Banach operator pairs and common fixed points in modular function spaces

N. Hussain; M. A. Khamsi; A. Latif

doi:10.1186/1687-1812-2011-75

Banach operator pairs and common fixed points in modular function spaces

N. Hussain, M. A. Khamsi, A. Latif

Mathematics

King Abdulaziz University

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

5 Scopus citations

Abstract

In this article, we introduce the concept of a Banach operator pair in the setting of modular function spaces. We prove some common fixed point results for such type of operators satisfying a more general condition of nonexpansiveness. We also establish a version of the well-known De Marr 's theorem for an arbitrary family of symmetric Banach operator pairs in modular function spaces without Δ₂-condition.

Original language	British English
Article number	75
Journal	Fixed Point Theory and Applications
Volume	2011
DOIs	https://doi.org/10.1186/1687-1812-2011-75
State	Published - Nov 2011

Keywords

Asymptotically pointwise ρ-nonexpansive mapping
Banach operator pair
Fixed point
Modular function space
Nearest point projection

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10.1186/1687-1812-2011-75

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abstract = "In this article, we introduce the concept of a Banach operator pair in the setting of modular function spaces. We prove some common fixed point results for such type of operators satisfying a more general condition of nonexpansiveness. We also establish a version of the well-known De Marr 's theorem for an arbitrary family of symmetric Banach operator pairs in modular function spaces without Δ2-condition.",

keywords = "Asymptotically pointwise ρ-nonexpansive mapping, Banach operator pair, Fixed point, Modular function space, Nearest point projection",

author = "N. Hussain and Khamsi, {M. A.} and A. Latif",

note = "Funding Information: The authors gratefully acknowledge the financial support from the Deanship of Scientific Research (DSR) at King Abdulaziz University (KAU) represented by the Unit of Research Groups through the Grant number (11/31/Gr) for the group entitled {"}Nonlinear Analysis and Applied Mathematics{"}. ",

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AU - Hussain, N.

AU - Khamsi, M. A.

AU - Latif, A.

N1 - Funding Information: The authors gratefully acknowledge the financial support from the Deanship of Scientific Research (DSR) at King Abdulaziz University (KAU) represented by the Unit of Research Groups through the Grant number (11/31/Gr) for the group entitled "Nonlinear Analysis and Applied Mathematics".

PY - 2011/11

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N2 - In this article, we introduce the concept of a Banach operator pair in the setting of modular function spaces. We prove some common fixed point results for such type of operators satisfying a more general condition of nonexpansiveness. We also establish a version of the well-known De Marr 's theorem for an arbitrary family of symmetric Banach operator pairs in modular function spaces without Δ2-condition.

AB - In this article, we introduce the concept of a Banach operator pair in the setting of modular function spaces. We prove some common fixed point results for such type of operators satisfying a more general condition of nonexpansiveness. We also establish a version of the well-known De Marr 's theorem for an arbitrary family of symmetric Banach operator pairs in modular function spaces without Δ2-condition.

KW - Asymptotically pointwise ρ-nonexpansive mapping

KW - Banach operator pair

KW - Fixed point

KW - Modular function space

KW - Nearest point projection

UR - http://www.scopus.com/inward/record.url?scp=84876592964&partnerID=8YFLogxK

U2 - 10.1186/1687-1812-2011-75

DO - 10.1186/1687-1812-2011-75

M3 - Article

AN - SCOPUS:84876592964

SN - 1687-1820

VL - 2011

JO - Fixed Point Theory and Applications

JF - Fixed Point Theory and Applications

M1 - 75

ER -

Banach operator pairs and common fixed points in modular function spaces

Abstract

Keywords

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