Related papers: Bernstein- and Markov-type inequalities for ration…
This paper studies the singularities of Cullen-regular functions of one quaternionic variable. The quaternionic Laurent series prove to be Cullen-regular. The singularities of Cullen-regular functions are thus classified as removable,…
We establish sharp trace- and Korn-type inequalities that involve vectorial differential operators, the focus being on situations where global singular integral estimates are not available. Starting from a novel approach to sharp Besov…
We present an elementary proof of a conjecture by I. Ra\c{s}a which is an inequality involving Bernstein basis polynomials and convex functions. It was affirmed in positive very recently by the use of stochastic convex orderings. Moreover,…
We consider the stochastic integrals of multivariate point processes and study their concentration phenomena. In particular, we obtain a Bernstein type of concentration inequality through Dol\'eans-Dade exponential formula and a uniform…
In this article we investigate the properties of Bernstein processes generated by infinite hierarchies of forward-backward systems of decoupled linear deterministic parabolic partial differential equations defined in Rd, where d is…
We consider functional equations (Cauchy's, Abel's and some other functional equations) and show that to find general solution of these equations is equivalent to establish that a space-transformation of a Brownian Motion by suitable…
In previous works, the second author defined directional Robin constants associated to a compact, nonpolar subset $K$ of an algebraic curve $A$ in $\mathbb{C}^N$ and related these to a natural class of Chebyshev constants for $K$. We define…
In this paper, we obtain some Simpson type inequalities for functions whose derivatives in absolute value are $\varphi$-convex.
For convex univalent functions we give instances where the sharp bound for various coefficient functionals are identical to those for the corresponding bound for the inverse function. We give instances where the sharp bounds differ and also…
A fundamental problem in numerical analysis and approximation theory is approximating smooth functions by polynomials. A much harder version under recent consideration is to enforce bounds constraints on the approximating polynomial. In…
A version of Markov's estimate for the derivative of a polynomial is proved with the interval [-1,1] replaced by an arbitrary continuum in the complex plane.
The combination of functional limit theorems with the pathwise analysis of deterministic and stochastic differential equations has proven to be a powerful approach to the analysis of fast-slow systems. In a multivariate setting, this…
Using the renewal approach we prove exponential inequalities for additive functionals and empirical processes of ergodic Markov chains, thus obtaining counterparts of inequalities for sums of independent random variables. The inequalities…
For a cubic rational function with coefficients in a non-archimedean field $K$ whose residue characteristic is $0$ or greater than $3$, there are $2$ possibilities for the shape of its Berkovich ramification locus, considered as an…
We present an elementary proof of a conjecture proposed by I. Rasa in 2017 which is an inequality involving Bernstein basis polynomials and convex functions. It was affirmed in positive by A. Komisarski and T. Rajba very recently by the use…
The Brunn-Minkowski and Pr\'{e}kopa-Leindler inequalities admit a variety of proofs that are inspired by convexity. Nevertheless, the former holds for compact sets and the latter for integrable functions so it seems that convexity has no…
A number of sharp inequalities are proved for the space ${\mathcal P}\left(^2D\left(\frac{\pi}{4}\right)\right)$ of 2-homogeneous polynomials on ${\mathbb R}^2$ endowed with the supremum norm on the sector…
New differential-recurrence properties of dual Bernstein polynomials are given which follow from relations between dual Bernstein and orthogonal Hahn and Jacobi polynomials. Using these results, a fourth-order differential equation…
In this article, we determine the Rogosinski radii for certain subclasses of close-to-convex functions defined on open unit disc $\mathbb{D}= \{z \in \mathbb{C}: |z| < 1\}$. Furthermore, we establish improved versions of the classical Bohr…
Four Jacobi settings are considered in the context of Hardy's inequality: the trigonometric polynomials and functions, and the corresponding symmetrized systems. In the polynomial cases sharp Hardy's inequality is proved for the type…