Convergence analysis of modified Abbas iteration process for two \(G\)-nonexpansive mappings. (English) Zbl 1522.47106
Summary: The purpose of this paper is to modify Abbas iteration for two \(G\)-nonexpansive mappings. We perform the convergence analysis of newly defined iteration process in uniformly convex Banach space. To compare the rate of convergence of the proposed method with well-known Ishikawa iteration, modified S-iteration and Thianwan new iteration processes, a numerical example is also constructed.
MSC:
| 47J26 | Fixed-point iterations |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
| 65J15 | Numerical solutions to equations with nonlinear operators |
Keywords:
\(G\)-nonexpansive mapping; Ishikawa iteration; modified S-iteration; weak convergence; strong convergence; common fixed point; directed graph; uniformly convex Banach spaceReferences:
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