Abstract
In this article, we consider an extensive class of monotone nonexpansive mappings. We use S -iteration to approximate the fixed point for monotone total asymptotically nonexpansive mappings in the settings of modular function space.
Highlights
In 1965, the existence results for nonexpansive mapping were initiated by Browder [1], Kirk [2], and Göhde [3] independently
The idea about asymptotically nonexpansive mappings was introduced by Goebel and Kirk [4] in 1972
Fixed point results of nonexpansive mapping were extended for monotone case by Bachar and Khamsi [5] in 2015
Summary
In 1965, the existence results for nonexpansive mapping were initiated by Browder [1], Kirk [2], and Göhde [3] independently. Fixed point results of nonexpansive mapping were extended for monotone case by Bachar and Khamsi [5] in 2015. Alfuraidan and Khamsi [6] extended the concept of asymptotically nonexpansive for the case of monotone in 2018. Alber et al [7] introduced the concept of total asymptotically nonexpansive mappings that generalizes family of mapping that are the extension of asymptotically nonexpansive mappings in 2006. Alfuraidan, Bachar, and Khamsi [13] in 2017 extended results of Goebel and Kirk [4] for monotone asymptotically nonexpansive mappings in MF spaces using Mann iteration process. We extend the notion of monotone total asymptotically nonexpansive mappings in MF space and generalize the results of Alfuraidan and Khamsi presented in [6, 13]. We use S-iteration process to approximate the fixed point, which is fastly convergent than the classic Picard [14], Mann [15], and Ishikawa [16] iterative processes
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