Statistical Functional Equations and p-Harmonious Functions
Keyword(s):
The Mean
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AbstractMotivated by the mean-value property characterizing harmonic functions and recently established asymptotic statistical formulas characterizing p-harmonic functions, we consider the Dirichlet problem for a functional equation involving a convex combination of the mean and median. We show that this problem has a continuous solution when it has both a subsolution and a supersolution. We demonstrate that solutions of these problems approximate p-harmonic functions and discuss connections with related results of Manfredi, Parviainen and Rossi.
1965 ◽
Vol 14
(1)
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pp. 109-111
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1962 ◽
Vol 102
(1)
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pp. 147-147
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Keyword(s):
1972 ◽
Vol 4
(3)
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pp. 311-312
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1995 ◽
Vol 123
(1)
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pp. 135-135
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1971 ◽
Vol 29
(2)
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pp. 341-341
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