ITERATIVE ALGORITHMS FOR SINGLE-VALUED AND MULTI-VALUED NONEXPANSIVE-TYPE MAPPINGS IN REAL LEBESGUE SPACES

📄 Project Abstract

Algorithms for single-valued and multi-valued nonexpansive-type mappings have continued to attract a lot of attentions because of their remarkable utility and wide applicability in modern mathematics and other reasearch areas,(most notably medical image reconstruction, game theory and market economy). The first part of this thesis presents contributions to some crucial new concepts and techniques for a systematic discussion of questions on algorithms for singlevalued and multi-valued mappings in real Hilbert spaces. Novel contributions are made on iterative algorithms for fixed points and solutions of the split equality fixed point problems of some single-valued pseudocontractive-type mappings in real Hilbert spaces. Interesting contributions are also made on iterative algorithms for fixed points of a general class of multivalued strictly pseudocontractive mappings in real Hilbert spaces using a new and novel approach and the thorems were gradually extended to a countable family of mul...