Viscosity Approximation Methods in Reflexive Banach Spaces with a Sequence of Contractions

Viscosity approximation methods with a sequence of contractions

The aim of this paper is to prove that, in an appropriate setting, every iterative sequence generated by the viscosity approximation method with a sequence of contractions is convergent whenever so is every iterative sequence generated by the Halpern type iterative method. Then, using our results, we show some convergence theorems for variational inequality problems, zero point problems, and fi...

Viscosity approximation methods for pseudocontractive mappings in Banach spaces

Strong convergence of implicit viscosity approximation methods for pseudocontractive mappings in Banach spaces Lu-Chuan Ceng a b , Adrian Petruşel c , Mu-Ming Wong d & Su-Jane Yu e a Department of Mathematics, Shanghai Normal University, Shanghai 200234, China b Scientific Computing Key Laboratory of Shanghai Universities, Shanghai, China c Department of Applied Mathematics, Babeş-Bolyai Univer...

A New Class of Banach Sequence Spaces

Q-reflexive Banach Spaces

Let E be a Banach space. There are several natural ways in which any polynomial P ∈ P(E) can be extended to P̃ ∈ P(E), in such a way that the extension mapping is continuous and linear (see, for example, [6]). Taking the double transpose of the extension mapping P → P̃ yields a linear, continuous mapping from P(E) into P(E). Further, since P(E) is a dual space, it follows that there is a natural ...

A non-reflexive Banach space with all contractions mean ergodic

We construct on any quasi-reflexive of order 1 separable real Banach space an equivalent norm, such that all contractions on the space and all contractions on its dual are mean ergodic, thus answering negatively a question of Louis Sucheston.