Homogeneous means generated by a mean-value theorem
نویسندگان
چکیده
منابع مشابه
Power Means Generated by Some Mean-value Theorems
According to a new mean-value theorem, under the conditions of a function f ensuring the existence and uniqueness of Lagrange’s mean, there exists a unique mean M such that f(x)− f(y) x− y = M ( f ′(x), f ′(y) ) . The main result says that, in this equality, M is a power mean if, and only if, M is either geometric, arithmetic or harmonic. A Cauchy relevant type result is also presented. Introdu...
متن کاملVinogradov’s Mean Value Theorem via Efficient Congruencing
We obtain estimates for Vinogradov’s integral which for the first time approach those conjectured to be the best possible. Several applications of these new bounds are provided. In particular, the conjectured asymptotic formula in Waring’s problem holds for sums of s kth powers of natural numbers whenever s > 2k + 2k − 3.
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 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 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: Journal of Mathematical Inequalities
سال: 2010
ISSN: 1846-579X
DOI: 10.7153/jmi-04-43