Strong convergence for the modified Mann’s iteration of λ-strict pseudocontraction

Abstract

In this paper, for an λ-strict pseudocontraction T , we prove strong convergence of the modified Mann's iteration defined by 1

Strong and weak convergence of Mann iteration of monotone α-nonexpansive mappings in uniformly convex Banach spaces

“…Subsequently, many mathematical workers paid their attentions to the strong and weak convergence of such an iteration and its modified version for many different mappings in the past several decades. For more details, see Opial [19] for nonexpansive mappings, Suzuki [27] for nonexpansive semigroups, Song [22] and Jung [10] for nonexpansive mappings sequence, Liu [15] for strongly accretive mappings, George and Nse [6] for hemi-contractive mappings, Kim et al [11] for strictly hemi-contractive mappings, Okeke and Kim [18] for random Picard-Mann hybrid iterations, Berinde [3] and George and Shaini [7] for Zamfirescu operators, Gu and Lu [9] for nonlinear variational inclusions, and Zhou et al [33], Song and Wang [25], Zhang and Su [31], and Zhou [32] for strict pseudo-contractions and the reference therein. For a Banach space E endowed with the partial order " ", Bachar and Khamsi [2] introduced the concept of a monotone nonexpansive mapping.…”

Pazy's fixed point theorem with respect to the partial order in uniformly convex Banach spaces

“…There had be many convergence conclusions of such an iteration in the past several decades. For more details, see Liu [15], Narghirad et al [17], Suzuki [26], Song [24], Opial [19], Kim et al [12], Okeke and Kim [18], Berinde [3], George and Shaini [6], Gu and Lu [10], Zhou et al [32], Song and Wang [23], zhang and Su [31], Zhou [33] and the reference therein. Very recently, Song et.…”