[PDF] Top 20 Strong Convergence Theorems for Nonexpansive Semigroups without Bochner Integrals

... Motivated by Suzuki’s result 1 and Nakajo-Takahashi’s results 2, He and Chen 3 recently proved a strong convergence theorem for nonexpansive semigroups in Hilbert spaces by hy- brid method in ... See full document

... show strong convergence theorems of the CQ method for nonexpansive semigroups in Hilbert spaces by hybrid method in the mathematical ... See full document

... -asymptotically nonexpansive semigroups; to modify the Halpern and Mann-type iteration algorithm [, ] for total quasi-φ-asymptotically nonexpansive semigroups; and to have the ... See full document

... Let C be a nonempty closed and convex subset of E. Throughout this paper, S will always denote a semigroup with an identity e. S is called left reversible if any two right ideals in S have nonvoid intersection, that is, ... See full document

... Using Theorem 3.1, Lemma 2.1, and Example 2.2, we have the following result. Corollary 3.4. Let E be a uniformly convex Banach space which admits a weakly sequentially continuous duality mapping J . Let S {T t : 0 ≤ t ... See full document

... Lemma 3.1. Let C be a nonempty weakly compact convex subset of a Banach space E and let ᏿ = { T(t) : t ∈ S } be a nonexpansive semigroup on C such that F( ᏿ ) = ∅ . Let X be a subspace of B(S) with 1 ∈ X such that ... See full document

... Recently many authors want to modify the Mann iteration method (1.3) so that strong convergence is guaranteed have recently been made. Nakajo and Takahashi [8] proposed the following modification of the ... See full document

... a strong convergence theorem for nonexpansive semigroups in Hilbert spaces by hybrid method in the mathematical ...a convergence theorem by the new iterative method introduced by ... See full document

... the convergence of iterative algo- rithms for quasi-φ-asymptotically nonexpansive (see [–]) and total quasi-φ-asymptoti- cally nonexpansive (see [–]) ...obtain strong convergence ... See full document

... establish strong convergence theorems for solving the fixed point problem of nonexpansive semigroups and strict pseudocontractions, and the zero-finding problem of maximal monotone ... See full document

... for each n ≥ 0 in a reflexive Banach space with a uniformly Gˆateaux differentiable norm such that each nonempty bounded closed and convex subset of E has the common fixed point property for nonexpansive mappings ... See full document

... reversible semigroups of asymp- totically nonexpansive ...and convergence of fixed points for left amenable semigroups of asymptotically nonexpansive type mappings in Banach ...amenable ... See full document

... and strong convergence theorems for a double Krasnoselskij- type iterative method to approximate coupled solutions of a bivariate nonexpansive operator T : K × K → K, where K is a nonempty ... See full document

... asymptotically nonexpansive mappings in CAT(0) ...the convergence behavior of the proposed algorithm and numerically compare the convergence of the proposed iteration scheme with the existing ... See full document

... sunny nonexpansive retraction is a sunny retraction, which is also ...Sunny nonexpansive retractions play an important role; see, ...sunny nonexpansive retraction if and only if there holds the ... See full document

... We give new hybrid variants of extragradient methods for finding a common solution of an equilibrium problem and a family of nonexpansive mappings. We present a scheme that combines the idea of an extragradient ... See full document

... Using δ-strongly accretive and λ-strictly pseudocontractive mapping, we introduce a general iterative method for finding a common fixed point of a semigroup of non-expansive mappings in a Hilbert space, with respect to a ... See full document

... relatively nonexpansive mappings in Banach spaces, and then prove weak and strong convergence theorems by using the notion of generalized ... See full document

... In order to prove our main results, we need the following well-known lemmas. Lemma 2.1 see 22, Demiclosed principle. Let C be a nonempty closed convex of a real Hilbert space H. Let T : C → C be a nonexpansive ... See full document

... Let H be a real Hilbert space, C a nonempty closed convex subset of H, and T : C → C a mapping. Recall that T is nonexpansive if Tx − T y ≤ x − y for all x, y ∈ C. A point x ∈ C is called a fixed point of T ... See full document