On Discontinuity Problem at Fixed Point

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

Research output: Contribution to journalArticlepeer-review

51 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 languageEnglish
Pages (from-to)499-517
Number of pages19
JournalBulletin of the Malaysian Mathematical Sciences Society
Volume43
Issue number1
DOIs
Publication statusPublished - 1 Jan 2020
Externally publishedYes

Keywords

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

ASJC Scopus subject areas

  • General Mathematics

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