Convergence of Ishikawa iterates of two mappings in modular function spaces

Afrah Ahmad Noan Abdou; Mohamed Amine Khamsi; Abdul Rahim Khan

doi:10.1186/1687-1812-2014-74

Convergence of Ishikawa iterates of two mappings in modular function spaces

Afrah Ahmad Noan Abdou^*, Mohamed Amine Khamsi, Abdul Rahim Khan

^*Corresponding author for this work

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

6 Scopus citations

Abstract

We establish convergence in the modular sense of an iteration scheme associated with a pair of mappings on a nonlinear domain in modular function spaces. In particular, we prove that such a scheme converges to a common fixed point of the mappings. Our results are generalization of known similar results in the non-modular setting. In particular, we avoid smoothness of the norm in the case of Banach spaces and that of the triangle inequality of the distance in metric spaces.

Original language	English
Article number	74
Journal	Fixed Point Theory and Algorithms for Sciences and Engineering
Volume	2014
DOIs	https://doi.org/10.1186/1687-1812-2014-74
State	Published - Mar 2014

Bibliographical note

Funding Information:
The authors MA Khamsi and AR Khan acknowledge gratefully KACST, Riyad, Saudi Arabia, for supporting Research Project ARP-32-34. The author AAN Abdou gratefully acknowledges the Deanship of Scientific Research at King Abdulaziz University, Jeddah, Saudi Arabia, for supporting this research.

Keywords

Fixed point
Fixed point iteration process
Ishikawa iterations
Modular function space
Nonexpansive mapping
Orlicz space
Strict convexity
ρ-convergence

ASJC Scopus subject areas

Geometry and Topology
Applied Mathematics

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title = "Convergence of Ishikawa iterates of two mappings in modular function spaces",

abstract = "We establish convergence in the modular sense of an iteration scheme associated with a pair of mappings on a nonlinear domain in modular function spaces. In particular, we prove that such a scheme converges to a common fixed point of the mappings. Our results are generalization of known similar results in the non-modular setting. In particular, we avoid smoothness of the norm in the case of Banach spaces and that of the triangle inequality of the distance in metric spaces.",

keywords = "Fixed point, Fixed point iteration process, Ishikawa iterations, Modular function space, Nonexpansive mapping, Orlicz space, Strict convexity, ρ-convergence",

author = "Abdou, \{Afrah Ahmad Noan\} and Khamsi, \{Mohamed Amine\} and Khan, \{Abdul Rahim\}",

note = "Funding Information: The authors MA Khamsi and AR Khan acknowledge gratefully KACST, Riyad, Saudi Arabia, for supporting Research Project ARP-32-34. The author AAN Abdou gratefully acknowledges the Deanship of Scientific Research at King Abdulaziz University, Jeddah, Saudi Arabia, for supporting this research. ",

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T1 - Convergence of Ishikawa iterates of two mappings in modular function spaces

AU - Abdou, Afrah Ahmad Noan

AU - Khamsi, Mohamed Amine

AU - Khan, Abdul Rahim

N1 - Funding Information: The authors MA Khamsi and AR Khan acknowledge gratefully KACST, Riyad, Saudi Arabia, for supporting Research Project ARP-32-34. The author AAN Abdou gratefully acknowledges the Deanship of Scientific Research at King Abdulaziz University, Jeddah, Saudi Arabia, for supporting this research.

PY - 2014/3

Y1 - 2014/3

N2 - We establish convergence in the modular sense of an iteration scheme associated with a pair of mappings on a nonlinear domain in modular function spaces. In particular, we prove that such a scheme converges to a common fixed point of the mappings. Our results are generalization of known similar results in the non-modular setting. In particular, we avoid smoothness of the norm in the case of Banach spaces and that of the triangle inequality of the distance in metric spaces.

AB - We establish convergence in the modular sense of an iteration scheme associated with a pair of mappings on a nonlinear domain in modular function spaces. In particular, we prove that such a scheme converges to a common fixed point of the mappings. Our results are generalization of known similar results in the non-modular setting. In particular, we avoid smoothness of the norm in the case of Banach spaces and that of the triangle inequality of the distance in metric spaces.

KW - Fixed point

KW - Fixed point iteration process

KW - Ishikawa iterations

KW - Modular function space

KW - Nonexpansive mapping

KW - Orlicz space

KW - Strict convexity

KW - ρ-convergence

UR - https://www.scopus.com/pages/publications/84899859815

U2 - 10.1186/1687-1812-2014-74

DO - 10.1186/1687-1812-2014-74

M3 - Article

AN - SCOPUS:84899859815

SN - 1687-1820

VL - 2014

JO - Fixed Point Theory and Algorithms for Sciences and Engineering

JF - Fixed Point Theory and Algorithms for Sciences and Engineering

M1 - 74

ER -

Convergence of Ishikawa iterates of two mappings in modular function spaces

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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