Some Common Fixed Circle Results on Metric and S-Metric Spaces with an Application to Activation Functions

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Taş N., KAPLAN E., Santina D., Mlaiki N., Shatanawi W.

Symmetry, vol.15, no.5, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 5
  • Publication Date: 2023
  • Doi Number: 10.3390/sym15050971
  • Journal Name: Symmetry
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: activation functions, common fixed circle, fixed point, S-metric spaces
  • Ondokuz Mayıs University Affiliated: Yes


In this paper, we modify various contractive conditions (C.C.)s such as Ciric type (C.C.), Rhoades type (C.C.), Seghal type (C.C.), Bianchini type (C.C.), and Berinde type (C.C.) for two self-mappings, considering that the contractive property plays a major role in establishing a fixed circle (F.C.) on both metric spaces (M-s) and (Formula presented.) -(M-s) where the symmetry condition is satisfied, and we utilize them to establish a common (F.C.). We prove new (F.C.) results on both (M-s) and (Formula presented.) -(M-s) with illustrative examples. Finally, we provide an application to activation functions such as rectified linear unit activation functions and parametric rectified linear unit activation functions.