On an open question of Takahashi for nonspreading mappings in Banach spaces

Attractive Point and Mean Convergence Theorems for New Generalized Nonspreading Mappings in Banach Spaces

In this paper, we first introduce a class of nonlinear mappings called generic generalized nonspreading which contains the class of generalized nonspreading mappings in a Banach space and then prove an attractive point theorem for such mappings in a Banach space. Furthermore, we prove a mean convergence theorem of Baillon’s type and a weak convergence theorem of Mann’s type for such nonlinear m...

The Equilibrium Problem for Nonspreading-type Mappings in Hilbert Spaces

In this paper, an iterative algorithm for equilibrium problems and a class of strictly pseudononspreading mappings which is more general than the class of nonspreading mappings studied recently in Kurokawa and Takahashi [23] is proposed. Some weak convergence theorems are proved under suitable conditions in Hilbert space.

Applications of Bregman-Opial property to Bregman nonspreading mappings in Banach spaces

The Opial property of Hilbert spaces and some other special Banach spaces is a powerful tool in establishing fixed point theorems for nonexpansive, and more generally, nonspreading mappings. Unfortunately, not every Banach space shares the Opial property. However, every Banach space has an alike Bregman-Opial property for Bregman distances. In this paper, using Bregman distances, we introduce t...

On fixed points of fundamentally nonexpansive mappings in Banach spaces

We first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a Banach space and next show that if the Banach space is having the Opial condition, then the fixed points set of such a mapping with the convex range is nonempty. In particular, we establish that if the Banach space is uniformly convex, and the range of such a mapping is bounded, closed and con...

Convergence of an Implicit Iteration for Affine Mappings in Normed and Banach Spaces