A STUDY OF COMMON FIXED POINT APPROXIMATIONS FOR FINITE FAMILIES OF TOTAL ASYMPTOTICALLY NONEXPANSIVE SEMIGROUP IN HYPERBOLIC SPACES
A STUDY OF COMMON FIXED POINT APPROXIMATIONS FOR FINITE FAMILIES OF TOTAL ASYMPTOTICALLY NONEXPANSIVE SEMIGROUP IN HYPERBOLIC SPACES
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Date
2017-10
Authors
GARBA, ISMA’IL, DANBABA
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Abstract
In this dissertation, a multi-step iterative scheme was used to establish the
strong and convergence theorems for finite families of uniformly asymptotic
regular, total asymptotically nonexpansive semigroup in a uniformly
convex hyperbolic space. We also used a different method of proof, to establish
the polar and convergence theorems for finite families of uniformly
asymptotic regular, uniformly L-Lipschitzian and total asymptotically nonexpansive
semigroup in a complete CAT(0) space. We then studied the modified
Mann iteration scheme for approximating common fixed point of a uniformly
asymptotic regular family of total asymptotically nonexpansive semigroup in
a complete CAT(0) space. We proved that the sequences generated by the
iterative schemes converges to a common fixed point of a finite family of uniformly
asymptotic regular and total asymptotically nonexpansive semigroup
in hyperbolic spaces.
Description
A DISSERTATION SUBMITTED TO THE SCHOOL OF
POST-GRADUATE STUDIES, AHMADU BELLO UNIVERSITY, ZARIA
IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR
THE AWARD OF MASTER DEGREE IN MATHEMATICS
DEPARTMENT OF MATHEMATICS
FACULTY OF PHYSICAL SCIENCES
AHMADU BELLO UNIVERSITY, ZARIA
NIGERIA
Keywords
STUDY,, COMMON FIXED POINT,, APPROXIMATIONS,, FINITE FAMILIES,, TOTAL ASYMPTOTICALLY NONEXPANSIVE SEMIGROUP,, HYPERBOLIC SPACES