Some Common Fixed-Circle Results on Metric Spaces

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Mlaiki N., Tas N., KAPLAN E., Aiadi S. S., Souayah A. K.

AXIOMS, vol.11, no.9, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 9
  • Publication Date: 2022
  • Doi Number: 10.3390/axioms11090454
  • Journal Name: AXIOMS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: metric spaces, fixed circle, common fixed circle, POINT, UNIQUE
  • Ondokuz Mayıs University Affiliated: No

Abstract

Recently, the fixed-circle problems have been studied with different approaches as an interesting and geometric generalization. In this paper, we present some solutions to an open problem CC: what is (are) the condition(s) to make any circle C-omega omicron nu as the common fixed circle for two (or more than two) self-mappings? To do this, we modify some known contractions which are used in fixed-point theorems such as the Hardy-Rogers-type contraction, Kannan-type contraction, etc.