convex Metric Space

Hafiz Fukhar-ud-din, Juan J. Nieto, Abdul Rahim Khan^*

^*Corresponding author for this work

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

3 Scopus citations

Abstract

We establish strong convergence of the modified Moudafi iterative scheme to a common fixed point of an asymptotically nonexpansive mapping in the intermediate sense and an asymptotically quasi-nonexpansive type mapping on a uniformly convex metric space. Our results either improve or generalize the corresponding results of Kim (Arab J Math 2:279–286, 2013), Kim and Kim (Comput Math Appl 42:1565–1570, 2001) and Rhoades (J Math Anal Appl 183:118–120, 1994).

Original language	English
Pages (from-to)	2061-2071
Number of pages	11
Journal	Mediterranean Journal of Mathematics
Volume	13
Issue number	4
DOIs	https://doi.org/10.1007/s00009-015-0619-y
State	Published - 1 Aug 2016

Bibliographical note

Publisher Copyright:
© 2015, Springer Basel.

Keywords

Condition (B)
Uniformly convex metric space
common fixed point
convergence
non-Lipschitzian mapping

ASJC Scopus subject areas

General Mathematics

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10.1007/s00009-015-0619-y

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title = "Common Fixed Point Iterations of Non-Lipschitzian Mappings in a Convex Metric Space",

abstract = "We establish strong convergence of the modified Moudafi iterative scheme to a common fixed point of an asymptotically nonexpansive mapping in the intermediate sense and an asymptotically quasi-nonexpansive type mapping on a uniformly convex metric space. Our results either improve or generalize the corresponding results of Kim (Arab J Math 2:279–286, 2013), Kim and Kim (Comput Math Appl 42:1565–1570, 2001) and Rhoades (J Math Anal Appl 183:118–120, 1994).",

keywords = "Condition (B), Uniformly convex metric space, common fixed point, convergence, non-Lipschitzian mapping",

author = "Hafiz Fukhar-ud-din and Nieto, \{Juan J.\} and Khan, \{Abdul Rahim\}",

note = "Publisher Copyright: {\textcopyright} 2015, Springer Basel.",

year = "2016",

month = aug,

day = "1",

doi = "10.1007/s00009-015-0619-y",

language = "English",

volume = "13",

pages = "2061--2071",

journal = "Mediterranean Journal of Mathematics",

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T1 - Common Fixed Point Iterations of Non-Lipschitzian Mappings in a Convex Metric Space

AU - Fukhar-ud-din, Hafiz

AU - Nieto, Juan J.

AU - Khan, Abdul Rahim

PY - 2016/8/1

Y1 - 2016/8/1

N2 - We establish strong convergence of the modified Moudafi iterative scheme to a common fixed point of an asymptotically nonexpansive mapping in the intermediate sense and an asymptotically quasi-nonexpansive type mapping on a uniformly convex metric space. Our results either improve or generalize the corresponding results of Kim (Arab J Math 2:279–286, 2013), Kim and Kim (Comput Math Appl 42:1565–1570, 2001) and Rhoades (J Math Anal Appl 183:118–120, 1994).

AB - We establish strong convergence of the modified Moudafi iterative scheme to a common fixed point of an asymptotically nonexpansive mapping in the intermediate sense and an asymptotically quasi-nonexpansive type mapping on a uniformly convex metric space. Our results either improve or generalize the corresponding results of Kim (Arab J Math 2:279–286, 2013), Kim and Kim (Comput Math Appl 42:1565–1570, 2001) and Rhoades (J Math Anal Appl 183:118–120, 1994).

KW - Condition (B)

KW - Uniformly convex metric space

KW - common fixed point

KW - convergence

KW - non-Lipschitzian mapping

UR - https://www.scopus.com/pages/publications/84937822032

U2 - 10.1007/s00009-015-0619-y

DO - 10.1007/s00009-015-0619-y

M3 - Article

AN - SCOPUS:84937822032

SN - 1660-5446

VL - 13

SP - 2061

EP - 2071

JO - Mediterranean Journal of Mathematics

JF - Mediterranean Journal of Mathematics

IS - 4

ER -

Common Fixed Point Iterations of Non-Lipschitzian Mappings in a Convex Metric Space

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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