Related papers: Some remarks about analytic functions defined on a…
We consider the angle in mathematics and arrive at a conclusion that there are two concepts on the issue. One is a descriptive geometrical one, while the other is from functional analysis. They are somewhat different, allow for different…
In this paper, some classes of discrete functions of $k$-valued logic are considered, that depend on sets of their variables in a particular way. Obtained results allow to "construct" these functions and to present them in their tabular,…
Algebraic characterizations of the computational aspects of functions defined over the real numbers provide very effective tool to understand what computability and complexity over the reals, and generally over continuous spaces, mean. This…
The main aim of this paper is to establish several Landau-type theorems for certain bounded poly-analytic functions and reduced poly-analytic functions that generalize some previously established results.
In this technical report, certain interesting classification of arithmetical functions is proposed. The notion of additively decomposable and multiplicatively decomposable arithmetical functions is proposed. The concepts of arithmetical…
We regard explanations as a blending of the input sample and the model's output and offer a few definitions that capture various desired properties of the function that generates these explanations. We study the links between these…
The present article is devoted to certain examples of functions whose argument represented in terms of Cantor series.
The paper discusses the role of interpretations, understood as multifunctions that preserve and reflect logical consequence, as refinement witnesses in the general setting of pi-institutions. This leads to a smooth generalization of the…
In this article, we impose a new class of fractional analytic functions in the open unit disk. By considering this class, we define a fractional operator, which is generalized Salagean and Ruscheweyh differential operators. Moreover, by…
Here I share a few notes I used in various course lectures, talks, etc. Some may be just calculations that in the textbooks are more complicated, scattered, or less specific; others may be simple observations I found useful or curious.
In the present work, we propose to investigate the second Hankel determinant inequalities for certain class of analytic and bi-univalent functions. Some interesting applications of the results presented here are also discussed.
The article discusses criteria for univalence of analytic functions in the unit disc. Various families of analytic functions depending on real parameters are considered. A unified method for creating new sets of conditions ensuring…
We will remark an extension of a linear functional on subalgebra of algebra of continuous functions on subset of $\mathbb{R}^n$ which preserves positivity.
We survey a few classes of analytic functions on the disk that have real boundary values almost everywhere on the unit circle. We explore some of their properties, various decompositions, and some connections these functions make to…
The proposed system of integer functions is logically fully independent from the traditional mathematical analysis of the real functions, but there is a well-defined mutual correspondence between the two disciplines. The system of integer…
We introduce the notion of the generalized-analytical function of the poly-number variable, which is a non-trivial generalization of the notion of analytical function of the complex variable and, therefore, may turn out to be fundamental in…
This short note contains elementary evaluations of some Euler sums.
Over 300 sequences and many unsolved problems and conjectures related to them are presented herein. These notions, definitions, unsolved problems, questions, theorems corollaries, formulae, conjectures, examples, mathematical criteria, etc.…
We study functions defined on a closed segment of the real line that belong to the class of Gonchar. We show that the graphs of such functions are pluripolar. We also discuss the generalizations of our result to functions defined on a…
This article defines a complement of a function and conditions for existence of such a complement function and presents few algorithms to construct a complement.