Fixed Point Theorems for an Elastic Nonlinear Mapping in Banach Spaces

الملخص EN

Let E be a smooth Banach space with a norm · .

Let V ( x , y ) = x 2 + y 2 - 2 x , J y for any x , y ∈ E , where · , · stands for the duality pair and J is the normalized duality mapping.

We define a V -strongly nonexpansive mapping by V ( · , · ) .

This nonlinear mapping is nonexpansive in a Hilbert space.

However, we show that there exists a V -strongly nonexpansive mapping with fixed points which is not nonexpansive in a Banach space.

In this paper, we show a weak convergence theorem and strong convergence theorems for fixed points of this elastic nonlinear mapping and give the existence theorem.