Browsing by Author "Worku, Tibebu"
Now showing 1 - 1 of 1
Results Per Page
Sort Options
Item Fixed Point Approximation for Some Nonlinear Mappings in Banach and Modular Metric Spaces With Graph Structure(Addis Ababa University, 2018-05-24) Worku, Tibebu; Zegeye, Habtu (Professor); Goa, Mengistu (PhD)In this thesis, we study _xed point approximation methods for some nonlinear mappings in Banach and Modular metric spaces with graph structure. We review the contemporary literature in these directions. Then we establish some weak and strong convergence results for _- nite Noor iterative method to approximate common _xed point of a _nite family of G-nonexpansive self mappings in uniformly convex Banach spaces with graph structure. Moreover, we introduce a new class of self mappings in Banach spaces called G-asymptotically nonexpansive mappings, which is more general than the class of G- nonexpansive mappings and obtain some weak and strong convergence of the modi_ed Noor iterative method to a common _xed point of a _nite family of such class of mappings in the setting of uniformly convex Banach spaces with graph structure under some mild conditions. Furthermore, we de_ne a class of self mappings in modular metric spaces called G-monotone generalized quasi contraction mappings and establish necessary and su_cient conditions for the convergence of the Picard iteration process to _xed point of such class of mappings on the setting of modular metric spaces with graph structure. Our results improve and extend these results in the contemporary literature.