Some fixed point theorems for convex contractive mappings in complete metric spaces with applications

Abstract In this research work, convexity condition is introduced to some classes of contraction mappings such as Chatterjea and Hardy and Rogers contractive mappings. The fixed points of these maps are proved in complete metric spaces. Example is equally provided to support the main result. The unique solution of nonlinear Fredholm integral equation is obtained via the Hardy and Rogers convex contraction mappings of type 2. The results obtained in this paper, extend and generalize some related works in the literature.