Sandwich with periodicity

Hayashi, Izumi; Li, Lin; Matkowski, Janusz; Wróbel, Małgorzata

doi:10.1007/s00010-018-0605-0

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2020

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“…Applying in turn (5) and (i), we have F (P (x)) = M ϕ P (x) = M (ϕ x 1 ) = M (ϕ x ) = F (x), so the function F is P -periodic. It is easy to see that…”

Section: Introductionmentioning

confidence: 96%

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Sandwich results for periodicity and conjugacy

Matkowski

Wójcik

2020

Aequat. Math.

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Let P be a nonconstant selfmap of a set M. A sandwich-type theorem for generalized sub-P -periodic functions defined on M with values in a reflexive Banach space is proved. In particular, given functions f, g : M → R, we obtain necessary and sufficient conditions for the existence of a generalized P -periodic function F : M → R such that f ≤ F ≤ g. The formula for F is given and its Lipschitz constant is discussed. Moreover the solvability of the functional equation f • p = r • f with the help of a new sandwich method, is considered.Mathematics Subject Classification. Primary 39B82, 39B12; Secondary 39B62, 46B20.

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“…Applying in turn (5) and (i), we have F (P (x)) = M ϕ P (x) = M (ϕ x 1 ) = M (ϕ x ) = F (x), so the function F is P -periodic. It is easy to see that…”

Section: Introductionmentioning

confidence: 96%

“…In a recent paper Izumi et al [5] proved the following sandwich (separation) type result: functions f, g : R → R satisfy the inequalities…”

Section: Introductionmentioning

confidence: 99%