Existence and Approximation of Fixed Points of Some New Classes of Nonlinear Mappings.
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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).
A Thesis Submitted to the School of Postgraduate Studies, University of Lagos.
Nonlinear Mappings , Fixed Points , Mapping , Research Subject Categories::MATHEMATICS
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.