Fejér monotonicity and fixed point theorems with applications to a nonlinear integral equation in complex valued Banach spaces

Godwin Amechi Okeke, Mujahid Abbas

Abstract

It is our purpose in this paper to prove some fixed point results and Fej´er monotonicity of some faster fixed point iterative sequences generated by some nonlinear operators satisfying rational inequality in complex valued Banach spaces. We prove that results in complex valued Banach spaces are valid in cone metric spaces with Banach algebras. Furthermore, we apply our results in solving certain mixed type VolterraFredholm functional nonlinear integral equation in complex valued Banach spaces.

Keywords

Complex valued Banach spaces; fixed point theorems; Féjer monotonicity; iterative processes; cone metric spaces with Banach algebras; mixed type Volterra-Fredholm functional nonlinear integral equation

Subject classification

47H09; 47H10; 49M05; 54H25

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