Retracted] On the Weak Relatively Nonexpansive Multivalued Mappings in Banach Spaces

Yongfu Su

doi:10.1155/2012/730619

Abstract

In recent years, the definition of relatively nonexpansive multivalued mapping and the definition of weak relatively nonexpansive multivalued mapping have been presented and studied by many authors. In this paper, we give some results about weak relatively nonexpansive multivalued mappings and give two examples which are weak relatively nonexpansive multivalued mappings but not relatively nonexpansive multivalued mappings in Banach space l2 and Lp[0,1](1 < p < +∞).

Highlights

Let E be a smooth Banach space and let C be a nonempty closed convex subset of E
This article has been retracted as it is found to contain a substantial amount of material, without referencing, from the paper “On the Weak Relatively Nonexpansive Mappings in Banach Spaces,” Yongchun Xu and Yongfu Su, Fixed Point Theory and Applications, Volume 2010, Article ID 189751, 7 pages. doi:10.1155/2010/189751 [1]
T denote by φ the function defined by φ x, y x 2 − 2 x, Jy y 2, for x, y ∈ E

Summary

Introduction

Let E be a smooth Banach space and let C be a nonempty closed convex subset of E. This article has been retracted as it is found to contain a substantial amount of material, without referencing, from the paper “On the Weak Relatively Nonexpansive Mappings in Banach Spaces,” Yongchun Xu and Yongfu Su, Fixed Point Theory and Applications, Volume 2010, Article ID 189751, 7 pages. “On the weak relatively nonexpansive multivalued mappings in Banach spaces,” Abstract and Applied Analysis, vol 2012, Article ID 730619, 7 pages, 2012.

Results

Conclusion