On Functions Satisfying Certain Differential Inequalities
نویسندگان
چکیده
منابع مشابه
On Spatial Adaptive Nonparametric Estimation of Functions Satisfying Differential Inequalities
The paper is devoted to developing spatial adaptive estimates of the signals satisfying linear differential inequalities with unknown differential operator of a given order. The classes of signals under consideration cover a wide variety of classes usual in the nonparametric regression problem; moreover, they contain the signals whose parameters of smoothness are not uniformly bounded, even loc...
متن کاملRegion of Variability for Certain Classes of Univalent Functions Satisfying Differential Inequalities
Abstract. For complex numbers α, β and M ∈ R with 0 < M ≤ |α| and |β| ≤ 1, let B(α, β,M) be the class of analytic and univalent functions f in the unit disk D with f(0) = 0, f (0) = α and f (0) = Mβ satisfying |zf (z)| ≤ M , z ∈ D. Let P(α,M) be the another class of analytic and univalent functions in D with f(0) = 0, f (0) = α satisfying Re (zf (z)) > −M , z ∈ D, where α ∈ C \ {0}, 0 < M ≤ 1/ ...
متن کاملRandom Functions Satisfying Certain Linear Relations
i1 "L-d! said my mother, what is all this story about?-A Cock and a Bull, said Yorick-" (Tristram Shandy) iii ACKNOWLEDGMENT At the outset, I would like to express my sincere and heartfelt thanks to Dr. Herbert Robbins for his constant advice and help, and for his patience with me. financial assistance and other facilities which were provided me during the progress of this work. summer of 1950;...
متن کاملOn a Bounded Subclass of Certain Analytic Functions Satisfying a Differential Inequality
In the present paper, using Jack’s lemma, the authors investigate the differential inequality ∣∣∣(1 − α) Ip(n,λ)f (z) zp + α Ip(n + 1, λ)f (z) Ip(n,λ)f (z) − 1 ∣∣∣ < μ, z ∈ E regarding multivalent functions defined by multiplier transfomation in the open unit disk E = {z : |z| < 1} . As consequences, sufficient conditions for univalence, starlikeness and strongly starlikeness of certain analyti...
متن کاملCertain Inequalities for Convex Functions
This is a review paper on some new inequalities for convex functions of one and several variables. The most important result presented for convex functions of one variable is the extension of Jensen’s inequality to affine combinations. The most interesting results presented for convex functions of several variables refer to inequalities concerning simplexes and its cones. Mathematics subject cl...
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: Proceedings of the American Mathematical Society
سال: 1962
ISSN: 0002-9939
DOI: 10.2307/2034478