EXISTENCE THEOREMS FOR ATTRACTIVE POINTS OF
EXISTENCE THEOREMS FOR ATTRACTIVE POINTS OF
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Date
2016-03
Authors
LAWAL, Yusuf Haruna
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Abstract
In this dissertation, we define new attractive point using Bregman distance
and establish its theorems in a reflexive Banach space only. The first attractive
point theorem for generalized hybrid mappings was establish in a Hilbert
space. Similar result but for nonexpansive semigroup of mappings was later
established.These two results were later unified by establishing attractive point
and mean convergence theorems for semigroup of mappings without continuity
in Hilbert space which was then extended to Banach spaces. The result was
establish in the framework of smooth, strictly convex and reflexive Banach
spaces. This raised a question as whether or not, the result can be established
in a reflexive Banach space only. Our results improved the results announced
by Lin and Takahashi (2013) and Takahashi et al. (2014a).
Description
A DISSERTATION SUBMITTED TO THE SCHOOL OF
POSTGRADUATE STUDIES, AHMADU BELLO UNIVERSITY, ZARIA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR
THE AWARD OF MASTER DEGREE IN MATHEMATICS
DEPARTMENT OF MATHEMATICS
FACULTY OF SCIENCE
AHMADU BELLO UNIVERSITY, ZARIA
NIGERIA
Keywords
EXISTENCE THEOREMS, ATTRACTIVE POINTS, BREGMAN SEMITOPOLOGICAL, REFLEXIVE BANACH SPACE