the main purpose of this paper is to define a new regular matrix by using fibonacci numbers and to investigate its matrix domain in the classical sequence spaces $ell _{p},ell _{infty },c$ and $c_{0}$, where $1leq p

in this paper, we introduce $p$-semilinear transformations for linear algebras over a field ${bf f}$ of positive characteristic $p$, discuss initially the elementary properties of $p$-semilinear transformations, make use of it to give some characterizations of linear algebras over a field ${bf f}$ of positive characteristic $p$. moreover, we find a one-to-one correspondence between $p$-semiline...

in this article we introduce the notion of textit{fractal $omega$-operad} emerging from  a natural $omega$-operad associated to any coglobular object in the category of higher operads in batanin's sense, which in fact is a coendomorphism $omega$-operads. we have in mind coglobular object of higher operads which algebras are kind of higher transformations. it follows that this natural $omega$-op...

The way super- and sub-additive transformations of aggregation functions are introduced involve suprema and infima taken over simplexes whose dimensions may grow arbitrarily. Exact values of such transformations may thus be hard to determine in general. In this note we discuss methods of algorithmic approximation of such transformations.

Super- and sub-additive transformations of aggregation functions have been recently introduced by Greco, Mesiar, Rindone and v{S}ipeky [The superadditive and the subadditive transformations of integrals and aggregation functions, {it Fuzzy Sets and Systems} {bf 291} (2016), 40--53]. In this article we give a survey of the recent development regarding the existence of aggregation functions with ...

In this paper, we introduce $p$-semilinear transformations for linear algebras over a field ${bf F}$ of positive characteristic $p$, discuss initially the elementary properties of $p$-semilinear transformations, make use of it to give some characterizations of linear algebras over a field ${bf F}$ of positive characteristic $p$. Moreover, we find a one-to-one correspondence between $p$-semiline...

‎in this article we discuss examples of fractal $omega$-operads‎. ‎thus we show that there is an $omega$-operadic approach to explain existence of‎ ‎the globular set of globular setsfootnote{globular sets are also called $omega$-graphs by the french school.}‎, ‎the reflexive globular set of reflexive globular sets‎, ‎the $omega$-magma of $omega$-magmas‎, ‎and also the reflexive $omega$-magma of...

In his paper mentioned in the title, which appears in the same issue of this journal, Mehdi Radjabalipour derives the cyclic decomposition of an algebraic linear transformation. A more general structure theory for linear transformations appears in Irving Kaplansky's lovely 1954 book on infinite abelian groups. We present a translation of Kaplansky's results for abelian groups into the terminolo...

We prove a continuity inheritance property for super- and sub-additive transformations of non-negative continuous multivariate functions defined on the domain of all non-negative points and vanishing at the origin. As a corollary of this result we obtain that super- and sub-additive transformations of continuous aggregation functions are again continuous aggregation functions.