On generalized α-nonexpansive mappings in Banach spaces

Deepak Khantwal; Rajendra Pant

doi:10.1007/s13226-025-00879-2

On generalized α-nonexpansive mappings in Banach spaces

Deepak Khantwal, Rajendra Pant

Mathematics and Applied Mathematics

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

Abstract

The purpose of this paper is to further investigate generalized α-nonexpansive mappings. We establish that this class of mappings admits an approximate fixed point sequence in the setting of Banach spaces. Additionally, for α>0, we prove that these mappings are asymptotically regular on nonempty bounded subsets of Banach spaces. Finally, we prove a new existence result for generalized α-nonexpansive mappings.

Original language	English
Journal	Indian Journal of Pure and Applied Mathematics
DOIs	https://doi.org/10.1007/s13226-025-00879-2
Publication status	Accepted/In press - 2025

Keywords

Fixed point
Fundamentally nonexpansive mapping
Generalized α-nonexpansive
Nonexpansive mapping
α-nonexpansive mapping

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1007/s13226-025-00879-2

Cite this

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title = "On generalized α-nonexpansive mappings in Banach spaces",

abstract = "The purpose of this paper is to further investigate generalized α-nonexpansive mappings. We establish that this class of mappings admits an approximate fixed point sequence in the setting of Banach spaces. Additionally, for α>0, we prove that these mappings are asymptotically regular on nonempty bounded subsets of Banach spaces. Finally, we prove a new existence result for generalized α-nonexpansive mappings.",

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AB - The purpose of this paper is to further investigate generalized α-nonexpansive mappings. We establish that this class of mappings admits an approximate fixed point sequence in the setting of Banach spaces. Additionally, for α>0, we prove that these mappings are asymptotically regular on nonempty bounded subsets of Banach spaces. Finally, we prove a new existence result for generalized α-nonexpansive mappings.

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KW - Fundamentally nonexpansive mapping

KW - Generalized α-nonexpansive

KW - Nonexpansive mapping

KW - α-nonexpansive mapping

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JO - Indian Journal of Pure and Applied Mathematics

JF - Indian Journal of Pure and Applied Mathematics

ER -

On generalized α-nonexpansive mappings in Banach spaces

Abstract

Keywords

ASJC Scopus subject areas

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