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Recently, in Axioms 10(2): 119 (2021), a nonclassical first-order theory T of sets and functions has been introduced as the collection of axioms we have to accept if we want a foundational theory for (all of) mathematics that is not weaker…
We introduce three classes of analytic functions with fixed second coefficient which are defined using the class $\mathcal{P}$ of analytic functions with positive real part. The objective is to determine radii such that the three classes…
The present research deals with generalizations of the Salem function with arguments defined in terms of certain alternating expansions of real numbers. The special attention is given to modelling such functions by systems of functional…
We define two versions of compositions of matrix-valued rational functions of appropriate sizes and whenever analytic at infinity, offer a set of formulas for the corresponding state-space realization, in terms of the realizations of the…
This work looks at the theory of octonionic slice regular functions through the lens of differential topology. It proves a full-fledged version of the Open Mapping Theorem for octonionic slice regular functions. Moreover, it opens the path…
Topological statistical theory provides the foundation for a modern mathematical reformulation of classical statistical theory: Structural Statistics emphasizes the structural assumptions that accompany distribution families and the set of…
It is possible to perform some operations with extrafunctions applying these operations separately to each coordinate. Operations performed in this manner are called regular. It is proved that it is possible to extend several operations…
In this memoir, we seek to construct a constructive theory that is as complete as possible to describe the algebraic properties of the real number field in constructive mathematics without a dependent choice axiom. To this purpose, we use a…
This work establishes the existence of addition theorems and double-angle formulas for Ck real scalar functions. Moreover, we determine necessary and sufficient conditions for a bivariate function to be an addition formula for a Ck real…
We study a new model theory for formal mathematical systems that we developed in a previous paper. We introduce isomorphic and homomorphic structures for formal languages, present some results and examples and conclude our paper with a…
These are lecture notes for a simple minicourse approaching the satistical properties of a dynamical system by the study of the associated transfer operator (considered on a suitable functions or measures spaces). The following questions…
We provide a setting-independent definition of reals by introducing the notion of a streak. We show that various standard constructions of reals satisfy our definition. We study the structure of reals by noting that its pieces correspond to…
In these self-contained low prerequisite introductory notes we first present (in part 1) basic concepts of set theory and algebra without explicit category theory. We then present (in part 2) basic category theory involving a somewhat…
The present article is an extended version of [6] containing new results and an updated list of references. We review the notion of polar analyticity introduced in a previous paper and succesfully applied in Mellin analysis and quadrature…
We define a function by refining Stern's diatomic sequence. We name it the {\it assembly function}. It is strictly increasing continuous. The first and the second main theorems are on an action to the function. The third theorem is on…
In this paper, we introduce the concept of the $\alpha$-fractal function and fractal approximation for a set-valued continuous map defined on a closed and bounded interval of real numbers. Also, we study some properties of such fractal…
In this paper we give a method, based on the characteristic function of a set, to solve some difficult problems of set theory in undergraduate research.
Operator $k$-tone functions on an open interval of the real line, which are higher order extensions of operator monotone and convex functions, are characterized via certain inequalities for the real and imaginary parts of analytic…
Expanding upon recent work, a new class of $A$-functions is introduced that can be viewed as an appropriate generalization of the class of regular $A$-functions, the class of structured $A$-functions, and the class of perfect $A$-functions.…
This book concentrates on functional analysis. The text is written so that it can be followed on the basis of high school mathematics. The book introduces the set theoretical foundations of mathematics, the basic theories of linear algebra…