Some approximate fixed point results and application on graph theory for partial (h-F)-generalized convex contraction mappings with special class of functions on complete metric space

Volume 10, Issue 4, pp 1695--1708 http://dx.doi.org/10.22436/jnsa.010.04.32

Publication Date: April 20, 2017 Submission Date: September 01, 2016

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Authors

M. M. M. Jaradat - Department of Mathematics, Statistics and Physics, Qatar University, Doha, Qatar. Z. Mustafa - Department of Mathematics, Statistics and Physics, Qatar University, Doha, Qatar. A. H. Ansari - Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran. S. Chandok - School Of Mathematics, Thapar University, Patiala-147004, India. C. Dolićanin - Department of Matheamtics, State University of Novi Pazar, Novi Pazar, Serbia.

Abstract

In this paper, we introduce a new concept called partial (h-F)-generalized (and (h-F)-subgeneralized) convex contractions of order 3 (and with rank 3) using some auxiliary functions. Also we present some approximate fixed point results in metric space and approximate fixed point results in metric space endowed with a graph. Some examples are provided to illustrate the main results and to show the essentiality of the given hypotheses.

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Keywords

• \(\varepsilon\)-fixed point
• \(\alpha\)-admissible
• partial (h-F)-generalized convex contractions of order 3
• partial (h-F)-subgeneralized convex contractions of order 3
• \(\alpha\)-complete metric spaces
• graph.

MSC

•  47H10
•  54H25

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