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

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.