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It is our purpose in this paper to prove some fixed point results and Fejer 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 Volterra-Fredholm functional nonlinear integral equation in complex valued Banach spaces.

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