ON APPLICATIONS OF GENERALIZED F-CONTRACTION TO DIFFERENTIAL EQUATIONS

Abstract

In the present work, we introduce the new concept of a generalization of Ger- aghty type F-Berinde contraction mappings and establish certain existence results for such mappings. Some examples will embellish the results, for the same computer simulation is done. Our examples involve a series of complicated structured functions which cannot be treated by classical fixed point methods. Our findings extend, unify and enrich a multitude results in the existing literature. As an application, we apply our abstract results to establish the existence of solution of differential equations of first and second order to exhibit the po- tency and viability of our results. At the end, as an open problem, we suggest storekeeper’s control problem in terms of Volterra integral equation whose solution may be procured from the established results.