? EXTENSION OF GENERALIZED α-φ CONTRACTIVE MAPPING THEOREMS WITH RATIONAL EXPRESSIONS IN CONE METRIC SPACES AND APPLICATION

摘要

T he aim of this paper, we introduce and extend the notion of generalized -contractive mappings involving rational expressions in cone metric spaces and state the existence and uniqueness of a fixed point for this mapping. Our results are generalizations and extend certain main result of [30]. Some examples are given to illustrate the obtained results and to show that these results are proper extensions of the existing ones. Then we apply the obtained theorem to study the existence of solutions to the nonlinear integral equation.