Asymptotic Strong Convergence of Nonlinear Contraction Semigroups

On the Convergence of Difference Approximations to Nonlinear Contraction Semigroups in Hubert Spaces

Convergence properties of the difference schemes k k (S) h S a-u +i + Z ß-Au ., = 0, n > 0, ;=0 ' nT' /=0 ' " ' for evolution equations (E) ^1 + Au(t) = o, t > 0; u(0) = "0 e dJÄ) are studied. Here A is a nonlinear, maximally monotone operator in a real Hubert space. It is shown, in particular, that if the scheme (S) is consistent and stable for the test equation x' = Xx for \ S C K, where K is...

Strong Convergence Theorems of the CQ Method for Nonexpansive Semigroups

Throughout this paper, letH be a real Hilbert space with inner product 〈·,·〉 and ‖ · ‖. We use xn⇀ x to indicate that the sequence {xn} converges weakly to x. Similarly, xn → x will symbolize strong convergence. we denote by N and R+ the sets of nonnegative integers and nonnegative real numbers, respectively. let C be a closed convex subset of a Hilbert space H , and Let T : C → C be a nonexpan...

Strong convergence for total asymptotically pseudocontractive semigroups in Banach spaces

*Correspondence: [email protected] Department of Mathematics, Yibin University, Yibin, Sichuan 644007, China Abstract In this article, the demiclosedness principle for total asymptotically pseudocontractions in Banach spaces is established. The strong convergence to a common fixed point of total asymptotically pseudocontractive semigroups in Banach spaces is established based on the demiclosednes...

Strong Convergence Theorems for Lipschitzian Demicontraction Semigroups in Banach Spaces

The purpose of this paper is to introduce and study the strong convergence problem of the explicit iteration process for a Lipschitzian and demicontraction semigroups in arbitrary Banach spaces. The main results presented in this paper not only extend and improve some recent results announced by many authors, but also give an affirmative answer for the open questions raised by Suzuki 2003 and X...

Strong Convergence Theorems for Nonexpansive Semigroups without Bochner Integrals