منابع مشابه
A Note on the Hypergeometric Mean Value
in terms of power means and other related means have precipitated the search for similar bounds for the more general 2F1(α, β; γ; r). In an early paper, B. C. Carlson considered the approximation of the hypergeometric mean values ( 2F1(−a, b; b + c; r)) in terms of means of order t, given by Mt(s, r) := {(1 − s) + s(1 − r)t}1/t. In this note, a refinement of one such approximation is establishe...
متن کاملOn Polynomials Characterized by a Certain Mean Value Property
for xER, 0<t<ex (R denotes an «-dimensionaI region; x and yt are abbreviations for (xi, • • • , x„), (yn, • • • , ytn))We assume that the y<'s span £„ so that I^m^JV. We furthermore assume, without loss of generality, that yi, • • • , y« are linearly independent. Friedman and Littman [5] have recently shown that V consists of polynomials of degrees ^N(N—l)/2. This bound is actually attained whe...
متن کاملOn the mean value property of superharmonic and subharmonic functions
Recall that a function u is harmonic (superharmonic, subharmonic) in an open set U ⊂ Rn (n ≥ 1) if u ∈ C2(U) and Δu = 0 (Δu ≤ 0,Δu ≥ 0) on U . Denote by H(U) the space of harmonic functions in U and SH(U) (sH(U)) the subset of C2(U) consisting of superharmonic (subharmonic) functions in U . If A ⊂ Rn is Lebesgue measurable, L1(A) denotes the space of Lebesgue integrable functions on A and |A| d...
متن کاملA note on unique solvability of the absolute value equation
It is proved that applying sufficient regularity conditions to the interval matrix $[A-|B|,A + |B|]$, we can create a new unique solvability condition for the absolute value equation $Ax + B|x|=b$, since regularity of interval matrices implies unique solvability of their corresponding absolute value equation. This condition is formulated in terms of positive deniteness of a certain point matrix...
متن کاملInvariant Mean Value Property and Harmonic Functions
We give conditions on the functions σ and u on R such that if u is given by the convolution of σ and u, then u is harmonic on R.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1962
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1962-0151629-0