Fixed Point Approximation For Some Nonlinear Mappings In Banach And Modular Metric Spaces With Graph Structure

In this thesis, we study _xed point approximation methods for somernnonlinear mappings in Banach and Modular metric spaces with graphrnstructure. We review the contemporary literature in these directions.rnThen we establish some weak and strong convergence results for _-rnnite Noor iterative method to approximate common _xed point ofrna _nite family of G-nonexpansive self mappings in uniformly convexrnBanach spaces with graph structure. Moreover, we introduce arnnew class of self mappings in Banach spaces called G-asymptoticallyrnnonexpansive mappings, which is more general than the class of G-rnnonexpansive mappings and obtain some weak and strong convergencernof the modi_ed Noor iterative method to a common _xedrnpoint of a _nite family of such class of mappings in the setting ofrnuniformly convex Banach spaces with graph structure under somernmild conditions. Furthermore, we de_ne a class of self mappingsrnin modular metric spaces called G-monotone generalized quasi contractionrnmappings and establish necessary and su_cient conditionsrnfor the convergence of the Picard iteration process to _xed point ofrnsuch class of mappings on the setting of modular metric spaces withrngraph structure. Our results improve and extend these results in therncontemporary literature.

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