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Fixed point theory in modular function spaces. (English) Zbl 0714.47040

From the text: “The purpose of this paper is to give an outline of a fixed point theory for nonexpansive mappings defined on some subsets of modular function spaces.”

The authors use constructive methods to prove fixed point theorems for contractive and nonexpansive mappings on modular spaces. They also study normal structure, uniform convexity and their related properties on modular function spaces, and prove a modular analogue of a fixed point theorem of W. A. Kirk [Amer. Math. Monthly 72, 1004-1006 (1965; Zbl 0141.324)].

Reviewer: S.L.Singh
MSC:
47H10Fixed point theorems for nonlinear operators on topological linear spaces
47H09Mappings defined by “shrinking” properties
46S30Constructive functional analysis
46E30Spaces of measurable functions
46A80Modular topological linear spaces