Fixed-Point Theorems Using α-Series in F-Metric Spaces

ÖZTÜRK V., TÜRKOĞLU A. D.

Mathematics, vol.12, no.16, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 16
  • Publication Date: 2024
  • Doi Number: 10.3390/math12162596
  • Journal Name: Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: contraction, F-metric, fixed point, α-series
  • Gazi University Affiliated: Yes

Abstract

Fixed-point theory, which has been developing since 1922, is widely used. Various contraction principles have been defined in the literature. In this work, we define rational-type contraction and weak Choudhury type contraction using (Formula presented.) -series in F-metric spaces and prove common fixed-point theorems for sequences of self-mappings. This method is based on the convergence series of coefficients. Our results are the generalized version of the results in the literature. Finally, we apply our main results to solve an integral equation and a differential equation.