Related papers: Refined Bohr inequality for bounded analytic funct…

In this note, we present a refinement of the well-known AM-GM inequality. We use this improved inequalty to establish corresponding inequalities on Hilbert space. We also give some refinements of the Kantorovich inequality.

An inequality refining the lower bound for a periodic (Breitenberger) uncertainty constant is proved for a wide class of functions. A connection of uncertainty constants for periodic and non-periodic functions is extended to this class. A…

The Bohr radius for a class $\mathcal{G}$ consisting of analytic functions $f(z)=\sum_{n=0}^{\infty}a_nz^n$ in unit disc $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$ is the largest $r^*$ such that every function $f$ in the class $\mathcal{G}$…

In the present paper, we define Morse-Bott functions on manifolds with boundary which are generalizations of Morse functions and show Morse-Bott inequalities for these manifolds.

We prove certain generalization of Hardy's inequality where the "boundary defining function" is replaced by a polynomial defining a singular algebraic variety. An application is given on the existence of a small time heat trace expansion…

The aim of this paper is to obtain the Schwarz-Pick type inequality for $\alpha$-harmonic functions $f$ in the unit disk and get estimates on the coefficients of $f$. As an application, a Landau type theorem of $\alpha$-harmonic functions…

We study arithmetic inequalities for multiplicative, sub(super)-multiplicative, sub(super)-homogeneous functions. Applications for the classical arithmetic functions are pointed out.

In this paper we study an algebraic and topological structure inside the following sets of special functions: Bloch functions defined on the open unit disk that are unbounded and analytic functions of bounded type defined a Banach algebra E…

We establish an operator extension of the following generalization of Bohr's inequality, due to M.P. Vasi\'c and D.J. Ke\v{c}ki\'{c}: $$|\sum_{i=1}^n z_i|^r \leq (\sum_{i=1}^n \alpha_i^{1/(1-r)})^{r-1}\sum_{i=1}^n \alpha_i|z_i|^r \quad…

We obtain weighted mixed inequalities for operators associated to a critical radius function. We consider Schr\"odinger Calder\'on-Zygmund operators of $(s,\delta)$ type, for $1<s\leq \infty$ and $0<\delta \leq 1$. We also give estimates of…

Construction of analytic functions, which determine bounded Toeplitz operators

Algebras of ultradifferentiable generalized functions are introduced. We give a microlocal analysis within these algebras related to the regularity type and the ultradifferentiable property.

In this paper we first extend a generalization of Ostrowski type inequality on time scales for functions whose derivatives are bounded and then unify corresponding continuous and discrete versions. We also point out some particular integral…

In this paper we further develop the theory of f-divergences for log-concave functions and their related inequalities. We establish Pinsker inequalities and new affine invariant entropy inequalities. We obtain new inequalities on functional…

In this paper, new integral inequalities of Hadamard type involving several differentiable \Phi-r-convex functions are given.

We compare possibilities of extension of bounded and unbounded Baire-one functions from subspaces of topological spaces.

Various miscellaneous functional inequalities are deduced for the so-called generalized inverse trigonometric and hyperbolic functions. For instance, functional inequalities for sums, difference and quotient of generalized inverse…

Some inequalities for functions of bounded variation that provide reverses for the inequality between the integral mean and the p-norm are established. Applications related to the celebrated Landau inequality between the norms of the…

In this article, we establish Hoeffding's inequality for bounded Lipschitz functions of a class of not necessarily irreducible Markov models. The result complements the existing literature on this topic where Hoeffding's inequality for…

The Bohr compactification is a well known construction for (topological) groups and semigroups. Recently, this notion has been investigated for arbitrary structures in \cite{har_kun:bohr_discrete} where the Bohr compactification is defined,…