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

Reny George, Ekta Tamrakar, Jelena Vujaković, Hemant Kumar Pathak and Selvavinayagam Velusamy
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Reny George: Department of Mathematics, College of Science, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
Ekta Tamrakar: School of Studies in Mathematics, Pt. Ravishankar Shukla University, Raipur (C.G.) 492010, India
Jelena Vujaković: Faculty of Sciences and Mathematics, University of Privstina, Kosovska Mitrovica 38220, Serbia
Hemant Kumar Pathak: School of Studies in Mathematics, Pt. Ravishankar Shukla University, Raipur (C.G.) 492010, India
Selvavinayagam Velusamy: Nasser Vocational Training Centre, Jau, Kingdom of Bahrain

Mathematics, 2019, vol. 7, issue 5, 1-19

Abstract: In this paper, we introduce the ( C , ? * , 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 ? -admissible set valued mappings in a metric space.

Keywords: fixed point; common fixed point; directed graph; edge preserving; transitivity property (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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