Related papers: Sharp Cusa type inequalities for trigonometric fun…
We prove sharp weak type weighted estimates for a class of sparse operators that includes majorants of standard $\alpha$-fractional singular integrals, fractional integral operators, Marcinkiewicz integral operators, and square functions.…
Sharp constants for an inequality of Poincar\'e type is studied. The problem is solved by using optimal control theory.
In this paper we use basic properties of strongly convex functions to obtain new inequalities including Jensen's type and Jensen-Mercer type inequalities. Applications for special means are pointed out as well. We also give a Jensen's…
Let $L$ be a linear operator in $L^2(\mathbb{R}^n)$ which generates a semigroup $e^{-tL}$ whose kernels $p_t(x,y)$ satisfy the Gaussian upper bound. In this paper, we investigate several kinds of weighted norm inequalities for the conical…
In this paper, new sharp bounds for circular functions are proved. We provide some improvements of previous results by using infinite products, power series expansions and a generalisation of the so-called Bernoulli inequality. New proofs,…
Some q-analysis variants of Hardy type inequalities of the form \int_0^b (x^{\alpha-1} \int_0^x t^{-\alpha} f(t) d_qt)^p d_qx \leq C \int_0^b f^p(t) d_qt with sharp constant C are proved and discussed. A similar result with the…
In this paper, we obtain some Simpson type inequalities for functions whose second derivatives absolute value or q-th power of them are Q-class functions. Also we give applications to numerical integration.
We prove various new trigonometric and hyperbolic inequalities of Jordan, Wilker, Huygens or Cusa-Huygens type. Connections with bivariate means, as well as monotonicity and convexity properties are pointed out, too.
We find uniform with respect to parameter $p \ (1\leq p\leq\infty)$ upper estimations of best approximations by trigonometric polynomials of classes $C^{\psi}_{\beta,p}$ of periodic functions generated by sequences $\psi(k)$, that decrease…
In this paper, we obtain some new estimations of Iyengar-type inequality in which quasi-convex(quasi-concave) functions are involved. These estimations are improvements of some recently obtained estimations. Some error estimations for the…
This paper extends the self-improvement result of Keith and Zhong in [16] to the two-measure case. Our main result shows that a two-measure $(p,p)$-Poincar\'e inequality for $1<p<\infty$ improves to a $(p,p-\varepsilon)$-Poincar\'e…
We revisit and prove some convexity inequalities for trace functions conjectured in the earlier part I. The main functional considered is \Phi_{p,q}(A_1,A_2,...,A_m) = (trace((\sum_{j=1}^m A_j^p)^{q/p}))^{1/q} for m positive definite…
Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the…
In this paper, a new lemma is proved and inequalities of Simpson type are established for co-ordinated convex functions and bounded functions.
We consider convexity and monotonicity properties for some functions related to the $q$-gamma function. As applications, we give a variety of inequalities for the $q$-gamma function, the $q$-digamma function $\psi_q(x)$, and the $q$-series.…
We introduce new generalizations of the Gamma and the Beta functions. Their properties are investigated and known results are obtained as particular cases.
The aim of this paper is to prove new trigonometric and hyperbolic inequalities, which constitute among others refinements or analogs of famous Cusa-Huygens, Wu-Srivastava, and related inequalities. In most cases, the obtained results are…
In this paper, we sharpen and generalize Carlson's double inequality for the arc cosine function.
Motivated by some results due to Burbea we prove that if a certain sharp integral inequality holds for functions in the unit polydisc which belong to concrete Hardy spaces, then it also holds, in an appropriate form, in the case of…
Gosper introduced the functions $\sin_q z$ and $\cos_q z$ as $q$-analogues for the trigonometric functions $\sin z$ and $\cos z$ respectively. He stated but did not prove a variety of identities involving these two $q$-trigonometric…