The viscosity iterative algorithms for the implicit midpoint rule of nonexpansive mappings in uniformly smooth Banach spaces

Luo, Ping; Cai, Gang; Shehu, Yekini

doi:10.1186/s13660-017-1426-8

Cited by 17 publications

(24 citation statements)

References 15 publications

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“…( ) This paper obtains strong convergence results. Results promote the work of Ke et al [19], Luo et al [20], and Yan et al [23] from Hilbert spaces to a general Banach spaces and their iterative algorithms and relevant conclusions. In the end, this paper gives six numerical examples to support the main results.…”

Section: Discussionsupporting

confidence: 73%

“…If we let s n = 1 2 and α n = 0, we can also get the main results of [20]. The results of Theorem 2 generalize the relevant results of [23].…”

Section: Corollary 3 ([19])supporting

confidence: 54%

“…Motivated and inspired by Xu et al [18], Ke et al [19], and Luo et al [20], this paper proposes the generalized viscosity implicit rules for nonexpansive mappings in Banach space and proves strong convergence results. Next, this paper applies the results to a general system of variational inequality problems in Banach space and fixed-point problems of strict pseudocontractive mappings.…”

Section: Introductionmentioning

confidence: 88%

“…If we let s n = 1 2 , we can get the main results of [20]. [20]) Let C be a closed convex subset of a uniformly smooth Banach space E. Let T : C → C be a nonexpansive mapping with F(T) ∅, and f : C → C a contraction with coefficient α ∈ [0, 1). Let {x n } be a sequence generated by the following viscosity implicit midpoint rule:…”

Section: Corollary 1 ([19]mentioning

confidence: 99%

“…In 2017, Luo et al [20] generalized the conclusions of Xu et al [18] from Hilbert space to uniformly smooth Banach space:…”

Section: Introductionmentioning

confidence: 99%

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