Some periodic and fixed point theorems on quasi-b-gauge spaces

N. Zikria, M. Samreen, T. Kamran, H. Aydi*, C. Park

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The notions of a quasi-b-gauge space (U, Qs;Ω) and a left (right) Js;Ω-family of generalized quasi-pseudo-b-distances generated by (U, Qs;Ω) are introduced. Moreover, by using this left (right) Js;Ω-family, we define the left (right) Js;Ω-sequential completeness, and we initiate the Nadler type contractions for set-valued mappings T:U→ClJs;Ω(U) and the Banach type contractions for single-valued mappings T: U→ U, which are not necessarily continuous. Furthermore, we develop novel periodic and fixed point results for these mappings in the new setting, which generalize and improve the existing fixed point results in the literature. Examples validating our obtained results are also given.

Original languageEnglish
Article number13
JournalJournal of Inequalities and Applications
Volume2022
Issue number1
DOIs
Publication statusPublished - 2022
Externally publishedYes

Keywords

  • Banach contraction
  • Fixed point
  • Generalized quasi-pseudo-b-distance
  • Nadler contraction
  • Periodic point
  • Quasi-b-gauge space

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