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On the Existence of Common Fixed Points for Semigroups of Nonlinear Mappings in Modular Function Spaces

Kozłowski W. M.

Commentationes Mathematicae

2011

Vol. 51, [Z] 1

81-98

Let C be a ρ-bounded, ρ -closed, convex subset of a modular function space Lρ. We investigate the existence of common fixed points for semigroups of nonlinear mappings Tt : C → C, i.e. a family such that T0(x) = x, Ts+t = Ts(Tt(x)), where each Tt is either ρ -contraction or ρ -nonexpansive. We also briefly discuss existence of such semigroups and touch upon applications to differential equations.