Some Fixed-Circle Results with Different Auxiliary Functions


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

JOURNAL OF FUNCTION SPACES, vol.2022, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2022
  • Publication Date: 2022
  • Doi Number: 10.1155/2022/2775733
  • Journal Name: JOURNAL OF FUNCTION SPACES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, MathSciNet, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Ondokuz Mayıs University Affiliated: No

Abstract

As the generalization of the fixed-point theory, the fixed-circle problems are interesting and notable geometric constructions. In this paper, we prove that some new necessary conditions are investigated for the existence of a fixed circle of a given self-mapping in G-metric spaces. The well-known Braincari and Chatterjea contractive conditions are generalized for proving the uniqueness of obtained theorems. Finally, an application to parametric rectified linear unit activation functions are given to show the importance of studying the fixed-circle problem.