A one-step implicit iterative method for two finite families of asymptotically nonexpansive mappings in a hyperbolic space

Hafiz Fukhar-ud-din; Amna Kalsoom; Safeer H. Khan

doi:10.1007/s11766-018-3370-x

A one-step implicit iterative method for two finite families of asymptotically nonexpansive mappings in a hyperbolic space

Hafiz Fukhar-ud-din^*
, Amna Kalsoom
, Safeer H. Khan

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

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

Abstract

We introduce a one-step implicit iterative method for two finite families of asymptotically nonexpansive mappings in a hyperbolic space and use it to approximate common fixed points of these families. The results presented in this paper are new in the setting of hyperbolic spaces. On top, these are generalizations of several results in literature from Banach spaces to hyperbolic spaces. At the end of the paper, we give an example to validate our results.

Original language	English
Pages (from-to)	274-286
Number of pages	13
Journal	Applied Mathematics
Volume	33
Issue number	3
DOIs	https://doi.org/10.1007/s11766-018-3370-x
State	Published - 1 Sep 2018

Bibliographical note

Publisher Copyright:
© 2018, Editorial Committee of Applied Mathematics-A Journal of Chinese Universities and Springer-Verlag GmbH Germany, part of Springer Nature.

Keywords

47H09
47H10
asymptotically nonexpansive mapping
common fixed point
strong convergence
uniformly convex hyperbolic space

ASJC Scopus subject areas

Applied Mathematics

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10.1007/s11766-018-3370-x

Cite this

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abstract = "We introduce a one-step implicit iterative method for two finite families of asymptotically nonexpansive mappings in a hyperbolic space and use it to approximate common fixed points of these families. The results presented in this paper are new in the setting of hyperbolic spaces. On top, these are generalizations of several results in literature from Banach spaces to hyperbolic spaces. At the end of the paper, we give an example to validate our results.",

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PY - 2018/9/1

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N2 - We introduce a one-step implicit iterative method for two finite families of asymptotically nonexpansive mappings in a hyperbolic space and use it to approximate common fixed points of these families. The results presented in this paper are new in the setting of hyperbolic spaces. On top, these are generalizations of several results in literature from Banach spaces to hyperbolic spaces. At the end of the paper, we give an example to validate our results.

AB - We introduce a one-step implicit iterative method for two finite families of asymptotically nonexpansive mappings in a hyperbolic space and use it to approximate common fixed points of these families. The results presented in this paper are new in the setting of hyperbolic spaces. On top, these are generalizations of several results in literature from Banach spaces to hyperbolic spaces. At the end of the paper, we give an example to validate our results.

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KW - 47H10

KW - asymptotically nonexpansive mapping

KW - common fixed point

KW - strong convergence

KW - uniformly convex hyperbolic space

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ER -

A one-step implicit iterative method for two finite families of asymptotically nonexpansive mappings in a hyperbolic space

Abstract

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Keywords

ASJC Scopus subject areas

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