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Differentiable conjugacies link dynamical systems that share properties such as the stability multipliers of corresponding orbits. It provides a stronger classification than topological conjugacy, which only requires qualitative similarity.…
A normalized analytic function f is shown to be univalent in the open unit disk D if its second coefficient is sufficiently small and relates to its Schwarzian derivative through a certain inequality. New criteria for analytic functions to…
For a more general notion of Cartan connection we define characteristic classes, we investigate their relation to usual characteristic classes.
In this paper, incremental exponential asymptotic stability of a class of switched Carath\'{e}odory nonlinear systems is studied based on the novel concept of measure of switched matrices via multiple norms and the transaction coefficients…
We develop a theory of "special functions" associated to a certain fourth order differential operator $\mathcal{D}_{\mu,\nu}$ on $\mathbb{R}$ depending on two parameters $\mu,\nu$. For integers $\mu,\nu\geq-1$ with $\mu+\nu\in2\mathbb{N}_0$…
In this paper, an upper semismooth function is defined to be a lower semicontinuous function whose radial subderivative satisfies a mild directional upper semicontinuity property. Examples of upper semismooth functions are the proper lower…
For given non-negative real numbers $\alpha_k$ with $ \sum_{k=1}^{m}\alpha_k =1$ and normalized analytic functions $f_k$, $k=1,\dotsc,m$, defined on the open unit disc, let the functions $F$ and $F_n$ be defined by $…
Starting from a recent result expressing the Lerch zeta function as a fractional derivative, we consider further fractional derivatives of the Lerch zeta function with respect to different variables. We establish a partial differential…
Functional equations satisfied by additive functions have a special interest not only in the theory of functional equations, but also in the theory of (commutative) algebra because the fundamental notions such as derivations and…
The purpose of the present paper is to find the necessary and sufficient conditions for the subclasses of analytic functions associated with Pascal distribution to be in subclasses of spiral-like univalent functions and inclusion relations…
In this paper a higher order non-linear differential equation is given and it becomes a higher order Airy equation (in our terminology) under the Cole-Hopf transformation. For the even case a solution is explicitly constructed, which is a…
A uniform gradient for functions u which satisfy a system of N second-order partial differential inequalities is given in this paper. Some structure conditions are given for the coefficients of the matrices of second-order terms and of…
We will provide sufficient conditions for the shifted hypergeometric function $z_2F_1(a,b;c;z)$ to be a member of a specific subclass of starlike functions in terms of the complex parameters $a,b$ and $c.$ For example, we study starlikeness…
In this paper we determine a number of meaningful compositions of higher order of a set of functions, which is considered in Malesevic (1998), in implicit and explicit form. Results which are obtained are applied to the vector analysis in…
We investigate some properties of balayage of charges and measures for subclasses of subharmonic functions and their relationship to the geometry of domain or open set in finite-dimensional Euclidean space where this balayage is considered.
We compute the cardinality $\mathfrak n_{\dim}(\mathcal M)$ of the sets of dimension functions on the ordered structures $\mathcal M$. The inequality $\mathfrak n_{\dim}(\mathcal M) \leq 1$ holds if $\mathcal M$ is a d-minimal expansion of…
Several categories look like categories of relations, but do not fit the established theory of relations in regular categories. They include the category of surjective multivalued functions, the category of injective partial functions, the…
First, we give the definition for quasi-nearly subharmonic functions, now for general, not necessarily nonnegative functions, unlike previously. We point out that our function class incudes, among others, quasisubharmonic functions, nearly…
Certain subclasses of $B_1(K)$, the Baire-1 functions on a compact metric space $K$, are defined and characterized. Some applications to Banach spaces are given.
A link between first-order ordinary differential equations (ODEs) and 2-dimensional Riemannian manifolds is explored. Given a first-order ODE, an associated Riemannian metric on the variable space is defined, and some properties of the…