Existence and approximation of fixed point of a nonlinear mapping satisfying rational type contractive inequality condition in complex-valued Banach spaces

Godwin Amechi  Okeke; Johnson O.  Olaleru; Memudu Olaposi  Olatinwo

Godwin Amechi Okeke Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600 Pakistan
Johnson O. Olaleru Department of Mathematics, University of Lagos, Nigeria.
Memudu Olaposi Olatinwo Department of Mathematics, Faculty of Science, Obafemi Awolowo University, Ile-Ife, Nigeria

Keywords: Complex-valued Banach spaces, existence of a unique fixed point, iterative processes, cone metric spaces with Banach algebras, delay dierential equations

Abstract

We prove the existence of a unique xed point for a mapping satisfying a rational type
contractive inequality condition in complex-valued Banach spaces. We approximate this xed
point via some xed point iterative processes with high rate of convergence. We then prove
that our results are valid in cone metric spaces with Banach algebras. Furthermore, our results
are applied in nding the solutions of delay dierential equations. Our results extend and
generalize several known results in the literature.

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