A new hybrid algorithm and its numerical realization for two nonexpansive mappings

Abstract

In the paper, first, we introduce a new hybrid projection algorithm and present its strong convergence theorem. Next, we analyze different hybrid algorithms in computing and conclude that our proposed algorithm has an advantage. Finally, the numerical experiments validate the efficiency and advantages of the new algorithm. MSC: 90C47; 49J35

Hybrid iterative methods for two asymptotically nonexpansive semigroups in Hilbert spaces

“…As the second part of this work, we extend the results of Dang, et al [1] for T is an asymptotically nonexpansive semigroup, then we consider be two asymptotically nonexpansive semigroups on C such that F = F(T) ∩ F(S) = ∅ and let x 0 ∈ C. Let C 1 = C, x 1 = P C 1 x 0 and {x n } be a sequence generated by (3.4) with satisfies α n , β n , γ n ∈ [0, 1], 0 α n a < 1 and 0 < b β n c < 1 for all n ∈ N ∪ {0} and t n → ∞, s n → ∞. Then {x n } converges strongly to z 0 = P F x 0 .…”

“…Inspired and motivated by above, the purpose of this paper is to extend the results of Dong et al [1] for S and T are two asymptotically nonexpansive mappings then we consider…”

“…In 2015, Dong et al [1], introduced a hybrid algorithm. Let T and S be two nonexpansive mappings into itself such that F(T ) ∩ F(S) = ∅, the sequence generated as follows:…”