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A new iteration scheme for approximating fixed points of nonexpansive mappings

Thakur Balwant Singh (Pt.Ravishankar Shukla University, School of Studies in Mathematics, Raipur, (C.G.), India)
Thakur Dipti (Pt.Ravishankar Shukla University, School of Studies in Mathematics, Raipur, (C.G.), India)
Postolache Mihai (University Politehnica of Bucharest, Department of Mathematics & Informatics, Bucharest, Romania)

In this paper, we introduce a new three-step iteration scheme and establish convergence results for approximation of fixed points of nonexpansive mappings in the framework of Banach space. Further, we show that the new iteration process is faster than a number of existing iteration processes. To support the claim, we consider a numerical example and approximated the fixed point numerically by computer using MATLAB.

Keywords: fixed point, nonexpansive mapping, strong and weak convergence theorems