Fixed Point Approximation for Some Nonlinear Mappings in Banach and Modular Metric Spaces With Graph Structure
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Date
2018-05-24
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Addis Ababa University
Abstract
In this thesis, we study _xed point approximation methods for some
nonlinear mappings in Banach and Modular metric spaces with graph
structure. We review the contemporary literature in these directions.
Then we establish some weak and strong convergence results for _-
nite Noor iterative method to approximate common _xed point of
a _nite family of G-nonexpansive self mappings in uniformly convex
Banach spaces with graph structure. Moreover, we introduce a
new class of self mappings in Banach spaces called G-asymptotically
nonexpansive mappings, which is more general than the class of G-
nonexpansive mappings and obtain some weak and strong convergence
of the modi_ed Noor iterative method to a common _xed
point of a _nite family of such class of mappings in the setting of
uniformly convex Banach spaces with graph structure under some
mild conditions. Furthermore, we de_ne a class of self mappings
in modular metric spaces called G-monotone generalized quasi contraction
mappings and establish necessary and su_cient conditions
for the convergence of the Picard iteration process to _xed point of
such class of mappings on the setting of modular metric spaces with
graph structure. Our results improve and extend these results in the
contemporary literature.
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Keywords
Fixed Point, Approximation, Nonlinear Mappings, Modular Metric, Spaces With Graph Structure