Methods of Functional Analysis
and Topology
Editors-in-Chief: A. N. Kochubei,
G. M. Torbin
ISSN: 1029-3531 (Print), 2415-7503 (Online)
Founded by Yu. M. Berezansky in 1995.
Methods of Functional Analysis and Topology (MFAT), founded in 1995, is a peer-reviewed journal publishing original articles and surveys on general methods and techniques of functional analysis and topology with a special emphasis on applications to modern mathematical physics.
MFAT is an open access journal, free for authors and free for readers.
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Latest Articles (December, 2025)
Laguerre-Bessel Wavelet Packets Transform
MFAT 31 (2025), no. 4, 325-335
325-335
In this paper, the Laguerre-Bessel wavelet packets transform is defined and studied. The scale discrete scaling function and the associated Plancherel and inversion formulas are given and established. Furthermore, the Calderón reproducing formula is given and proved for the proposed transform.
Matrices Induced by Scaled Hypercomplex Numbers over the Real Field $\mathbb{R}$
MFAT 31 (2025), no. 4, 261-309
261-309
In this paper, we construct, and study a certain type of definite, or indefinite inner product spaces over the real field $\mathbb{R}$, induced by the scaled hypercomplex numbers $\mathbb{H}_{t}$ for a fixed scale $t\in\mathbb{R}$, and some bounded operators acting on such vector spaces. In particular, we are interested in the vector spaces $\mathbb{H}_{t}^{N}$ consisting of all $N$-tuples of scaled hypercomplex numbers of $\mathbb{H}_{t}$, and the $\left(N\times N\right)$-matrices acting on $\mathbb{H}_{t}^{N}$ whose entries are from $\mathbb{H}_{t}$, i.e., $\mathbb{H}_{t}$-matrices, for all $N\in\mathbb{N}$. For an arbitrarily fixed $N\in\mathbb{N}$, we define $\mathbb{H}_{t}^{N}$ as a subspace of a certain functional vector space $\mathbf{H}_{t:2}$ equipped with a well-defined definite (if $t<0$), or indefinite (if $t\geq0$) inner product introduced in [6, 7, 8]. So, one can check immediately that our subspace $\mathbb{H}_{t}^{N}$ becomes a restricted definite, or indefinite inner product Banach space. Operator-theoretic, operator-algebraic and free-probabilistic properties of $\mathbb{H}_{t}$-matrices are considered and characterized on $\mathbb{H}_{t}^{N}$.
Hyperstability of some functional equations in modular spaces
Abderrahman Baza, Mohamed Rossafi, Mohammed Mouniane
MFAT 31 (2025), no. 4, 310-324
310-324
This paper is devoted to the study of hyperstability phenomena in the context of convex modular spaces. In particular, we investigate the hyperstability of three fundamental functional equations: the quadratic equation \begin{equation} \varphi(x+y)+\varphi(x-y)=2\varphi(x)+2\varphi(y) \end{equation} the general linear equation \begin{equation} \varphi(ax+by)=A\varphi(x)+B\varphi(y)+C \end{equation} and the $n$-dimensional quadratic equation \begin{equation} f\left(\sum_{i=1}^{m}x_{i}\right)+\sum_{1\leq i < j\leq m}f\big(x_{i}-x_{j}\big)=m\sum_{i=1}^{m}f(x_{i}). \end{equation} Using the direct method, we establish sufficient conditions under which every approximate solution of these equations in modular spaces coincides exactly with an exact solution. Our results extend earlier contributions obtained in Banach spaces via fixed point techniques, and provide new insights into the stability of functional equations in the broader context of modular spaces.
New Definition of $\mathcal{N}^{\alpha}_F$-Sumudu conformable transform
Bahloul Rachid, Rachad Houssame
MFAT 31 (2025), no. 4, 336-343
336-343
Using the new definition of the $\mathcal{N}^{\alpha}_F$-derivative function introduced by Juan E. Nápoles Valdés and al. (2020), we provide a new definition for the $\mathcal{N}^{\alpha}_F$-Sumudu transform, $\mathcal{N}^{\alpha}_F$-Sumudu conformable transform. Additionally, we establish several important results related to these new transforms. We also give a new definition of convolution related to this $\mathcal{N}^{\alpha}_F$-derivative and we show that it is commutative and associative.