Existence and Approximation of Fixed Points of Some New Classes of Nonlinear Mappings.
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Date
2014
Authors
Okeke, G.A
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Abstract
Several researchers have obtained very useful xed point results for some classes of non-
linear mappings which include: contraction mappings, non-expansive maps and various
classes of pseudocontractive maps among others (see, for example Banach (1922), Cac-
cioppoli (1931), Sahu (2005), Xiang (2009), Zhou (2009), Qin et al. (2010), Chidume
(2008), Agarwal et al. (2009), Olaleru (2006), Olaleru (2007)). In this study, the fol-
lowing new classes of nonlinear maps which are extensions of similar maps known in
literature are introduced: the class of asymptotically demicontractive mappings in the
intermediate sense, the class of asymptotically hemicontractive mappings in the inter-
mediate sense, the class of asymptotically generalized -pseudocontractive mappings
in the intermediate sense, the class of asymptotically generalized -hemicontractive
mappings in the intermediate sense, the class of asymptotically quasi-nonexpansive
nonself-mappings in the intermediate sense, the class of -nearly contraction mappings, the class of -nearly nonexpansive mappings, the class of -nearly asymptotically non-
expansive mappings, the class of -nearly uniformly k-Lipschitzian mappings and the
class of -nearly uniformly k-contraction mappings. Furthermore, the existence results
are proved for the xed points of these maps and the approximation of xed points of
all these maps are established, through convergence of some iterative schemes, when-
ever their xed points exist. Thus, our results improve, generalise and extend many
celebrated results in this area of research, including the famous Banach Contraction
Mapping Principle, Banach (1922).
Description
A Thesis Submitted to the School of Postgraduate Studies, University of Lagos.
Keywords
Nonlinear Mappings , Fixed Points , Mapping , Research Subject Categories::MATHEMATICS
Citation
Okeke, G.A (2014), Existence and Approximation of Fixed Points of Some New Classes of Nonlinear Mappings. A Thesis Submitted to University of Lagos School of Postgraduate Studies Phd Thesis and Dissertation, 136pp.