Weak Convergence of Mann Iteration for a Hybrid Pair of Mappings in a Banach Space

Authors: Alemayehu Geremew Negash

Abstract:

We prove the weak convergence of Mann iteration for a hybrid pair of maps to a common fixed point of a selfmap f and a multivalued f nonexpansive mapping T in Banach space E.  

Keywords: Common fixed point, Mann iteration, Multivalued mapping, weak convergence.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1337023

References:

[1] G. V. R. Babu, G.N. Alemayehu, Strong Convergence of Mann Iteration for a Hybrid Pair of Mappings in a Banach Space, Mathematica Aeterna, 3 (2013)(7), 501–507.
[2] S. B. Nadler Jr., Multivalued contraction mappings, Pacific J. Math. 30 (1969) 475–487.
[3] Z. Opial, Weak Convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967) 591–597.
[4] H. F. Senter, W. G. Dotson, Approximating fixed points of nonexpansive mappings, Proc. Amer. Math. Soc. 44 (1974) 375–380.
[5] Y. Song, H. Wang, Convergence of iterative algorithms for multivalued mappings in Banach spaces, Nonlinear Analysis 70 (2009) 1547–1556.
[6] T. Suzuki, Strong convergence theorems for infinite families of nonexpansive mappings in general Banach spaces, Fixed Point Theory Appl. 2005 (1) (2005) 103–123, doi:10.1155 \ FPTA.2005.103.