Iterative Approximation Of Fixed Points Ofp-nonexpansive Multivalued Mappings In Modular Function

The existence and iterative approximation offxed points of single-rnvalued and multi-valued mappings in modular function spaces havernbeen studied by many well known Mathematicians. Due to its appli-rncability in real world problems such as Market Economy and Gamerntheory and other applied mathematics such as Diferential equationsrnand Optimization theory, the study of fxed point theory has contin-rnued in modular function spaces.rnIn this thesis, we constructed a Mann-type iterative scheme andrnproved the fconvergence of the scheme to common _xed point ofrnnite family of -nonexpansive multi-valued mappings. We alsornproved the convergence of Ishikawa-type iterative scheme to com-rnmon fxed point of two nonexpansive multivalued mappings un-rnder certain mild conditions on the mappings and the set on whichrnthe mappings are defned. Moreover, we introduced a new class ofrnmulti-valued mappings in modular function spaces called quasirnnonexpansive mapping and proved the fconvergence of Mann-typerniterative scheme to common fxed point of fnite family of this classrnof mappings in modular function spaces.

Get Full Work

Report copyright infringement or plagiarism