Generalization of common fixed Points Theorems for C-T-Contraction mappings with application to partial differential equations and Modified Meir-Keeler’s Theorem

Résumé

In this paper, we prove two common fixed point theorems for pairs of self-mappings
satisfying L-weak commuting condition. Then we prove some fixed point theorems
for more general self-mappings which not depends on L-weakly commuting condition
called T-contractions which include a class that satisfies a generalized Meir-Keeler type
contractive condition using C-Functions. We also present examples that support and
strengthen our results. In the end, we consider an application in partial differential
equations. We ensure the existence of a common fixed point, which turns to be an exact
solution of a nonlinear equation.