相关论文: On Lazarevic and Cusa type inequalities for hyperb…

A Sobolev type embedding for radially symmetric functions on the unit ball $B$ in $\mathbb R^n$, $n\geq 3$, into the variable exponent Lebesgue space $L_{2^\star + |x|^\alpha} (B)$, $2^\star = 2n/(n-2)$, $\alpha>0$, is known due to J.M. do…

In this paper, we present some operator and eigenvalue inequalities involving operator monotone, doubly concave and doubly convex functions. These inequalities provide some variants of operator Acz\'{e}l inequality and its reverse via…

Motivated by the work of J. S\'andor [19], in this paper we establish a new Wilker type and Huygens type inequalities involving the trigonometric and hyperbolic functions. Moreover, in terms of hyperbolic functions, the upper and lower…

This work studies mixtures of probability measures on $\mathbb{R}^n$ and gives bounds on the Poincar\'e and the log-Sobolev constant of two-component mixtures provided that each component satisfies the functional inequality, and both…

We investigate several functional and geometric inequalities on the hyperbolic space $\mathbb{H}^N$, with a primary emphasis on logarithmic Sobolev inequalities, Poincar\'e inequalities, and Beckner-type inequalities, all studied within the…

Several negative results are presented concerning the solvability in Sobolev classes of the Cauchy problem for the inhomogeneous second-order uniformly parabolic equations without lower order terms in one space dimension. The main…

The purpose of this paper is to investigate the invariance of the arithmetic mean with respect to two weighted Bajraktarevi\'c means, i.e., to solve the functional equation $$…

In this paper, we investigate an inverse Cauchy problem for a stochastic hyperbolic equation. A Lipschitz type observability estimate is established using a pointwise Carleman identity. By minimizing the constructed Tikhonov-type…

We prove two-weight norm inequalities for parabolic fractional maximal functions using parabolic Muckenhoupt weights. In particular, we prove a two-weight, weak-type estimate and Fefferman-Stein type inequalities for the centered parabolic…

Motivated by open questions in the papers " Refinements and sharpenings of some double inequalities for bounding the gamma function" and "Complete monotonicity and monotonicity of two functions defined by two derivatives of a function…

The focus of this article is on entropy and Markov processes. We study the properties of functionals which are invariant with respect to monotonic transformations and analyze two invariant "additivity" properties: (i) existence of a…

In this paper, we investigate the monotonicity and inequalities for some functions involving the arc lemniscate and the hyperbolic arc lemniscate functions. In particular, sharp Shafer-Fink type inequalities for the arc lemniscate and the…

Log-Sobolev inequalities (LSIs) upper-bound entropy via a multiple of the Dirichlet form (i.e. norm of a gradient). In this paper we prove a family of entropy-energy inequalities for the binary hypercube which provide a non-linear…

In this article we establish new inequalities, both conditional and unconditional, for the restriction problem associated to the hyperbolic, or one-sheeted, hyperboloid in three dimensions, endowed with a Lorentz-invariant measure. These…

We introduce a class of analytic functions subordinate to the function $1+\sinh \left( z\right) $ and obtain various necessary and sufficient conditions for functions to be in the class. These conditions mainly comprise of the coefficient…

In this article, we have considered a time-dependent two-parameter singularly perturbed parabolic problem with discontinuous convection coefficient and source term. The problem contains the parameters $\epsilon$ and $\mu$ multiplying the…

We study one-dimensional linear hyperbolic systems with $L^{\infty}$-coefficients subjected to periodic conditions in time and reflection boundary conditions in space. We derive a priori estimates and give an operator representation of…

It is shown that generalized trigonometric functions and generalized hyperbolic functions can be transformed from each other. As an application of this transformation, a number of properties for one immediately lead to the corresponding…

This is a survey paper concerning some theorems on stochastic convex ordering and their applications to functional inequalities for convex functions. We present the recent results on those subjects

We provide a mild sufficient condition for a probability measure on the real line to satisfy a modified log-Sobolev inequality for convex functions, interpolating between the classical log-Sobolev inequality and a Bobkov-Ledoux type…