(C ,Ψ *, G ) Class of Contractions and Fixed Points in a Metric Space Endowed with a Graph

Mathematics

Reny George¹  Jelena Vujaković²  Selvavinayagam Velusamy³  Ekta Tamrakar⁴  Hemant Kumar Pathak⁴ 

[1] Department of Mathematics, College of Science, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia;Faculty of Sciences and Mathematics, University of Privstina, Kosovska Mitrovica 38220, Serbia;Nasser Vocational Training Centre, Jau, Kingdom of Bahrain;School of Studies in Mathematics, Pt. Ravishankar Shukla University, Raipur (C.G.) 492010, India;

关键词: fixed point;    common fixed point;    directed graph;    edge preserving;    transitivity property;   

DOI  :  10.3390/math7050482

来源: DOAJ

【 摘 要 】

In this paper, we introduce the $(C,{\Psi }^{*},G)$ class of contraction mappings using C-class functions and some improved control functions for a pair of set valued mappings as well as a pair of single-valued mappings, and prove common fixed point theorems for such mappings in a metric space endowed with a graph. Our results unify and generalize many important fixed point results existing in literature. As an application of our main result, we have derived fixed point theorems for a pair of $\alpha$ -admissible set valued mappings in a metric space.

【 授权许可】

Unknown