Approximating Fixed Points of Relatively Nonexpansive Mappings via Thakur Iteration

Symmetry

V. Pragadeeswarar¹  R. Gopi²  M. De la Sen³ 

[1] Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore 641105, Tamil Nadu, India;Department of Mathematics, School of Engineering, Presidency University, Bengaluru 560064, Karnataka, India;Institute of Research and Development of Processes IIDP, Campus of Leioa, University of the Basque Country, 48940 Leioa, Bizkaia, Spain;

关键词: von Neumann sequences;    relatively nonexpansive mappings;    best proximity point;    fixed point;   

DOI  :  10.3390/sym14061107

来源: DOAJ

【 摘 要 】

The study of symmetry is a major tool in the nonlinear analysis. The symmetricity of distance function in a metric space plays important role in proving the existence of a fixed point for a self mapping. In this work, we approximate a fixed point of noncyclic relatively nonexpansive mappings by using a three-step Thakur iterative scheme in uniformly convex Banach spaces. We also provide a numerical example where the Thakur iterative scheme is faster than some well known iterative schemes such as Picard, Mann, and Ishikawa iteration. Finally, we provide a stronger version of our proposed theorem via von Neumann sequences.

【 授权许可】

Unknown