Weak and strong convergence theorems of a multistep iteration to a common fixed point of a family of nonself asymptotically nonexpansive mappings in banach spaces

Shrabani Banerjee; Binayak S. Choudhury

doi:10.4067/S0719-06462012000300010

DOI:

https://doi.org/10.4067/S0719-06462012000300010

Abstract

In this paper we have defined a multistep iterative scheme with errors involving a family of asymptotically nonexpansive nonself mappings in Banach spaces. A retraction has been used in the construction of the iteration. We prove here weak and strong convergences of the iteration to common fixed points of the family of asymptotically nonexpansive nonself mappings. We have used several concepts of Banach space geometry. Our results improve and extend some recent results.

Keywords

Modified multistep iterative process with errors , nonself asymptotically nonexpansive mapping , retraction , Opial‘s condition , uniformly convex Banach space , common fixed point , Kadec-klee property , Condition (B) , weak and strong convergence

Shrabani Banerjee Department of Mathematics, Bengal Engineering and Science University, Shibpur, Howrah-711103, India.
Binayak S. Choudhury Department of Mathematics, Bengal Engineering and Science University, Shibpur, Howrah-711103, India.

Pages: 143–166
Date Published: 2012-10-01
Vol. 14 No. 3 (2012): CUBO, A Mathematical Journal