Fixed Points of Subadditive Maps with an Application to a System of Volterra–Fredholm Type Integrodifferential Equations

Abstract

In this paper, some fixed-point theorems are established for strongly subadditive maps on CΩ,ϒ (where CΩ,ϒ denotes the space of ϒ-valued continuous functions on a compact Hausdorff space Ω and ϒ is a unital Banach algebra). Finally, the result is applied to prove the existence and uniqueness of a solution for a system of nonlinear integrodifferential equations.

Fredholm type integral equation in extended $M_{b}$-metric spaces

“…Lately, fixed point theory has become the focus of many researchers and that is due to its applications in many fields, such as engineering and computer sciences. Also fixed point theory can be used to solve differential equations along with integral equations [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. M-metric spaces were introduced by Asadi, Karapinar and Salimi, in [15], they are an extension of a partial metric space.…”