EXISTENCE AND CONVERGENCE RESULTS FOR A CLASS OF NON-EXPANSIVE TYPE MAPPINGS IN BANACH SPACES

Ashis Bera, Ankush Chanda, Lakshmi Kanta Dey, Hiranmoy Garai, Vladimir Rakocevic

Abstract


In this article, we concentrate on common fixed points of a pair of generalized
non-expansive mappings, viz., generalized \alpha-Reich-Suzuki non-expansive mappings. In this sequel, we introduce the three-step Abbas-Nazir iterative algorithm for a pair of mappings. Then we obtain some results related to weak and strong convergence of sequences, satisfying this iterative algorithm, to obtain the common fixed points of two generalized \alpha-Reich-Suzuki
non-expansive mappings. Finally, we compare the convergence rate of our iteration technique to that of some well-known iteration techniques by some constructive numerical examples.


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