/ Fixed points of rotative nonexpansive mappings

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Thesis Type: Postgraduate

Institution Of The Thesis: Gazi University, Fen Bilimleri Enstitüsü, Turkey

Approval Date: 2021

Thesis Language: Turkish

Student: FETTAH VURAL

Supervisor: Cüneyt Çevik

Abstract:

In general,some assumptions about the geometry of space are added to the hypotheses to ensure the existence of fixed points for nonexpansive mappings.However,in 1981 K.Goebel and M.Koter obtained the conclusion that no assumptions of compactness ın a closed convex subset of a Banach space and special geometric conditions are not required in the Banach space. In this study, which is created based on this result,some results are given on the fixed points of the rotational nonexpansive mappings in Banach spaces. A fundamental proof is presented that the requirement of rotation in Banach spaces guarantees the existence of fixed points of nonexpansive mappings,even if there is no weak compactness or other special geometrical structure.This proof is based on constructing a sequence that converges to the fixed point of the mapping that is the subject of research.