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Volume 7, Number 3, 2017, Pages 1112-1126                                                                DOI:10.11948/2017069
New type of fixed point result of F-contraction with applications
Aftab Hussain,Muhammad Arshad and Mujahid Abbas
Keywords:Coincidence point, generalized dynamic process, F-contraction, integral equations, dynamic programming.
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.
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