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

Authors

  • Mina Dinarvand Faculty of Mathematics, K. N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran Author

Keywords:

Fixed point, connected graph, Picard operator, (φ,ψ)-type contraction

Subjects:

47H10, 05C40, 54H25

Abstract

In the present work, we introduce the concepts of(G,φ,ψ)-contraction and (G,φ,ψ)-graphiccontraction defined on metric spaces endowed with a graph G andwe show that these two types of contractions generalize a largenumber of contractions. Subsequently, we investigate variousresults which assure the existence and uniqueness of fixed pointsfor such mappings. According to the applications of our mainresults, we further obtain a fixed point theorem for cyclicoperators and an existence theorem for the solution of a nonlinearintegral equation. Moreover, some illustrative examples areprovided to demonstrate our obtained results.

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Published

2017-01-15