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 Generalized Flett's Mean Value Theorem
We present a new proof of generalized Flett’s mean value theorem due to Pawlikowska (from 1999) using only the original Flett’s mean value theorem. Also, a Trahan-type condition is established in general case.
متن کاملThe First Mean Value Theorem for Integrals
For simplicity, we use the following convention: X is a non empty set, S is a σ-field of subsets of X, M is a σ-measure on S, f , g are partial functions from X to R, and E is an element of S. One can prove the following three propositions: (1) If for every element x of X such that x ∈ dom f holds f(x) ≤ g(x), then g − f is non-negative. (2) For every set Y and for every partial function f from...
متن کاملThe Mean Value Theorem and Its Consequences
The point (M,f(M)) is called an absolute maximum of f if f(x) ≤ f(M) for every x in the domain of f . The point (m, f(m)) is called an absolute minimum of f if f(x) ≥ f(m) for every x in the domain of f . More than one absolute maximum or minimum may exist. For example, if f(x) = |x| for x ∈ [−1, 1] then f(x) ≤ 1 and there are absolute maxima at (1, 1) and at (−1, 1), but only one absolute mini...
متن کاملMEAN VALUE INTERPOLATION ON SPHERES
In this paper we consider multivariate Lagrange mean-value interpolation problem, where interpolation parameters are integrals over spheres. We have concentric spheres. Indeed, we consider the problem in three variables when it is not correct.
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: Annales Polonici Mathematici
سال: 1956
ISSN: 0066-2216,1730-6272
DOI: 10.4064/ap-3-1-29-31