Annales Mathematicae Silesianae Feed

Lacunary p-Distance Convergence of Sequences of Complex Uncertain Variables

Mon, 17 Aug 2026 00:00:00 GMT

This paper introduces the concept of lacunary p-distance convergence for sequences of complex uncertain variables. This generalization allows the study of convergence over irregular index sets under uncertainty, extending existing convergence frameworks in uncertainty theory. Various properties, algebraic operations, and geometric aspects of the related function space are discussed.

On Examples of Witt Functors in Quadratic Number Fields

Wed, 08 Jul 2026 00:00:00 GMT

In this paper we provide a series of examples of nonmaximal orders in a quadratic number field K whose Witt ring does not embed into the Witt ring of K.

Boundedness of Lasota–Myjak Attractors for Iterated Function Systems

Tue, 07 Jul 2026 00:00:00 GMT

We consider topological attractors of (possibly infinite) iterated function systems. It is shown that for some class of non-expansive mappings the boundedness of the set of all globally attractive fixed points is equivalent to the boundedness of the attractor. Moreover, such a system fullfils the so-called address theorem.

Alternative Functional Equations. A Survey

Wed, 01 Jul 2026 00:00:00 GMT

This paper provides a survey of several results on alternative functional equations, related to the Cauchy equation and to the quadratic equation, and involving one or more unknown functions.

Report of Meeting: The Twenty-fifth Katowice–Debrecen Winter Seminar on Functional Equations and Inequalities Kościelisko-Zakopane, Poland, February 3–6, 2026

Tue, 30 Jun 2026 00:00:00 GMT

On Some Inequalities with Fibonacci Numbers via Weighted Reverse Hölder Inequalities

Fri, 17 Apr 2026 00:00:00 GMT

In this paper, we introduce new inequalities for weighted sums of powers. By utilizing known Fibonacci identities alongside our generalized inequalities, we derive new sequences of inequalities for Fibonacci numbers.

On Strict Ranking by Pairwise Comparisons

Sat, 04 Apr 2026 00:00:00 GMT

This paper addresses the problem of obtaining a strict ranking (i.e., a ranking without equally ranked items) of n items based on a pairwise comparisons matrix. The basic structures are described and a heuristic approach based on a condition, the ℛ-condition is proposed. The limitations of this ranking procedure are analyzed.

Jensen Type Inequality for L-Gap Convex Functions

Sat, 04 Apr 2026 00:00:00 GMT

The concept of l-gap convex functions is defined, which is more general than convex functions and allows some non-convex parts of the function. A Jensen type inequality is established and some examples are discussed. As an application and generalization, we prove that the majorization theorem also holds for l-gap convex functions. Then we use the conclusions from the above sections to establish a Hermite-Hadamard type inequality for l-gap convex functions.

Jensen-Type Inequalities for Divided Differences via Generalized Convex Functions

Wed, 25 Feb 2026 00:00:00 GMT

In this paper, we use (m+4)-convex functions to derive an estimate for Jensen’s inequality in the context of divided differences. In addition, we extend these results for (h, g; α − n)-convex functions. Finally, we present some results for g-convex functions, (h, g)-convex functions and provide a discussion and examples concerning h-convex functions.

Classification of Lipschitz Derivatives in Terms of Semicontinuity and the Baire Limit Functions

Tue, 24 Feb 2026 00:00:00 GMT

We introduce the generalized notion of semicontinuity of a function defined on a topological space and derive the useful classification of the so-called Lipschitz derivatives of functions defined on a metric space. Secondly, we investigate some connections of the Lipschitz derivatives defined on normed spaces to the Fréchet derivative and relations between little, big and local Lipschitz derivatives (denoted by lip f, 𝕃ip f and Lip f respectively) in terms of Baire limit functions. In particular, we prove that lip f is ℱσ-lower, Lip f is ℱσ-upper, 𝕃ip f is upper semicontinuous. Moreover, for a function f defined on an open or convex subset of a normed space, the upper Baire limit function of functions lip f and Lip f are equal to 𝕃ip f.

A Pexiderized Cosine Functional Equation

Tue, 24 Feb 2026 00:00:00 GMT

Let S be a semigroup and K be a field. In a recent article we introduced a new cosine functional equation g(xyz) − g(x)g(yz) − g(y)g(xz) − g(z)g(xy) + 2g(x)g(y)g(z) = 0 for an unknown function g : S → K. It was shown that this equation is closely connected to the sine addition formula, and for K = ℂ its solutions are expressible in terms of multiplicative functions. Here we solve the more general functional equation f(xyz)+g(x)g(yz)+g(y)g(xz)+ g(z)g(xy) + h(x)h(y)h(z) = 0 for three unknown functions f, g, h : S → ℂ, where S is a monoid. The solutions are linear combinations of two multiplicative functions.

On Powers, Roots and Moore–Penrose Inverses of Matrices Via Generalized Fibonacci Numbers

Thu, 19 Feb 2026 00:00:00 GMT

The purpose of this work is to introduce some new results about the relations between powers, roots and Moore–Penrose inverses of square matrices satisfying a cubic matrix equation and the generalized Fibonacci numbers. The results can also be used for rectangular matrices. Moreover, we give some numerical examples to verify theoretical results.

A note on the fuzzy Xor

Sat, 15 Nov 2025 00:00:00 GMT

In this paper we will try to answer what conditions must be met by the fuzzy Xor to be used for cryptographic purposes. We will also show that defining the fuzzy Xor using other fuzzy connectives is not suitable for this purpose.

Generalized Commutative Mersenne and Mersenne–Lucas Quaternion Polynomials

Sat, 15 Nov 2025 00:00:00 GMT

Generalized commutative quaternions generalize elliptic, parabolic and hyperbolic quaternions, bicomplex numbers, complex hyperbolic numbers and hyperbolic complex numbers. In this paper, we use the Mersenne numbers and polynomials in the theory of these quaternions. We introduce and study generalized commutative Mersenne quaternion polynomials and generalized commutative Mersenne–Lucas quaternion polynomials.

Convex Sequence and Convex Polygon

Sun, 02 Nov 2025 00:00:00 GMT

In this paper, we deal with the question: under what conditions n distinct points Pi(xi, yi) (i = 1,…, n) provided x1 <…< xn form a convex polygon? One of the main findings of the paper can be stated as follows: Let P1(x1, …, y1),…, Pn(xn, yn) be n distinct points (n ≥ 3) with x1 <…< xn. Then P1P2¯,…,PnP1¯ \overline {{P_1}{P_2}} , \ldots ,\overline {{P_n}{P_1}} form a convex n-gon lying in the half-space ℋ¯=x,y|x∈ℝ and y≤y1+x−x1xn−x1(yn−y1)⊆ℝ2 \underline {\cal H} = \left\{{\left({x,y} \right)|x \in {\mathbb R}\,{\rm{and}}\,y \le {y_1} + \left({{{x - {x_1}} \over {{x_n} - {x_1}}}} \right)({y_n} - {y_1})} \right\} \subseteq {\mathbb R}^2 if and only if the following inequality holds yi−yi−1xi−xi−1≤yi+1−yixi+1−xifor alli∈{2,…,n−1}. \matrix{{{{{y_i} - {y_{i - 1}}} \over {{x_i} - {x_{i - 1}}}} \le {{{y_{i + 1}} - {y_i}} \over {{x_{i + 1}} - {x_i}}}} & {{\rm{for}}\,{\rm{all}}} & {i \in \{2, \ldots ,n - 1\}.} \cr} Based on this result, we establish a connection between the property of sequential convexity and convex polygon. We show that in a plane if any n points are scattered in such a way that their horizontal and vertical distances preserve some specific monotonic properties, then those points form a 2-dimensional convex polytope.

Conditional Equations Related to Drygas Functional Equations

Fri, 31 Oct 2025 00:00:00 GMT

We determine the solutions of the conditional Drygas equation for functions f1 and f2 that satisfy (y2 + y)f1(x) = (x2 + x)f2(y) for all (x, y) ∈ ℝ2 under the additional conditions y = x2, or y = log(x), x > 0 or y = exp(x).

On Matrices with Bidimensional Fibonacci Numbers

Mon, 22 Sep 2025 00:00:00 GMT

In this paper, the bidimensional extensions of the Fibonacci numbers are explored, along with a detailed examination of their properties, characteristics, and some identities. We introduce and study the matrices with bidimensional Fibonacci numbers, focusing in particular on their recurrence relation, key properties, determinant, and various other identities. It is our purpose to study the matrix version of bidimensional Fibonacci numbers and provide new results and sometimes extensions of some results existing in the literature. We aim to introduce these matrices using the bidimensional Fibonacci numbers and to give the determinant of these matrices.

New and Original Integral Inequalities under Monotonicity and Convexity Assumptions

Wed, 02 Jul 2025 00:00:00 GMT

This article examines integral inequalities dealing with functions of the form “a function raised to the power of another function” under varying monotonicity and convexity assumptions. First, we assess the validity of a referenced theorem on the subject. Specifically, we present a counterexample and identify a gap in its proof. We then propose an alternative version of the theorem with more flexible convexity assumptions. In addition, we establish new lower and upper bounds for the same integral using refined Hermite–Hadamard integral inequalities. A complementary variant is also discussed. Thus, our results fill gaps in the literature and extend existing results on integral inequalities under classical assumptions.

Algebraic Properties of Semi-Direct Sums of Rings

Mon, 02 Jun 2025 00:00:00 GMT

Let R be an associative ring not necessarily with unity. We say that R is a semi-direct sum of rings S and I, if R = S + I, where S is a subring of a ring R, I is an ideal of R and S ∩ I = {0}.The aim of this paper is to investigate certain algebraic properties of semidirect sums of associative rings with applications to amalgamated rings. We generalize several results from the literature to associative rings without unity. In particular we show that the class of semi-direct sums of rings is equal to the class of amalgamated rings, we provide a description of the Jacobson radical of semi-direct sums and we offer a characterization of semi-direct sums that are left Steinitz rings.

The Twenty-fourth Debrecen–Katowice Winter Seminar on Functional Equations and Inequalities Hajdúszoboszló (Hungary), February 6 – 9, 2025

Tue, 20 May 2025 00:00:00 GMT