Solution of integral equations via coupled fixed point theorems in F-complete metric spaces

Abstract

The concept of coupled F-orthogonal contraction mapping is introduced in this paper, and some coupled fixed point theorems in orthogonal metric spaces are proved. The obtained results generalize and extend some of the well-known results in the literature. An example is presented to support our results. Furthermore, we apply our result to obtain the existence theorem for a common solution of the integral equations: {zeta(nu) = partial derivative(nu) + integral(m)(0) Xi(nu, beta)Omega(beta, zeta(beta), xi(beta))d beta, nu is an element of [0, H], xi(nu) = partial derivative(nu) + integral(m)(0) Xi(nu, beta)Omega(beta, xi(beta), zeta(beta))d beta, nu is an element of [0, H], where (a) partial derivative : m -> R and Omega : m x R x R -> R are continuous; (b) Xi : m x m is continuous and measurable at beta is an element of m, for all nu is an element of m; (c) Xi(nu, beta) >= 0, for all nu, beta is an element of m and integral(H)(0) Xi(nu, beta)d beta <= 1, for all nu is an element of m.