Fixed points and continuity of contractive maps

Abhijit Pant, R. P. Pant

Research output: Contribution to journalArticlepeer-review

71 Citations (Scopus)

Abstract

The aim of this paper is to generalize celebrated results due to Boyd and Wong [2] and Matkowski [9] and also to provide yet new solutions to the once open problem on the existence of a contractive mapping which possesses a fixed point but is not continuous at the fixed point. Besides continuous mappings our results also apply to discontinuous mappings which include threshold operations that are integral part of many a phenomena.

Original languageEnglish
Pages (from-to)3501-3506
Number of pages6
JournalFilomat
Volume31
Issue number11
DOIs
Publication statusPublished - 2017
Externally publishedYes

Keywords

  • Contractive condition
  • Fixed point
  • K-continuity
  • Non-expansive mapping
  • Threshold operation
  • Upper semi-continuous

ASJC Scopus subject areas

  • General Mathematics

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