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Discrete analogs of the index transforms with squares of Bessel functions of the first and second kind $J_\nu(z),\ Y_\nu(z)$ are introduced and investigated. The corresponding inversion theorems for suitable classes of functions and…
In two recent articles we have examined a generalization of the binomial distribution associated with a sequence of positive numbers, involving asymmetric expressions of probabilities that break the symmetry {\it win-loss}. We present in…
In a series of previous articles by the author, it was shown that one could effectively give a variational formulation to non-conservative mechanical systems, as well as ones that subject to non-holonomic constraints by starting with the…
In this note we derive some interesting definite integrals involving Malmsten logarithm forms, reciprocal logarithm forms and K\"{o}lbig type integrals in terms of special functions.
I consider general reflection coefficients for arbitrary one-dimensional whole line differential or difference operators of order $2$. These reflection coefficients are semicontinuous functions of the operator: their absolute value can only…
The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.
In this paper, we introduce the concept of the m-generalized right group inverse. This serves as a natural extension of both the m-weak group inverse and the generalized group inverse. We characterize this new generalized inverse using the…
Let $f$ be a measurable, real function defined in a neighbourhood of infinity. The function $f$ is said to be of generalised regular variation if there exist functions $h \not\equiv 0$ and $g > 0$ such that $f(xt) - f(t) = h(x) g(t) +…
Let $n$ and $k$ be nonnegative integers such that $1\le k\le n+1$. The convex cone $\mathcal{F}_+^{k:n}$ of all functions $f$ on an arbitrary interval $I\subseteq\mathbb{R}$ whose derivatives $f^{(j)}$ of orders $j=k-1,\dots,n$ are…
The theory of generalized inverses of matrices and operators is closely connected with projections, i.e., idempotent (bounded) linear transformations. We show that a similar situation occurs in any associative ring $\mathcal{R}$ with a unit…
In this paper we study the inverse of so-called unfair permutations, and explore various properties of them. Our investigation begins with comparing this class of permutations with uniformly random permutations, and showing that they behave…
This article is centered around generalizing a previous implicit function theorem of the author to be applicable for maps f:E sqcap F to F which can be lifted to Keller C^k_pi maps f_i:E sqcap F_i to F_i with F_i Banach and F=projlim F_i .…
The paper is devoted to a comprehensive second-order study of a remarkable class of convex extended-real-valued functions that is highly important in many aspects of nonlinear and variational analysis, specifically those related to…
An equivariant version of the twisted inverse pseudofunctor is defined, and equivariant versions of some important properties, including the Grothendieck duality of proper morphisms and flat base change are proved. As an application, a…
Recent work has generalized the Furstenberg correspondence between sets of integers and dynamical systems to versions which involve sequences of finite graphs or sequences of $L^\infty$ functions. We give a unified version of the theorem…
We present an extensive analysis of relative deviation bounds, including detailed proofs of two-sided inequalities and their implications. We also give detailed proofs of two-sided generalization bounds that hold in the general case of…
We give estimates for the convolution product of an arbitrary number of endlessly continuable functions. This allows us to deal with nonlinear operations for the corresponding resurgent series, e.g. substitution into a convergent power…
There are several extensions of the classical Banach Fixed Point Theorem in technical literature. A branch of generalizations replaces usual contractivity by weaker but still effective assumptions. Our note follows this stream, presenting…
A recognized trend of research investigates generalizations of the Hadamard's inversion theorem to functions that may fail to be differentiable. In this vein, the present paper explores some consequences of a recent result about the…
Discrete analogs of the index transforms, involving Bessel and the modified Bessel functions are introduced and investigated. The corresponding inversion theorems for suitable classes of functions and sequences are established.