


Paper Title:
Iterative Approximation of Zeros of Accretive Type Maps, with Applications
Author(s):
Charles Ejike Chidume, Chinedu Godwin Ezea, and Emmanuel Ezzaka Otubo
African University of Science and
Technology, Abuja,
Nigeria.
Email: cchidume@aust.edu.ng
Email: chinedu.ezea@gmail.com
Email: mrzzaka@yahoo.com
Department of Mathematics,
Nnamdi Azikiwe University,
Awka,
Nigeria
Email: chinedu.ezea@gmail.com
Ebonyi State University,
Abakaliki,
Nigeria
Email: mrzzaka@yahoo.com
Abstract:
Let E be a reflexive real Banach space with uniformly Gâteaux differentiable norm. Let J:E→ E^{*} be the normalized duality map on E and let A:E^{*}→ E be a map such that AJ is an accretive and uniformly continuous map. Suppose that (AJ)^{1}(0) in nonempty. Then, an iterative sequence is constructed and proved to converge strongly to some u^{*} in (AJ)^{1}(0). Application of our theorem in the case that E is a real Hilbert space yields a sequence which converges strongly to a zero of A. Finally, nontrivial examples of maps A for which AJ is accretive are presented..
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