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).
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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
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