Vol. 69, No. 1, pp. 23–38 (2017)

Previous Article

Next Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home


Pick a mirror


Fixed point results for (φ,ψ)-contractions in metric spaces endowed with a graph and applications

Mina Dinarvand

Faculty of Mathematics, K. N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran E-mail: dinarvandmina@yahoo.com

Abstract: In the present work, we introduce the concepts of (G,φ,ψ)-contraction and (G,φ,ψ)-graphic contraction defined on metric spaces endowed with a graph G and we show that these two types of contractions generalize a large number of contractions. Subsequently, we investigate various results which assure the existence and uniqueness of fixed points for such mappings. According to the applications of our main results, we further obtain a fixed point theorem for cyclic operators and an existence theorem for the solution of a nonlinear integral equation. Moreover, some illustrative examples are provided to demonstrate our obtained results.

Keywords: Fixed point; connected graph; Picard operator; (φ,ψ)-type contraction.

Classification (MSC2000): 47H10; 05C40, 54H25

Full text of the article: (for faster download, first choose a mirror)

Electronic fulltext finalized on: 29 Dec 2016. This page was last modified: 10 Jan 2017.

© 2016 Mathematical Society of Serbia (Društvo matematičara Srbije)
© 2016–2017 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition