Afrika Matematika最新文献

In the present paper with the aid of subordination, the authors introduce two subclasses of analytic functions denoted by ({mathcal {S}}_{alpha , beta }(lambda )~~(alpha ,~beta ,~ lambda in {mathbb {R}},~alpha <1, beta >1, lambda ge 0)) and ({mathcal {G}}(lambda )) defined in the open unit disk ({mathbb {D}}:={z in {mathbb {C}}:|z|<1}). These subclasses are defined through a certain univalent function ({mathcal {S}}_{alpha , beta }) and the generating function of the Gregory coefficients ({mathcal {G}}(lambda )). We determine upper bounds of the initial coefficients, Fekete–Szeg(ddot{o}) functional, Hankel determinant of second order, logarithmic coefficients and inverse coefficients of the functions belongs to these subclasses. Some of the corollaries of the main results are also pointed out.

In this article, we introduce the notion of quasi covered hyperideal (QC-hyperideal) in semihypergroups. The greatest quasi covered hyperideal and the quasi hyperbase of a semihypergroup are studied. We discuss some attributes of these hyperideals, as well as their union and intersection properties and their characterizations in semihypergroups and regular semihypergroups. Finally, we establish a relationship between covered hyperideals, the greatest hyperideal, QC-hyperideals, and the quasi hyperbase with the greatest quasi covered hyperideal.

In this paper, we have determined the necessary and sufficient conditions so that Tribonacci numbers can be written as the differences of two elements of generalized Lucas sequences. We have also shown that the number of solutions of the equation in the title is finite. For application, we have determined the Tribonacci numbers written as the difference of two Fibonacci numbers.

Attracted by the importance of ordinary differential equations in many physical situations like, engineering, business and health care in particular, an effective and successful numerical algorithm is needed in order to explain many of the ambiguities about the phenomena in many fields of human endeavor. In this study, an interpolation and collocation technique are adopted in deriving a Block Hybrid Algorithm (BHA) for the numerical solution of systems of first-order Initial Value Problems (IVPs). To derive the BHA, the shifted Legendre polynomials was interpolated at two selected points and its derivative was collocated at seven selected points. This led to a continuous scheme which was eventually evaluated at some points to obtain the discrete schemes used in the numerical computation. Furthermore, some illustrative examples are introduced to show the applicability and validity of the proposed algorithm. It was observed that the proposed algorithm has the desired rate of convergence to the exact solution. The suggested method utilizes data at points other than the step numbers which is viewed as an important landmark; another major advantage of this algorithm is that it possesses remarkably small error constants (Table 2). Some graphical representations of the exact and numerical results are presented to show how accurate the numerical results agree with the exact solutions.

In this paper we highlight a type of hyperbolic equation relating the logarithmic source term with distributed delay and dynamic boundary condition. We get, under comfortable primary data is the weak solution to local existence. The results of the solutions were found using the Faydo–Galerkin method and Schoder’s fixed point theorem. Then, the minimum blow-up result was studied. Our work is an extension of some previous work.

The concepts of multiresolution analysis (MRA) and wavelets in Sobolev space over local fields of positive characteristic ((H^s(mathbb {K}))) are developed by Pathak and Singh [9]. In this paper, we constructed wavelet packets in Sobolev space (H^s(mathbb {K})) and derived their orthogonality at each level. By using convolution theory, an example of wavelet packets in (H^s(mathbb {K})) is presented

The aim of this paper is to study the sufficient conditions for the existence of fixed points of Perov type T-contractive mappings in the setup of complete cone b-metric space associated with generalized c-distance. Some examples are presented to support our main results and concepts defined herein. The results proved in the paper extend and generalize various well known results in the existing literature.

In our research, we broaden the scope of Fourier–Stieltjes transforms to encompass locally compact groups, denoted as G. We achieve this extension by leveraging the induced representation from a closed subgroup K. From this, we deduce the Fourier transform ({hat{f}}) of a Haar-integrable function f defined on G. Specifically, we express ({hat{f}}) as the Fourier–Stieltjes transform ({hat{mu }}) of the measure (mu = f lambda ), where ( lambda ) denotes the Haar measure of G. Our work is significant because when applied to Lie groups with compact subgroups K, our Fourier–Stieltjes transform ({hat{m}}) exhibits more nuanced characteristics compared to the traditionally defined one via the Gel’fand transform, which is standard in the context of Lie groups. We rigorously substantiate this observation. One of the principal challenges we confront is the construction of the “trigonometric functions”, which serve as the foundation for building the Fourier transform.

The Cayley sum graph is a graph whose vertex comprises elements of an abelian group G and edges are the sum of these vertices belonging to a subset of G, namely, S. We introduce Cayley sum signed graph by giving the sign to these edges. An edge receives a positive sign if any of the incident vertices belong to S; otherwise, it receives a negative sign. We discuss the balance, clusterability and some properties of derived Cayley sum signed graph.

In this paper, we modify the Thakur three-step iterative algorithm and provide sufficient conditions and a useful lemma to ensure the convergence of a best proximity pair for a noncyclic relatively Suzuki’s nonexpansive mapping in uniformly convex Banach spaces. Additionally, we present an example to illustrate the results, accompanied by a numerical simulation for the proposed algorithm.