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Convergence and stability theorems for the Picard-Mann hybrid iterative scheme for a general class of contractive-like operators. (English) Zbl 1312.47078
Summary: In this paper we use the general class of contractive-like operators introduced by A. O. Bosede and B. E. Rhoades [J. Adv. Math. Stud. 3, No. 2, 23–25 (2010; Zbl 1210.47093)] to prove strong convergence and stability results for Picard-Mann hybrid iterative schemes considered in a real normed linear space. We establish the strong convergence and stability of the Picard iterative scheme as a corollary. Our results generalize and improve a multitude of results in the literature, including the recent results of C. E. Chidume [Fixed Point Theory Appl. 2014, Article ID 233 (2014; doi:10.1186/1687-1812-2014-233)].

47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
Full Text: DOI
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