ITERATIVE APPROXIMATION OF COMMON FIXEDPOINTS FOR FAMILIE S OF SOME CLASSES OF NONLINEAR OPERATORS
ITERATIVE APPROXIMATION OF COMMON FIXEDPOINTS FOR FAMILIE S OF SOME CLASSES OF NONLINEAR OPERATORS
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Date
2016-03
Authors
UGWUNNADI, GODWIN CHIDI
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Abstract
In this research, some iterative methods used to approximate common fixed
pointsofsomenonlinearoperatorsinBanachspaceareintroducedandstudied.
In particular, modified iterative schemes for fixed point of family of asymptotically
nonexpansive mappings are introduced and studied. Therefrom, strong
convergence theorem for members of this family of mapping which is also
in some cases solution of some variational inequality problems is established.
Furthermore, a hybrid projection method is studied and strong convergence
theorem for a family of generalized asymptotically quasi- φ-strict pseudocontractive
mappings in a real reflexive, strictly convex and smooth Banach
space with Kadec-Klee property and whose dual also possesses Kadec Klee
propertyisproved. Alsoestablishedthisthesisisastrongconvergencetheorem
for infinite family of uniformlyL−Lipschitzian total quasi-φ-asymptotically
nonexpansive multi-valued mappings. This is done using a generalized fprojection
operator in a real uniformly convex and uniformly smooth Banach
space using a new iterative scheme. Thus a new iterative scheme by set of fixed points of a finite family of closed quasi-Bregman strictly pseudocontractive
mappings is proved.
hybrid method is introduced and its convergence to a common element in the
Description
A THESIS SUBMITTED TO THE SCHOOL OF POST GRADUATE STUDIES
AHMADU BELLO UNIVERSITY, ZARIA
IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE AWARD
OF DOCTOR OF PHILOSOPHY (Ph.D) DEGREE IN MATHEMATICS
DEPARTMENT OF MATHEMATICS
AHMADU BELLO UNIVERSITY, ZARIA,
NIGERIA
Keywords
ITERATIVEAPPROXIMATION,, COMMON FIXED POINTS,, FAMILIES,, CLASSES,, NONLINEAR OPERATORS,