# Arabian Journal of Mathematics

## List of Papers (Total 201)

#### On dynamic coloring of certain cycle-related graphs

Coloring the vertices of a particular graph has often been motivated by its utility to various applied fields and its mathematical interest. A dynamic coloring of a graph G is a proper coloring of the vertex set V(G) such that for each vertex of degree at least 2, its neighbors receive at least two distinct colors. A dynamic k-coloring of a graph is a dynamic coloring with k...

#### q-Difference equations for the 2-iterated q-Appell and mixed type q-Appell polynomials

In this article, the authors establish the recurrence relations and q-difference equations for the 2-iterated q-Appell polynomials. The recurrence relations and the q-difference equations for the 2-iterated q-Bernoulli polynomials, the q-Euler polynomials and the q-Genocchi polynomials are also derived. An analogous study of certain mixed type q-special polynomials is also...

#### Pointwise minimal extensions

We characterize pointwise minimal extensions of rings, introduced by Cahen et al. (Rocky Mt J Math 41:1081–1125, 2011), in the special context of domains. We show that pointwise minimal extensions are either integral or integrally closed. In the closed case, they are nothing but minimal extensions. Otherwise, there are four cases: either all minimal sub-extensions are of the same...

#### Stability of 2nd conjugate Banach algebras

In general the stability of normed algebras is a non hereditary property. We shall prove that second conjugate Banach algebras may be non stable even if the underlying Banach algebra is stable. We shall characterize stability of second conjugate Banach algebras. Finally, we shall study kinds of stability induced on an algebra with an stable second conjugate algebra.

#### Conformable fractional approximations by max-product operators using convexity

Here, we consider the approximation of functions by a large variety of max-product operators under conformable fractional differentiability and using convexity. These are positive sublinear operators. Our study relies on our general results about positive sublinear operators. We derive Jackson-type inequalities under conformable fractional initial conditions and convexity. So our...

In this paper, we study various arithmetic properties of the function $$\overline{p}_{2,\,\, k}(n)$$, which denotes the number of $$(2,\,\, k)$$-regular overpartitions of n with odd $$k > 1$$. We prove several infinite families of congruences modulo 8 for $$\overline{p}_{2,\,\, k}(n)$$. For example, we find that for all non-negative integers $$\beta , n$$ and $$k\equiv 1\pmod {8... #### Refinements on the discrete Hermite–Hadamard inequality In this paper, we use techniques and tools from time scale calculus to state and prove many refinements on the discrete Hermite–Hadamard inequality. Open image in new window #### On formulae for the determinant of symmetric pentadiagonal Toeplitz matrices We show that the characteristic polynomial of a symmetric pentadiagonal Toeplitz matrix is the product of two polynomials given explicitly in terms of the Chebyshev polynomials. #### Evaluation of various partial sums of Gaussian q-binomial sums We present three new sets of weighted partial sums of the Gaussian q-binomial coefficients. To prove the claimed results, we will use q-analysis, Rothe’s formula and a q-version of the celebrated algorithm of Zeilberger. Finally we give some applications of our results to generalized Fibonomial sums. Open image in new window #### On wave equation: review and recent results The aim of this paper is to give an overview of results related to nonlinear wave equations during the last half century. In this regard, we present results concerning existence, decay and blow up for classical nonlinear equations. After that, we discuss briefly some important results of the variable-exponent Lebesgue and Sobolev spaces. Results related to nonexistence and blow... #### Weighted majorization inequalities for n-convex functions via extension of Montgomery identity using Green function New identities and inequalities are given for weighted majorization theorem for n-convex functions by using extension of the Montgomery identity and Green function. Various bounds for the reminders in new generalizations of weighted majorization formulae are provided using Čebyšev type inequalities. Mean value theorems are also discussed for functional related to new results. #### On Picard value problem of some difference polynomials In this paper, we study the value distribution of zeros of certain nonlinear difference polynomials of entire functions of finite order. #### General solution for MHD-free convection flow over a vertical plate with ramped wall temperature and chemical reaction The aim of the article is to study the unsteady magnetohydrodynamic-free convection flow of an electrically conducting incompressible viscous fluid over an infinite vertical plate with ramped temperature and constant concentration. The motion of the plate is a rectilinear translation with an arbitrary time-dependent velocity. Closed-form solutions for the temperature... #### Stability and nonstability of octadecic functional equation in multi-normed spaces In this paper, we introduce octadecic functional equation. Moreover, we prove the stability of the octadecic functional equation in multi-normed spaces by using the fixed point method. #### Non-differentiability and fractional differentiability on timescales This work deals with concepts of non-differentiability and a non-integer order differential on timescales. Through an investigation of a local non-integer order derivative on timescales, a mean value theorem (a fractional analog of the mean value theorem on timescales) is presented. Then, by illustrating a vanishing property of this derivative, its objectivity is discussed. As a... #### NSE characterization of the Chevalley group \(\varvec{G}_{\varvec{2}} {\varvec{(4)}}$$

Let G be a group and $$\omega (G)=\{o(g)|g\in G\}$$ be the set of element orders of G. Let $$k\in \omega (G)$$ and $$s_k=|\{g\in G |o(g)=k\}|$$. Let $$nse(G)=\{s_k|k\in \omega (G) \}$$. In this paper, we prove that if G is a group and $$G_2 (4)$$ is the Chevalley group such that $$nse(G)=nse(G_2 (4))$$, then $$G\cong G_2 (4)$$.

#### Methods of the theory of critical points at infinity on Cauchy Riemann manifolds

Sub-Riemannian spaces are spaces whose metric structure may be viewed as a constrained geometry, where motion is only possible along a given set of directions, changing from point to point. The simplest example of such spaces is given by the so-called Heisenberg group. The characteristic constrained motion of sub-Riemannian spaces has numerous applications in robotic control in...

#### Fractional parts and their relations to the values of the Riemann zeta function

A well-known result, due to Dirichlet and later generalized by de la Vallée–Poussin, expresses a relationship between the sum of fractional parts and the Euler–Mascheroni constant. In this paper, we prove an asymptotic relationship between the summation of the products of fractional parts with powers of integers on the one hand, and the values of the Riemann zeta function, on the...

#### Hyponormality of generalised slant weighted Toeplitz operators with polynomial symbols

For a sequence of positive numbers $$\beta =\{\beta _{n}\}_{n\in \mathbb {Z}}$$, the space $$L^2(\beta )$$ consists of all $$f(z)=\sum _{-\infty }^\infty a_nz^n$$, $$a_n\in \mathbb {C}$$ for which $$\sum _{-\infty }^\infty |a_n|^2\beta _n^2<\infty$$. For a bounded function $$\varphi (z)=\sum _{-\infty }^\infty a_nz^n$$, the slant weighted Toeplitz operator \(A_\varphi ^{(\beta...