Analytical Meir–Keeler type contraction mappings and equivalent characterizations

Abhijit Pant; Rajendra Prasad Pant; Wutiphol Sintunavarat

doi:10.1007/s13398-020-00939-8

Analytical Meir–Keeler type contraction mappings and equivalent characterizations

Abhijit Pant, Rajendra Prasad Pant, Wutiphol Sintunavarat

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

5 Citations (Scopus)

Abstract

The aim of this paper is to obtain a fixed point theorem which gives a new solution to the Rhoades’ problem on the existence of contractive mappings that admit discontinuity at the fixed point; and it is the first Meir–Keeler type solution of this problem. We prove that our theorem characterizes the completeness of the metric space. We also give the structure of complete subspaces of the real line in which contractive mappings do not admit discontinuity at the fixed point and, thus, in the setting of the real line we completely resolve the Rhoades’ question.

Original language	English
Article number	37
Journal	Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
Volume	115
Issue number	1
DOIs	https://doi.org/10.1007/s13398-020-00939-8
Publication status	Published - Jan 2021
Externally published	Yes

Keywords

Completeness
Contractive condition
Discontinuity
k-continuity

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Geometry and Topology
Computational Mathematics
Applied Mathematics

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10.1007/s13398-020-00939-8

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Analytical Meir–Keeler type contraction mappings and equivalent characterizations

Abstract

Keywords

ASJC Scopus subject areas

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