Results 11 to 20 of about 18,466 (195)
On the inequality of different metrics for trigonometric polynomials
Қарағанды университетінің хабаршысы. Математика сериясы, 2019 The article is devoted to the research question of inequalities for different metrics with trigonometric polynomials. The structure of this exploring, its main components and types, as well as its classical approaches are presented in this article ...
G.A. Yessenbayeva +2 more
doaj +1 more source
BERNSTEIN-TYPE ESTIMATES FOR THE DERIVATIVES OF TRIGONOMETRIC POLYNOMIALS
Проблемы анализа, 2021 Using the method of amplitude and phase transformations, we obtain sharp inequalities for the derivatives of real-valued trigonometric polynomials. The inequalities are sharp, as there are the corresponding extremal polynomials, for which they become ...
V. I. Danchenko, D. G. Chkalova
doaj +1 more source
Geometric convexity of the generalized sine and the generalized hyperbolic sine [PDF]
, 2013 In the paper, the authors prove that the generalized sine function $\sin_{p,q}(x)$ and the generalized hyperbolic sine function $\sinh_{p,q}(x)$ are geometrically concave and geometrically convex, respectively.
Jiang, Wei-Dong, Qi, Feng
core +1 more source
Weighted inequalities for generalized polynomials with doubling weights
Journal of Inequalities and Applications, 2017 Many weighted polynomial inequalities, such as the Bernstein, Marcinkiewicz, Schur, Remez, Nikolskii inequalities, with doubling weights were proved by Mastroianni and Totik for the case 1 ≤ p < ∞ $1 \leq p < \infty$ , and by Tamás Erdélyi for 0 < p ≤ 1 $
Haewon Joung
doaj +1 more source
New Masjed Jamei–Type Inequalities for Inverse Trigonometric and Inverse Hyperbolic Functions
Mathematics, 2022 In this paper, we establish two new inequalities of the Masjed Jamei type for inverse trigonometric and inverse hyperbolic functions and apply them to obtain some refinement and extension of Mitrinović–Adamović and Lazarević inequalities.
Ling Zhu
doaj +1 more source
Extension of Oppenheim's Problem to Bessel Functions
Journal of Inequalities and Applications, 2008 Our aim is to extend some trigonometric inequalities to Bessel functions. Moreover, we deduce the hyperbolic analogue of these trigonometric inequalities, and we extend these inequalities to modified Bessel functions.
Ling Zhu, Árpád Baricz
doaj +1 more source
On the Generalization for Some Power-Exponential-Trigonometric Inequalities
Mathematics, 2019 In this paper, we introduce and prove several generalized algebraic-trigonometric inequalities by considering negative exponents in the inequalities.
Aníbal Coronel +3 more
doaj +1 more source
Axioms, 2022 In the paper, the authors establish a general inequality for the hyperbolic functions, extend the newly-established inequality to trigonometric functions, obtain some new inequalities involving the inverse sine and inverse hyperbolic sine functions, and ...
Wen-Hui Li, Qi-Xia Shen, Bai-Ni Guo
doaj +1 more source
On approximations by trigonometric polynomials of classes of functions defined by moduli of smoothness [PDF]
, 2017 In this paper, we give a characterization of Nikol'ski\u{\i}-Besov type classes of functions, given by integral representations of moduli of smoothness, in terms of series over the moduli of smoothness.
Berisha, Faton M. +3 more
core +3 more sources
Journal of Inequalities and Applications, 2016 An interplay between the sum of certain series related to harmonic numbers and certain finite trigonometric sums is investigated. This allows us to express the sum of these series in terms of the considered trigonometric sums, and permits us to find ...
Omran Kouba
doaj +1 more source