ON G-ASYMPTOTIC QUASI-CONTRACTION IN METRIC SPACES WITH APPLICATION TO SOLOW GROWTH MODEL

Abstract

In this paper, we introduce a new class of mappings called G-asymptotic quasi-contraction mappings which is a genfieralization of some existing contraction mappings in theliterature. The fixed point theorem for this newly introduced maps is proved in a metricspace equipped with a graph structure. The solution of the nonlinear differential equationof Solow growth model in Economics is established via fixed point theorem of this map. Weequally provide examples to validate our results. Our results are generalization and extensionof some related works in the literature.