Iterative Approximation of Fixed Points ofp-nonexpansive Multivalued Mappings in Modular Function
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Date
2017-04-20
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Addis Ababa University
Abstract
The existence and iterative approximation offxed points of single-
valued and multi-valued mappings in modular function spaces have
been studied by many well known Mathematicians. Due to its appli-
cability in real world problems such as Market Economy and Game
theory and other applied mathematics such as Diferential equations
and Optimization theory, the study of fxed point theory has contin-
ued in modular function spaces.
In this thesis, we constructed a Mann-type iterative scheme and
proved the fconvergence of the scheme to common _xed point of
nite family of -nonexpansive multi-valued mappings. We also
proved the convergence of Ishikawa-type iterative scheme to com-
mon fxed point of two nonexpansive multivalued mappings un-
der certain mild conditions on the mappings and the set on which
the mappings are defned. Moreover, we introduced a new class of
multi-valued mappings in modular function spaces called quasi
nonexpansive mapping and proved the fconvergence of Mann-type
iterative scheme to common fxed point of fnite family of this class
of mappings in modular function spaces.
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Iterative Approximation, of Fixed Points of p-nonexpansive