On Discontinuity Problem at Fixed Point

R. P. Pant; Nihal Yilmaz Özgür; Nihal Taş

doi:10.1007/s40840-018-0698-6

On Discontinuity Problem at Fixed Point

R. P. Pant, Nihal Yilmaz Özgür, Nihal Taş

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

52 Citations (Scopus)

Abstract

We obtain some fixed point theorems under contractive conditions which admit discontinuity at the fixed point. Our results subsume all the known results of similar type, provide new answers to the question of continuity of contractive mappings at their fixed points, and also extend some recent results. Furthermore, we consider the fixed-circle problem on metric spaces. We obtain new fixed-circle results as the generalizations of some known fixed-circle theorems. Some applications of obtained results to discontinuous activation functions are also given.

Original language	English
Pages (from-to)	499-517
Number of pages	19
Journal	Bulletin of the Malaysian Mathematical Sciences Society
Volume	43
Issue number	1
DOIs	https://doi.org/10.1007/s40840-018-0698-6
Publication status	Published - 1 Jan 2020
Externally published	Yes

Keywords

(ε- δ) Condition
Fixed circle
Fixed point
k-continuity

ASJC Scopus subject areas

General Mathematics

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10.1007/s40840-018-0698-6

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AU - Taş, Nihal

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AB - We obtain some fixed point theorems under contractive conditions which admit discontinuity at the fixed point. Our results subsume all the known results of similar type, provide new answers to the question of continuity of contractive mappings at their fixed points, and also extend some recent results. Furthermore, we consider the fixed-circle problem on metric spaces. We obtain new fixed-circle results as the generalizations of some known fixed-circle theorems. Some applications of obtained results to discontinuous activation functions are also given.

KW - (ε- δ) Condition

KW - Fixed circle

KW - Fixed point

KW - k-continuity

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JF - Bulletin of the Malaysian Mathematical Sciences Society

IS - 1

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On Discontinuity Problem at Fixed Point

Abstract

Keywords

ASJC Scopus subject areas

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