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The Alesker-Bernig-Schuster theorem asserts that each irreducible representation of the special orthogonal group appears with multiplicity at most one as a subrepresentation of the space of continuous translation-invariant valuations with…
Characterizations of all continuous, additive and $\mathrm{GL}(n)$-equivariant endomorphisms of the space of convex functions on a Euclidean space $\mathbb{R}^n$, of the subspace of convex functions that are finite in a neighborhood of the…
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…
This paper shows a simple construction of the continuous involutions of real intervals in terms of the continuous even functions. We also study the smooth involutions defined by symmetric equations. Finally, we review some applications, in…
First, we provide an exposition of a theorem due to Slodkowski regarding the largest "eigenvalue" of a convex function. In his work on the Dirichlet problem, Slodkowski introduces a generalized second-order derivative which for $C^2$…
In this paper, we derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in absolute value at certain power are h-convex and we point out the results for some special…
During the study of the topic of limit summability of functions (introduced by the author in 2001), we encountered some types of functions that are related to the mean value theorem. In this paper, we formally define mean value and…
We study the composition of two set-valued functions defined on locally convex topological linear spaces. We assume that these functions map into certain complete lattices of sets that have been used to establish a conjugation theory for…
Replacing operators with continuous operator-valued functions, we prove time-dependent versions of well-known results on compressions and diagonals of bounded operators. The setting of smooth functions is also addressed. Our results have no…
Complex-valued harmonic functions that are univalent and sense-preserving in the open unit disk are widely studied. A new methodology is employed to construct subclasses of univalent harmonic mappings from a given subfamily of univalent…
We introduce and investigate the concept of harmonical $h$-convexity for interval-valued functions. Under this new concept, we prove some new Hermite-Hadamard type inequalities for the interval Riemann integral.
The convolution properties are discussed for the complex-valued harmonic functions in the unit disk $\mathbb{D}$ constructed from the harmonic shearing of the analytic function $\phi(z):=\int_0^z…
The paper is devoted to the study, characterizations, and applications of variational convexity of functions, the property that has been recently introduced by Rockafellar together with its strong counterpart. First we show that these…
A subclass of complex-valued close-to-convex harmonic functions that are univalent and sense-preserving in the open unit disc is investigated. The coefficient estimates, growth results, area theorem, boundary behavior, convolution and…
In this paper we consider some properties of the initial logarithmic coefficients for inverse functions of functions univalent in the unit disc. The case of convex functions is treated separately. We give estimate, in some cases sharp, of…
We introduce notions of concavity for functions on balanced polyhedral spaces, and we show that concave functions on such spaces satisfy several strong continuity properties.
We generalize the notion of harmonic conjugate functions and Hilbert transforms to higher dimensional euclidean spaces, in the setting of differential forms and the Hodge-Dirac system. These conjugate functions are in general far from being…
In this paper, the Authors establish a new identity for differentiable functions. By the well-known H\"older and power mean inequality, they obtain some integral inequalities related to the convex functions and apply these inequalities to…
A function is exponentially concave if its exponential is concave. We consider exponentially concave functions on the unit simplex. In a previous paper we showed that gradient maps of exponentially concave functions provide solutions to a…
We study stochastic convolutions providing by fundamental solutions of a class of integrodifferential equations which interpolate the heat and the wave equations. We give sufficient condition for the existence of function--valued…