NEW TYPE OF FIXED POINT RESULT OF FCONTRACTION WITH APPLICATIONS

Aftab Hussain; Muhammad Arshad; Mujahid Abbas

doi:10.11948/2017069

2017 Volume 7 Issue 3

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Aftab Hussain, Muhammad Arshad, Mujahid Abbas. NEW TYPE OF FIXED POINT RESULT OF FCONTRACTION WITH APPLICATIONS[J]. Journal of Applied Analysis & Computation, 2017, 7(3): 1112-1126. doi: 10.11948/2017069

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Aftab Hussain, Muhammad Arshad, Mujahid Abbas. NEW TYPE OF FIXED POINT RESULT OF FCONTRACTION WITH APPLICATIONS[J]. Journal of Applied Analysis & Computation, 2017, 7(3): 1112-1126. doi: 10.11948/2017069

NEW TYPE OF FIXED POINT RESULT OF FCONTRACTION WITH APPLICATIONS

1 Khwaja Fareed University of Engineering & Information Technology, Rahim Yar Khan, Pakistan;
2 Department of Mathematics and Statistics, International Islamic University, H-10, 44000-Islamabad, Pakistan;
3 Department of Mathematics, University of Management and Technology, Johar Town Lahore;
4 Department of Mathematics and Applied Mathematics, University of Pretoria, Lynnwood road, Pretoria 0002, South Africa

Abstract

Abstract

The purpose of this paper is to prove theorem which generalize the corresponding results of Rhoades[B. E. Rhoades, Two New Fixed Point Theorems, Gen. Math. Notes, 2015, 27(2), 123-132]. This paper is to introduce the notion of dynamic process for generalized 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.
- Coincidence point /
- generalized dynamic process /
- F-contraction /
- integral equations /
- dynamic programming
MSC: 47H10;47H04;60H25;54H25

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References

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