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

Demonstratio mathematica

article

Sajan Aggarwal¹  Izhar Uddin¹ 

[1] Department of Mathematics

关键词: hyperbolic metric space;    nearly asymptotically nonexpansive mapping;    Fibonacci-Mann iteration;    monotone non-Lipschitzian mapping;    fixed point theorems;   

DOI  :  10.1515/dema-2019-0030

学科分类：外科医学

来源: De Gruyter

【 摘 要 】

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].

【 授权许可】

CC BY