Extended Φ-contraction mappings

R. P. Pant

doi:10.1007/s41478-023-00712-1

Extended Φ-contraction mappings

R. P. Pant

Dalhousie Villa Compound

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

Abstract

We extend the concept of Φ-contraction mappings and introduce a condition that applies to contraction mappings as well as nonexpansive mappings. The fixed-point sets and domains of such mappings display interesting algebraic, geometric and dynamical features. A method for determining the cardinality of the fixed-point set is also given. Various examples and an application in obtaining a unique solution of a boundary value problem of second order differential equations substantiate our results.

Original language	English
Journal	Journal of Analysis
DOIs	https://doi.org/10.1007/s41478-023-00712-1
Publication status	Accepted/In press - 2024
Externally published	Yes

Keywords

Cardinality
Eventual fixed points
Fixed points
Non-expansive mappings
Φ-contraction

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Geometry and Topology
Applied Mathematics

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10.1007/s41478-023-00712-1

Cite this

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title = "Extended Φ-contraction mappings",

abstract = "We extend the concept of Φ-contraction mappings and introduce a condition that applies to contraction mappings as well as nonexpansive mappings. The fixed-point sets and domains of such mappings display interesting algebraic, geometric and dynamical features. A method for determining the cardinality of the fixed-point set is also given. Various examples and an application in obtaining a unique solution of a boundary value problem of second order differential equations substantiate our results.",

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AB - We extend the concept of Φ-contraction mappings and introduce a condition that applies to contraction mappings as well as nonexpansive mappings. The fixed-point sets and domains of such mappings display interesting algebraic, geometric and dynamical features. A method for determining the cardinality of the fixed-point set is also given. Various examples and an application in obtaining a unique solution of a boundary value problem of second order differential equations substantiate our results.

KW - Cardinality

KW - Eventual fixed points

KW - Fixed points

KW - Non-expansive mappings

KW - Φ-contraction

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SN - 0971-3611

JO - Journal of Analysis

JF - Journal of Analysis

ER -

Extended Φ-contraction mappings

Abstract

Keywords

ASJC Scopus subject areas

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