Invariant Translative Mappings and a Functional Equation

H. Izumi; J. Matkowski

doi:10.1007/s10474-014-0399-z

Invariant Translative Mappings and a Functional Equation

H. Izumi, J. Matkowski

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

Let K, M, N: ℝ² → ℝ be translative functions. Then K is invariant with respect to the mapping (M,N): ℝ² → ℝ² if and only if the functions h = K(·, 0), f = M (·, 0), g = N(·, 0) satisfy the functional equation h(x) = h(f(x) - g(x)) + g(x), x ∈ ℝ. If K, M, N are means, then h(0) = f(0) = g(0) = 0. The formal power solutions and analytic solutions of this functional equation, satisfying these initial conditions, are considered.

Original language	English
Pages (from-to)	220-231
Number of pages	12
Journal	Acta Mathematica Hungarica
Volume	143
Issue number	1
DOIs	https://doi.org/10.1007/s10474-014-0399-z
Publication status	Published - 2014 Jun
Externally published	Yes

Keywords

39B22
39B32
analytic function
entire function
formal powers series
functional equation
invariant mean
mean
primary 30D05
secondary 26E60

ASJC Scopus subject areas

Mathematics(all)

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10.1007/s10474-014-0399-z

Cite this

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AU - Matkowski, J.

PY - 2014/6

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N2 - Let K, M, N: ℝ2 → ℝ be translative functions. Then K is invariant with respect to the mapping (M,N): ℝ2 → ℝ2 if and only if the functions h = K(·, 0), f = M (·, 0), g = N(·, 0) satisfy the functional equation h(x) = h(f(x) - g(x)) + g(x), x ∈ ℝ. If K, M, N are means, then h(0) = f(0) = g(0) = 0. The formal power solutions and analytic solutions of this functional equation, satisfying these initial conditions, are considered.

AB - Let K, M, N: ℝ2 → ℝ be translative functions. Then K is invariant with respect to the mapping (M,N): ℝ2 → ℝ2 if and only if the functions h = K(·, 0), f = M (·, 0), g = N(·, 0) satisfy the functional equation h(x) = h(f(x) - g(x)) + g(x), x ∈ ℝ. If K, M, N are means, then h(0) = f(0) = g(0) = 0. The formal power solutions and analytic solutions of this functional equation, satisfying these initial conditions, are considered.

KW - 39B22

KW - 39B32

KW - analytic function

KW - entire function

KW - formal powers series

KW - functional equation

KW - invariant mean

KW - mean

KW - primary 30D05

KW - secondary 26E60

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Invariant Translative Mappings and a Functional Equation

Abstract

Keywords

ASJC Scopus subject areas

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