Afrika Matematika最新文献

In this paper, we introduce the modified q-Genocchi polynomials, investigate their properties, and give their generating function. We obtain a number of new relations and properties for q-Genocchi polynomials, such as addition formula, explicit formula, derivative formula, and multiplication formula. As an application, a new q-analogue of Genocchi zeta function is presented by applying the Mellin transform to the generating function of the modified q-Genocchi polynomials. Finally, we define the q-Genocchi zeta-type functions and then prove their interpolation by the modified q-Genocchi polynomials at negative integers.

The objective of this article is to obtain coincidence points and common fixed point theorem in complete partial metric space. We provide some examples to support the usability of our results.

In this paper, we revisit pseudo-almost periodic and Stepanov-almost periodic functions. We study their properties and show in particular some composition theorems and fundamental results related to these classes. Some illustrating applications and concrete examples on existence and uniqueness of pseudo-almost periodic solutions to differential equations are given.

A climate-based metapopulation malaria model is formulated by incorporating human travel between zones with varying climatic factors, effective and counterfeit drug treatments, and time-periodic parameters for the mosquito population to understand the effect of human travel on malaria transmission. We study the existence, uniqueness, and stability of positive periodic solutions in the model and carry out numerical simulations for three climatic zones of Ghana. The study shows that the climate effects introduce fluctuations in the solutions, while human travel between zones affects the disease prevalence in each zone and the local transmission dynamics of malaria. We observed different outcomes depending on various restrictions imposed on human travels. The study also suggests that it is essential to ban the sale, importation or manufacture of counterfeit drugs and punish the offenders to ensure the effective use of high-quality drugs in the population.

In this paper, we establish an inequality for scalars, which we then apply to refine some classical inequalities for inner product and numerical raduis. For example, we establish that for any (mathcal {E}in mathcal {B}(mathcal {H}),) (u,vin mathcal {H},) and (0le theta le 1),

Moreover, we have (left( mathcal {U}_{(n,xi )}left( eta ,|langle mathcal {E}u,vrangle |,sqrt{leftlangle |mathcal {E}|^{2 theta } u,urightrangle leftlangle left| mathcal {E}^*right| ^{2(1-theta )} v, vrightrangle }right) right) _{n geqslant 0}) is an increasing sequence satisfying

which presents a novel refinement of the well-known mixed Schwartz inequality. Our results extend and refine well-established inequalities found in the literature.

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.