Afrika Matematika最新文献

Let S be a semigroup and K a field. A function (f:S rightarrow K) is additive if (f(xy) = f(x) + f(y)) for all (x,y in S), and functions (g,h:S rightarrow K) form a sine pair if they satisfy the sine addition law (g(xy) = g(x)h(y) + h(x)g(y)) for all (x,y in S). Adding these two equations we arrive at the functional equation (*) (f(xy) + g(xy) = f(x) + f(y) + g(x)h(y) + h(x)g(y)). The alienation question for additivity and sine additivity asks whether (*) implies that f is additive and (g, h) is a sine pair. To fully answer this question we find the general solution of (*) for unknown functions (f,g,h:S rightarrow {mathbb {C}}). The solution illustrates a significant amount of interdependence between additivity and sine additivity.

In this paper, we extend the study of the Cesáro function spaces to the Cesáro-Morrey function spaces. We establish a general principle on the boundedness of integral operators on the Cesáro-Morrey function spaces. By applying this principle, we have the boundedness of the Erdélyi-Kober fractional integrals and the Hadamard fractional integrals on the Cesáro-Morrey function spaces. In addition, we also extend the study of Tandori spaces to Tandori-Morrey spaces.

We give several lower and upper bounds for the Euclidean operator radius of two operators on a Hilbert space. We improve some earlier related bounds. Also, as applications of these bounds, we deduce some new bounds for the classical numerical radius. Some of these bounds are refinements of certain existing bounds.

A renewed interest in combinatorial and arithmetic properties as well as applications to differential equations, identities, formulas, and probability theory has been sparked by the study of degenerate versions of several specific numbers and polynomials. The article aims to explore a 3D unified degenerate class of generalized Fubini polynomials by utilizing 2D generalized degenerate polynomials. The potential of applications are provided by deriving certain computational formulas and identities,recurrence relations and derivative expressions for the 3D degenerated Gould–Hopper–Fubini, 3D degenerate Hermite-Fubini and 3D degenerate 2-iterated Fubini polynomials, which are extracted out of the 3D degenerate generalized Fubini polynomials. Finally, the behaviour of zeros of two concrete degenerate polynomials with some specific set of parameters is shown by drawing graphs using Mathematica

Let G be a simple graph with vertex set (V={v_{1},v_{2},ldots ,v_{n}}). The notion (isim j) is used to indicate that the vertices (v_{i}) and (v_{j}) of G are adjacent. For a vertex (v_{i}in V), let (d_{i}) be the degree of (v_{i}). The harmonic-arithmetic (HA) index of G is defined as (HA(G) =sum _{isim j} 4d_id_j(d_i+d_j)^{-2}). In this paper, a considerable number of inequalities involving the HA index and other topological indices are derived. For every obtained inequality, all the graphs that satisfy the equality case are also characterized.

We compute certain inequalities for B-Berezin radius of (2times 2) operator matrices in the study that generalize and refine earlier inequalities. Furthermore, we construct A-Berezin radius inequalities of operators in (mathbb {B}_{A,Upsilon }(mathcal {H})) that improve on the current inequalities in Huban (Turk J Math 46(1):189–206, 2022). In addition, we establish A-Berezin radius bounds for sum of product of operators in (mathbb {B}_{A,Upsilon } (mathcal {H}),) which improve on the previous bounds.

In this paper, we investigate the existence and specific form of finite order transcendental entire solutions of certain equations including a Fermat-type functional first-order linear difference equation in (mathbb {C}^n), (ngeqslant 2) and a kth order partial differential difference equation in (mathbb {C}^2). The paper builds upon the previous works of Xu and Cao (Mediterr J Math 15:1–14, 2018; Mediterr J Math 17:1–4, 2020) and Haldar (Mediterr J Math 20: 50, 2023) whose results are extended and further developed in this study. We exhibit several examples to demonstrate the precision and applicability of our results to illustrate how our findings can be utilized in different scenarios or problem contexts. Towards the end of the paper, in the last section, we discuss some relevant questions that have emerged from one of the examples in the paper which also suggest potential directions for further research.

In this paper we establish some fixed point results for continuous countably condensing maps. We derive results of Altman’s type, Leray-Schauder’s type, Krasnosel’skii’s type and Krasnoselskii-Schafer’s type. One of the main tools in our analysis is a result due to S. J. Daher (Theorem 2.1). We conclude the paper by discussing existence results for a nonlinear Volterra integral equation.

Fuzzy rough set theory gives a mathematical tool for studying unsettled knowledge that is beclouded, inexact, and mutually exclusive. The perception and conclusions of fuzzy rough sets theory are inextricably linked to topological perception. The topological appearance and its applications in fuzzy rough sets theory have been extensively discussed by researchers. The underlying subordinate of topology and classic fuzzy rough sets theory, as well as the expressive work done in this area over the previous years, are highlighted in this research.

The generator of the semigroup associated with linear age-structured population models including spatial diffusion is shown to have compact resolvent.