Generalized dynamic process for generalized (f,L)-almost F-contraction with applications

Volume 9, Issue 4, pp 1702--1715 http://dx.doi.org/10.22436/jnsa.009.04.26

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Authors

Nawab Hussain - Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia. Muhammad Arshad - Department of Mathematics, International Islamic University, H-10, Islamabad-44000, Pakistan. Mujahid Abbas - Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia. - Department of Mathematics and Applied Mathematics, University of Pretoria, Lynnwood road, Pretoria 0002, South Africa. Aftab Hussain - Department of Mathematics, International Islamic University, H-10, Islamabad-44000, Pakistan.

Abstract

Recently Abbas [M. Abbas, Fixed Point Theory, 13 (2012), 3-10] introduced the concept of f-almost contraction which in turn extended the class of multivalued almost contraction mapping and obtained coincidence point results for this new class of mappings. The aim of this paper is to introduce the notion of dynamic process for generalized (f;L)-almost F-contraction mappings and to obtain coincidence and common fixed point results for such process. It is worth mentioning that our results do not rely on the commonly used range inclusion condition. We provide some examples to support our results. As an application of our results, we obtain the existence and uniqueness of solutions of dynamic programming and integral equations. Our results provide extension as well as substantial generalizations and improvements of several well known results in the existing comparable literature.

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Keywords

• Coincidence point
• generalized dynamic process
• integral equations
• (f،L)-almost F-contraction
• dynamic programming.

MSC

•  47H04
•  47H10
•  54H25
•  60H25

References

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