Afrika Matematika最新文献

The Bessel function and its various generalizations have extensively been studied in various branches of applied mathematics and theoretical physics, including the Geometric Function Theory. In this paper, we study basic characteristics of Bessel functions of order (mu ) and degree (nu ). Among the results that we investigate are the results giving the characteristic properties of univalence, convexity and starlikeness. We further investigate the conditions under which the function (L_{mu ,nu }) are strongly convex and strongly starlike. Several corollaries are also mentioned depicting the usefulness of the main results, one of the Corollary providing improvement in a result for normalized Bessel function.

In this paper, we consider a finite delay integro-differential equation with a nonlinear kernel in a general Banach space. The nonlinear part is assumed to be continuous with respect to a fractional power of the linear part in the second variable. We prove, using the semigroup theory, the local existence, continuous dependence of the initial data, the phenomena of blowing up, regularity, and compactness properties of the so-called mild solution. An application is provided to illustrate our results.

The reconstruction of potential function using nodal parameters is an inverse problem that has been studied in this work. An efficient and highly helpful transformation allowed for the extraction of a reconstruction formula for the problem’s potential function by a narrow collection of nodal data only. Additionally, the method’s efficacy was shown by a few numerical illustrations.

In this work, we investigate the existence of mild solution for semilinear integro-differential systems and semilinear neutral integro-differential systems with state-dependent delay in Banach spaces. Using Mönch’s fixed point theorem, the theory of Grimmer’s resolvent operator and the idea of measures of non-compactness, we prove the existence results. At the end, an example is given to further illustrate the conclusions drawn from the theoretical study.

The degree of approximation (in Hölder metric) of a periodic function belonging to a specific Hölder class by its Abel–Poisson means of Fourier series and of the conjugate function by the conjugate Abel–Poisson means of the conjugate series of the Fourier series is obtained.

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.