PPF dependent fixed point in modified Razumikhin class with applications

Volume 9, Issue 1, pp 270--286 http://dx.doi.org/10.22436/jnsa.009.01.26

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Authors

M. Paknazar - Department of Mathematics, Farhangian University, Iran. M. A. Kutbi - Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia. M. Demma - Università degli Studi di Palermo, Italy. P. Salimi - Young Researchers and Elite Club, Islamic Azad University--Rasht Branch, Rasht, Iran.

Abstract

In this paper we introduce the concepts of \(c-C_{\alpha\beta}-\)admissible mapping, \((\alpha\beta)_c-\Theta-\)contraction, weak \((\alpha\beta)_c-\Theta-\)contraction, generalized \((\alpha\beta)_c-\Theta-\)contraction and establish the existence of PPF dependent fixed point theorems for such classes of contractive nonself-mappings in the Razumikhin class. We give, also, a result of existence of a PPF dependent fixed point by a condition of Suzuki type. As applications of our theorems, we deduce some PPF dependent fixed point theorems for nonself-mappings valued in a Banach space endowed with a graph or a partial order, and furnish an illustrative example to support our main theorem.

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Keywords

• Razumikhin class
• PPF dependent fixed point
• \((\alpha\beta)_c-\Theta-\)contraction
• generalized \((\alpha\beta)_c-\Theta-\)contraction.

MSC

•  46N40
•  47H10
•  54H25
•  46T99

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