ISSN: 1304-7191 | E-ISSN: 1304-7205
A three steps iterative process for approximating the fixed points of multivalued generalized 𝜶-nonexpansive mappings in uniformly convex hyperbolic spaces
1Department of Mathematics , Erzurum Technical University, ERZURUM;
2School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, SOUTH AFRICA
Sigma J Eng Nat Sci 2020; 38(2): 1031-1050
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In this paper, we prove some fixed point properties and demiclosedness principle for multivalued generalized 𝛼-nonexpansive mappings in uniformly convex hyperbolic spaces. We also proposed a three steps iterative scheme for approximating the common fixed points of generalized 𝛼-nonexpansive mapping and prove some strong and Δ-convergence theorems for such operator in the setting of uniformly convex hyperbolic space. We provide a numerical example to show that the three steps scheme proposed in this paper performs better than the modified SP-iterative scheme. The results obtained in this paper extend and generalized the corresponding results in uniformly convex Banach spaces, CAT(0) space and many other results in this direction.
Keywords: Generalized nonexpansive, three steps iteration, multivalued mappings, hyperbolic spaces, fixed point theorems.