József Bukor
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
József Bukor has a total of 15 co-authors. Here are the top co-authors by number of shared publications:
- Ferdinánd Filip
Department of Mathematics, J. Selye University, 94501 Komarno, Slovakia
7 shared publications - Janos T. Toth
Department of Mathematics, J. Selye University, Komarno, Slovakia
7 shared publications - Annamaria. R. Varkonyi-Koczy
J. Selye University
3 shared publications - Alireza Baghban
Department of Process Engineering, NISOC Company, Ahvaz, Iran
2 shared publications - Amir Mosavi
Óbuda University
2 shared publications - László Zsilinszky
Department of Mathematics and Computer Science, University of North Carolina at Pembroke, Pembroke, NC 28372, USA
2 shared publications
Latest Publications
- Open Access
- 25 August 2026
- Published by MDPI AG in Mathematics
- Vol. 14 (17) , 3058
A New Density Hierarchy Based on Riesz and Hölder Summability
Let be an Erdős–Ulam function satisfying as , and let denote the associated Riesz matrix. Furthermore, let be the Riesz matrix generated by the weights , . The main result establishes that the matrix density induced by an arbitrary power of —or, equivalently, by a generalized Hölder mean of arbitrary order—is stronger than the matrix density induced by .- 25 August 2026
- Published by MDPI AG in Mathematics
- Vol. 14 (17) , 3058
Open AccessA New Density Hierarchy Based on Riesz and Hölder Summability
Let be an Erdős–Ulam function satisfying as , and let denote the associated Riesz matrix. Furthermore, let be the Riesz matrix generated by the weights , . The main result establishes that the matrix density induced by an arbitrary power of —or, equivalently, by a generalized Hölder mean of arbitrary order—is stronger than the matrix density induced by . - 12 February 2026
- Published by Prof. Marin Drinov Publishing House of BAS (Bulgarian Academy of Sciences) in Notes on Number Theory and Discrete Mathematics
- Vol. 32 (1)
A note on periodic linear recurrence relations
We provide an elementary proof of the fact that a sequence defined by a linear recurrence relation with integer coefficients is periodic if and only if all characteristic roots are distinct roots of unity. Additionally, we discuss the case in which the coefficients of the recurrence relation are restricted to the set {–1,0,1}.
- 12 February 2026
- Published by Prof. Marin Drinov Publishing House of BAS (Bulgarian Academy of Sciences) in Notes on Number Theory and Discrete Mathematics
- Vol. 32 (1)
A note on periodic linear recurrence relations
We provide an elementary proof of the fact that a sequence defined by a linear recurrence relation with integer coefficients is periodic if and only if all characteristic roots are distinct roots of unity. Additionally, we discuss the case in which the coefficients of the recurrence relation are restricted to the set {–1,0,1}.
- Open Access
- 27 November 2025
- Published by Springer Nature in Periodica Mathematica Hungarica
- Vol. 92 (2) , 240-266
On structure of the family of regularly distributed sets
- 27 November 2025
- Published by Springer Nature in Periodica Mathematica Hungarica
- Vol. 92 (2) , 240-266
Open AccessOn structure of the family of regularly distributed sets
- 1 October 2024
- Published by Springer Nature in Acta Universitatis Sapientiae, Informatica
- Vol. 16 (1) , 39-43
Density of a-powers in repetitions of a primitive word
We consider words over fixed alphabet. A word 푢 is said to be primitive if it cannot be expressed as a nontrivial power of another word. For a positive real 훼 > 1 the 훼-power of a word 푣 is defined by 푣 훼 = 푣 b훼c 푝 where 푝 is a prefix of 푣 of length (훼− b훼c)|푣| . We prove that for any primitive word 푢 and for any 훼 > 1 the number of distinct 훼-powers in 푢 푘 is asymptotically equal to 1 훼 |푢 푘 | for 푘 → ∞.
- 1 October 2024
- Published by Springer Nature in Acta Universitatis Sapientiae, Informatica
- Vol. 16 (1) , 39-43
Density of a-powers in repetitions of a primitive word
We consider words over fixed alphabet. A word 푢 is said to be primitive if it cannot be expressed as a nontrivial power of another word. For a positive real 훼 > 1 the 훼-power of a word 푣 is defined by 푣 훼 = 푣 b훼c 푝 where 푝 is a prefix of 푣 of length (훼− b훼c)|푣| . We prove that for any primitive word 푢 and for any 훼 > 1 the number of distinct 훼-powers in 푢 푘 is asymptotically equal to 1 훼 |푢 푘 | for 푘 → ∞.
- Open Access
- 1 October 2024
- Published by Prof. Marin Drinov Publishing House of BAS (Bulgarian Academy of Sciences) in Notes on Number Theory and Discrete Mathematics
- Vol. 30 (3) , 538-546
On positive sequences of reals whose block sequence has an asymptotic distribution function
In this paper we study the properties of the unbounded sequence $0 < y_1 \le y_2 \le y_3 \le \cdots$ of positive reals having asymptotic distribution function of the form $x^\lambda$. As a consequence, we immediately get information on the asymptotic behavior of the power means of order $r>0$ of function values of some arithmetic functions, e.g., the first $n$ prime numbers or the values of the prime counting function.- 1 October 2024
- Published by Prof. Marin Drinov Publishing House of BAS (Bulgarian Academy of Sciences) in Notes on Number Theory and Discrete Mathematics
- Vol. 30 (3) , 538-546
Open AccessOn positive sequences of reals whose block sequence has an asymptotic distribution function
In this paper we study the properties of the unbounded sequence $0 < y_1 \le y_2 \le y_3 \le \cdots$ of positive reals having asymptotic distribution function of the form $x^\lambda$. As a consequence, we immediately get information on the asymptotic behavior of the power means of order $r>0$ of function values of some arithmetic functions, e.g., the first $n$ prime numbers or the values of the prime counting function. - Open Access
- 6 May 2024
- Published by SCIK Publishing Corporation in International Journal of Analysis and Applications
- Vol. 22, 72
Typical Sequence of Real Numbers From the Unit Interval Has All Distribution Functions
This note is devoted to the study of typical properties (in Baire category sense) of sequences of real numbers in [0, 1]. We prove that the subset of sequences that have all distribution functions forms a residual set.
- 6 May 2024
- Published by SCIK Publishing Corporation in International Journal of Analysis and Applications
- Vol. 22, 72
Open AccessTypical Sequence of Real Numbers From the Unit Interval Has All Distribution Functions
This note is devoted to the study of typical properties (in Baire category sense) of sequences of real numbers in [0, 1]. We prove that the subset of sequences that have all distribution functions forms a residual set.
- 1 June 2021
- Published by Springer Nature in Periodica Mathematica Hungarica
- Vol. 82 (2) , 125-135
On I - and I≤q-convergence of arithmetic functions
- 1 June 2021
- Published by Springer Nature in Periodica Mathematica Hungarica
- Vol. 82 (2) , 125-135
On I - and I≤q-convergence of arithmetic functions
- Open Access
- 1 January 2021
- Published by National Library of Serbia in Filomat
- Vol. 35 (12) , 3945-3955
On ideals defined by asymptotic distribution functions of ratio block sequences
In this paper we study ratio block sequences possessing an asymptotic distribution function. By means of these distribution functions we define new families of subsets of N which appear to be admissible ideals. We characterize these ideals using the exponent of convergence and this characterization is useful in decision if a given set belongs to a given ideal of this kind.
- 1 January 2021
- Published by National Library of Serbia in Filomat
- Vol. 35 (12) , 3945-3955
Open AccessOn ideals defined by asymptotic distribution functions of ratio block sequences
In this paper we study ratio block sequences possessing an asymptotic distribution function. By means of these distribution functions we define new families of subsets of N which appear to be admissible ideals. We characterize these ideals using the exponent of convergence and this characterization is useful in decision if a given set belongs to a given ideal of this kind.
- Open Access
On $\mathcal I(<q)$- and $\mathcal I(\leq q)$-convergence of arithmetic functions
Let $\mathbb N$ be the set of positive integers, and denote by $\lambda(A)=\inf\{t>0:\sum_{a\in A} a^{-t}<\infty\}$ the convergence exponent of $A\subset\mathbb N$. For $0<q\le 1$, $0\le q\le 1$, respectively, the admissible ideals $\mathcal I(<q)$, $\mathcal I(\leq q)$ of all subsets $A\subset \mathbb N$ with $\lambda(A)<q$, $\lambda(A)\le q$, respectively, satisfy $\mathcal I(<q)\subsetneq\mathcal I_c^{(q)}\subsetneq \mathcal I(\leq q)$, where $\mathcal I_c^{(q)}=\{A\subset\mathbb N: \sum_{a\in A}a^{-q}<\infty\}$. In this note we sharpen the results of Bal\'az, Gogola and Visnyai from [2], and of others papers, concerning characterizations of $\mathcal I_c^{(q)}$-convergence of various arithmetic functions in terms of $q$. This is achieved by utilizing $\mathcal I(<q)$- and $\mathcal I(\leq q)$-convergence, for which new methods and criteria are developed.Open AccessOn $\mathcal I(<q)$- and $\mathcal I(\leq q)$-convergence of arithmetic functions
Let $\mathbb N$ be the set of positive integers, and denote by $\lambda(A)=\inf\{t>0:\sum_{a\in A} a^{-t}<\infty\}$ the convergence exponent of $A\subset\mathbb N$. For $0<q\le 1$, $0\le q\le 1$, respectively, the admissible ideals $\mathcal I(<q)$, $\mathcal I(\leq q)$ of all subsets $A\subset \mathbb N$ with $\lambda(A)<q$, $\lambda(A)\le q$, respectively, satisfy $\mathcal I(<q)\subsetneq\mathcal I_c^{(q)}\subsetneq \mathcal I(\leq q)$, where $\mathcal I_c^{(q)}=\{A\subset\mathbb N: \sum_{a\in A}a^{-q}<\infty\}$. In this note we sharpen the results of Bal\'az, Gogola and Visnyai from [2], and of others papers, concerning characterizations of $\mathcal I_c^{(q)}$-convergence of various arithmetic functions in terms of $q$. This is achieved by utilizing $\mathcal I(<q)$- and $\mathcal I(\leq q)$-convergence, for which new methods and criteria are developed. - Open Access
- 1 January 2020
- Published by SCIK Publishing Corporation in International Journal of Analysis and Applications
- Vol. 18 (3) , 332-336
A NOTE ON OLIVIER'S THEOREM AND CONVERGENCE IN ERDOS-ULAM DENSITY
Olivier's Theorem says that if Sigma a(n) is a convergent positive series and (a(n)) is monotone decreasing, then na(n) -> 0. Salat and Toma [4] proved that the monotonicity condition can be omitted if the convergence of (na(n))(n) is replaced by the statistical convergence. The aim of this note is to give an alternative proof and generalization of this result.
- 1 January 2020
- Published by SCIK Publishing Corporation in International Journal of Analysis and Applications
- Vol. 18 (3) , 332-336
Open AccessA NOTE ON OLIVIER'S THEOREM AND CONVERGENCE IN ERDOS-ULAM DENSITY
Olivier's Theorem says that if Sigma a(n) is a convergent positive series and (a(n)) is monotone decreasing, then na(n) -> 0. Salat and Toma [4] proved that the monotonicity condition can be omitted if the convergence of (na(n))(n) is replaced by the statistical convergence. The aim of this note is to give an alternative proof and generalization of this result.