Bulletin of the Malaysian Mathematical Sciences Society最新文献

The primary objective of this research article is to introduce and study an approximation operator involving the Tricomi function by using Korovkin’s theorem and a conventional method based on the modulus of continuity. In Lipschitz-type spaces, we demonstrate the rate of convergence, and we are also able to determine the convergence properties of our operators. In addition, we illustrate the convergence of our proposed operators using various graphs and error-estimating tables for numerical instances.

In this paper we establish an angular characteristic for the class of quasimöbius mappings in metric spaces.

This paper is motivated by the problem of determining the related chromatic numbers of some hypergraphs. A hypergraph (Pi _{q}(n,k)) is defined from a projective space PG((n-1,q)), where the vertices are points and the hyperedges are ((k-1))-dimensional subspaces. For the perfect balanced rainbow-free colorings, we show that ({overline{chi }}_{p}(Pi _{q}(n,k))=frac{q^n-1}{l(q-1)}), where (kge lceil frac{n+1}{2}rceil ) and l is the smallest nontrivial factor of (frac{q^n-1}{q-1}). For the complete colorings, we prove that there is no complete coloring for (Pi _{q}(n,k)) with (2le k<n). We also provide some results on the related chromatic numbers of subhypergraphs of (Pi _{q}(n,k)).

A greedy block extended Kaczmarz method is introduced for solving the least squares problem where the greedy rule combines the maximum-distances with relaxation parameters. In order to save the computational cost of Moore–Penrose inverse, an average projection technique is used. The convergence theory of the greedy block extended Kaczmarz method is established and an upper bound for the convergence rate is also derived. Numerical experiments show that the proposed method is efficient and better than the randomized block extended Kaczmarz methods in terms of the number of iteration steps and computational time.

In this paper, we study a general class of half-linear difference equations. Applying a version of the discrete Riccati transformation, we prove a non-oscillation criterion for the analyzed equations. In the formulation of the criterion, we do not use auxiliary sequences, but we consider directly the coefficients of the treated equations. Since the obtained criterion is new in many cases, we also formulate new simple corollaries and mention illustrative examples.

While a number of bounds are known on the zero forcing number Z(G) of a graph G expressed in terms of the order of a graph and maximum or minimum degree, we present two bounds that are related to the (upper) total domination number (gamma _t(G)) (resp. (Gamma _t(G))) of G. We prove that (Z(G)+gamma _t(G)le n(G)) and (Z(G)+frac{Gamma _t(G)}{2}le n(G)) holds for any graph G with no isolated vertices of order n(G). Both bounds are sharp as demonstrated by several infinite families of graphs. In particular, we show that every graph H is an induced subgraph of a graph G with (Z(G)+frac{Gamma _t(G)}{2}=n(G)). Furthermore, we prove a characterization of graphs with power domination equal to 1, from which we derive a characterization of the extremal graphs attaining the trivial lower bound (Z(G)ge delta (G)). The class of graphs that appears in the corresponding characterizations is obtained by extending an idea of Row for characterizing the graphs with zero forcing number equal to 2.

We describe the structure of those finite groups whose maximal subgroups are either 2-nilpotent or normal. Among other properties, we prove that if such a group G does not have any non-trivial quotient that is a 2-group, then G is solvable. Also, if G is a solvable group satisfying the above conditions, then the 2-length of G is less than or equal to 2. If, on the contrary, G is not solvable, then G has exactly one non-abelian principal factor and the unique simple group involved is one of the groups (textrm{PSL}_2(p^{2^a})), where p is an odd prime and (age 1), or p is a prime satisfying (pequiv pm 1) ((textrm{mod}~ 8)) and (a=0).

This article focuses on the improvement of the classic Bohr’s inequality for bounded analytic functions on the unit disk. We give some sharp versions of Bohr’s inequality, generalizing the previous results.

The usual theory of negative type (and p-negative type) is heavily dependent on an embedding result of Schoenberg, which states that a metric space isometrically embeds in some Hilbert space if and only if it has 2-negative type. A generalisation of this embedding result to the setting of bi-lipschitz embeddings was given by Linial, London and Rabinovich. In this article we use this newer embedding result to define the concept of distorted p-negative type and extend much of the known theory of p-negative type to the setting of bi-lipschitz embeddings. In particular we show that a metric space ((X,d_{X})) has p-negative type with distortion C ((0le p<infty ), (1le C<infty )) if and only if ((X,d_{X}^{p/2})) admits a bi-lipschitz embedding into some Hilbert space with distortion at most C. Analogues of strict p-negative type and polygonal equalities in this new setting are given and systematically studied. Finally, we provide explicit examples of these concepts in the bi-lipschitz setting for the bipartite graphs (K_{m,n}).

In this paper, with the help of potential function, we extend the classical Brezis–Lieb lemma on Euclidean space to graphs, which can be applied to the following Kirchhoff equation

on a connected locally finite graph (G=(mathbb {V}, mathbb {E})), where (b, lambda >0), (p>2) and V(x) is a potential function defined on (mathbb {V}). The purpose of this paper is four-fold. First of all, using the idea of the filtration Nehari manifold technique and a compactness result based on generalized Brezis–Lieb lemma on graphs, we prove that there admits a positive solution (u_{lambda , b} in E_lambda ) with positive energy for (b in (0, b^*)) when (2<p<4). In the sequel, when (p geqslant 4), a positive ground state solution (w_{lambda , b} in E_lambda ) is also obtained by using standard variational methods. What’s more, we explore various asymptotic behaviors of (u_{lambda , b}, w_{lambda , b} in E_lambda ) by separately controlling the parameters (lambda rightarrow infty ) and (b rightarrow 0^{+}), as well as jointly controlling both parameters. Finally, we utilize iteration to obtain the (L^{infty })-norm estimates of the solution.