Afrika Matematika最新文献

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.

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 the 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 properties of the Cayley sum signed graph.

In this paper principal right congruences on completely 0-simple semigroups are identified which consequently leads to identifying principal right congruences on classes of semigroups namely, Brandt semigroups, right groups, left groups, right zero semigroups, left zero semigroups and rectangular bands. As a consequence of this characterization, we show that the class of right subdirectly irreducible completely 0-simple semigroups with more than 3 elements is that of cocyclic 0-groups. Moreover, we prove that right irreducible completely 0-simple semigroups with more than 3 elements are 0-groups for which nontrivial subgroups have nontrivial intersections.

In this study, the resolvent operator of the impulsive dynamic singular Sturm–Liouville problem is considered. The spectral function was first established. The integral representation of the resolvent operator is obtained using this function.

In this work, we establish exponential and polynomial decay results for a one-dimensional porous-elastic system with microtemperatures depending on the system’s parameters. Our results are new and improve some previous literature results where additional damping terms were required to establish the exponential decay result. We also present some numerical tests to illustrate our theoretical results.

This paper deals with the existence and uniqueness results for a class of non-coercive Dirichlet elliptic problems whose model example is

where (Omega ) is a bounded open subset of ({mathbb {R}}^N (Nge 2)), (1< p < N), (m>0), (0< beta <1), (q>0), |c| belongs to (L^{frac{N}{p-1}}(Omega )) and g is a continuous function in ({mathbb {R}}) which satisfies the sign condition and the data f belongs to (L^1(Omega )).