Convergence and stability of Fibonacci-Mann iteration for a monotone non-Lipschitzian mapping

Abstract

In this paper, we prove strong convergence and Δ−convergence of Fibonacci-Mann iteration for a monotone non-Lipschitzian mapping (i.e. nearly asymptotically nonexpansive mapping) in partially ordered hyperbolic metric space. Moreover, we prove stability of Fibonacci-Mann iteration. Further, we construct a numerical example to illustrate results. Our results simultaneously generalize the results of Alfuraidan and Khamsi [Bull. Aust. Math. Soc., 2017, 96, 307–316] and Schu [J. Math. Anal. Appl., 1991, 58, 407–413].

Keywords

• hyperbolic metric space
• nearly asymptotically nonexpansive mapping
• fibonacci-mann iteration
• monotone non-lipschitzian mapping
• fixed point theorems
• 47h10
• 54h25