Asian-European Journal of Mathematics

In the year 2003, Srivastava–Gupta proposed a general family of linear positive operators, having some well-known operators as special cases. They investigated and established the rate of convergence of these operators for bounded variations. In the last decade for modified form of Srivastava–Gupta operators, several other generalizations also have been discussed. In this paper, we discuss the generalized modified Srivastava–Gupta operators considered in [H. M. Srivastava and V. Gupta, A certain family of summation-integral type operators, Math. Comput. Modelling 37(12–13) (2003) 1307–1315], by using iterative combinations in ordinary and simultaneous approximation. We may have better approximation in higher order of modulus of continuity for these operators.

In this paper, we introduce the concept of generalized asymmetric metric spaces and we prove some fixed point theorems in the setting of this metric spaces and also some illustrative examples are given. The presented results generalize and improve several results of the topics in the literature.

By using a recursive method, we determine the project completion time when the activity times are distributed according to a beta distribution. The $k$th moment of the maximum of non-identical independent random variables following this distribution-type is evaluated. Applicability and appropriateness of the beta model are illustrated by some examples, which show that the suggested estimate program evaluted and review technique of the project completion time is located between the lower bound estimate (PERT) and the upper estimate that was obtained by Kambarowski An upper bound on the expected completion time of PERT networks, Eur. J. Oper. Res. 21(2) (1985b) 206–212. Moreover, this estimate gives less values of the approximation errors than most of the other known estimates.

A group $G$ has the Basis Property if every subgroup $H$ of $G$ has an equivalent basis (minimal generating set). We studied a special case of the finite group with the Basis Property, when $p$-group $P$ is an abelian group. We found the necessary and sufficient conditions on an abelian $p$-group $P$ of $G$ with the Basis Property to be kernel of Frobenius group.

Several authors have introduced various types of coherent-like rings and proved analogous results on these rings. It appears that all these relative coherent rings and all the used techniques can be unified. In $n$-$\mathcal{𝒳}$-coherent rings, Int. Electron. J. Algebra, 7 (2010) 128–139, several coherent-like rings are unified. In this paper, we continue this work and we introduce coherent-like module which also emphasizes our point of view by unifying the existed relative coherent concepts. Several classical results are generalized and some new results are given.

In this paper, we prove the commutativity of the square in the chain level of both Chevalley Eilenberg complex of Lie homology and Hochschild complex, where the antisymmetrization map is used between the complexes. Originally, Loday proved this isomorphism by constructing a certain map satisfying relations of a presimplicial homotopy to prove the commutativity of the square mentioned above. Here, we present a different approach for the proof of the commutativity without constructing that certain map satisfying the relations of the presimplicial homotopy.

The motivation of this paper is to introduce Henstock–Orlicz space with non-absolute integrable functions. We prove that $C_0^{\infty }$ is dense in the Henstock–Orlicz space, which is not dense in the classical Orlicz space.

In this study, we use Lie symmetry method to reduce a generalized KdV equation with initial and boundary conditions with non-homogeneous variable coefficients to initial value problem. In particular, we concentrate on the cases that the reduced IVP cannot be solved analytically. We also compare the approximated solutions of IVP using numerical methods with IBVP, and note that they are more efficient than doing the same procedure for IBVP. In fact, it is shown that reducing IBVP to IVP and solving the reduced problem numerically will lead to more accurate solutions.

In this paper, we deal with a new class of Moufang–Klingenberg planes and study with the concepts of 4-transitivity and 6-figures on the class of planes. So, we reach some algebraic and geometric results related on the concepts. For instance, we show that the group of collineations of these planes acts transitively on 4-gons. Finally, we obtain some properties of 6-figures.

The main goal of this paper is to study properties of the linear canonical transform (LCT) on Schwartz-type space ${{𝒮}}_A(ℝ)$. The symbol class ${{𝒮}}_{\rho ,\sigma }^{m,A}$ is introduced. The pseudo-differential operator (p.d.o.) involving LCT is defined and also some of its properties including boundedness are investigated in Sobolev-type space. Kernel and integral representation of p.d.o. are obtained. Some applications of LCT to generalized partial differential equations and canonical convolution integral equation have been solved.

For a ring endomorphism $\alpha$, a generalization of semiprime rings and right p.q.-Baer rings, which we call quasi-Armendariz rings of skew Hurwitz series type (or simply, $\alpha$-${𝒮}{\mathscr{H}}{𝒬}{𝒜}$), is introduced and studied. It is shown that the ${𝒮}{\mathscr{H}}{𝒬}{𝒜}$-rings are closed upper triangular matrix rings, full matrix rings and Morita invariance. Some characterizations for the skew Hurwitz series ring $(HR,\alpha )$ to be quasi-Baer, generalized quasi-Baer, primary, nilary, reflexive, ideal-symmetric and semiprime are concluded.

In this paper, we introduce all Green’s relations on the ternary semihypergroup and study some properties of these equivalence relations in view of those obtained in binary and ternary semigroups. We also define crossed hyperproduct of two hypergroups.

In this paper, the concept of generalized weak contraction mapping in the setting of generating space of $b$-dislocated metric space endowed with partial order is introduced and some fixed-point theorems for the mappings in space satisfying the generalized weak contraction are proved. Example is also given in order to justify our main result.

In this study, we determine the analytic solutions of sequential space fractional differential equations with Dirichlet boundary conditions and initial conditions in one dimension. We constructed a Fourier series solution for the eigenfunctions of a corresponding Sturm–Liouville eigenvalue problem, including fractional derivative in Caputo sense using the separation of variables. We defined a new inner product with a weighted function to get coefficients in the Fourier series.

By making use of Wanas operator, we aim to introduce and investigate a certain family of univalent holomorphic functions with negative coefficients defined on complex Hilbert space. We present some important geometric properties of this family such as coefficient estimates, convexity, distortion and growth, radii of starlikeness and convexity. We also discuss the extreme points for functions belonging to this family.

This paper addresses linear quadratic control optimal problems for non-autonomous linear control systems using strongly continuous quasi semigroups. Riccati equations are implemented to investigate the control optimal problems of cost functional with finite and infinite horizons. The unique optimal pair for the cost functional is determined by the mild solution of the associated closed-loop problem and the feedback control of the solution of the corresponding Riccati equation. In addition for the infinite horizon, the stabilizability of the system is a sufficiency for the solvability to the Riccati equation. An application in a parabolic system is proposed.

For a given nonabelian finite group $G$ and $S\subseteq G\setminus Z(G),$ where $Z(G)$ denotes the center of $G,$ we introduce a new graph $\mathrm{\Gamma }(G,S)$ associated to the group $G$ as follows: Take $G\setminus (S\cup Z(G))$ as its vertex set and two distinct vertices $x$ and $y$ being adjacent if and only if there exists an element $s\in S$ such that $[x,s]=1=[y,s].$ This paper is devoted to investigate the properties of graphs $\mathrm{\Gamma }(G,S)$ and establish some graph theoretical properties. Moreover, we describe the planarity of these graphs when $\left|S\right|=1.$ Also, we provide some examples of finite nonabelian groups $G$ with the property that if $\mathrm{\Gamma }(G,S)\cong \mathrm{\Gamma }(H,S^{\prime })$ and $\left|S\right|=\left|S^{\prime }\right|=1$ for some group $H$ and $S^{\prime }\subseteq H\setminus Z(H),$ then $\left|G\right|=\left|H\right|.$

Let $R$ be a commutative ring and $M$ be an $R$-module. The compressed essential graph of $M$, denoted by $EG(M)$ is a simple undirected graph associated to $M$ whose vertices are classes of torsion elements of $M$ and two distinct classes $[m]$ and $[m^{\prime }]$ are adjacent if and only if ${\mathrm{\text{Ann}}}_R(m)+{\mathrm{\text{Ann}}}_R(m^{\prime })$ is an essential ideal of $R$. In this paper, we study diameter and girth of $EG(M)$ and we characterize all modules for which the compressed essential graph is connected. Moreover, it is proved that $\omega (EG(M))=|{\mathrm{\text{Ass}}}_R(M)|$, whenever $R$ is Noetherian and $M$ is a finitely generated multiplication module with $r({\mathrm{\text{Ann}}}_R(M))=0$.

The Franklin wavelet (piecewise linear wavelet) is a wavelet function $\psi \in L^2(ℝ)$ with dilation factor 2 which is continuous on $ℝ$, linear on $[k,k+\frac{1}{2}]$ and $[k+\frac{1}{2},k+1]$ for all $k\in \mathbb{Z}$; which is constructed from a multiresolution analysis(MRA) with a scaling function $\varphi \in L^2(ℝ)$ which is continuous on $ℝ$, linear on $[2k,2k+1]$ and $[2k+1,2k+2]$ for every $k\in \mathbb{Z}$. Wavelets with composite dilation factor have the ability to produce long and narrow window functions, with varied orientations, well-suited to applications of image processing; also it is more effective and flexible for the construction of multiscale image representation. This motivates us to consider the following problem to construct some composite dilation Franklin wavelets. Given a natural number $N\ge 2$, we ask, is there a continuous $\varphi \in L^2(ℝ)$ that is linear on $[Nk+Nl\alpha ,Nk+N(l+1)\alpha ]$ and $[Nk+N(N-1)\alpha ,Nk+N]$, for $l=0,1,\dots ,N-2$, $\alpha \in (0,\frac{1}{N-1})$ and for all $k\in \mathbb{Z}$, which generates an MRA with dilation factor $N$ to construct an orthonormal $N$- wavelet, i.e. a wavelet with dilation factor $N$? For $N=2$ and $\alpha \in (0,1)$ we have proved that $\varphi \in L^2(ℝ)$ generates an MRA with dilation factor $2$ only if $\alpha =\frac{1}{2}$. Next for $N=3,4$ and $\alpha \in (0,\frac{1}{N-1})\setminus \{\frac{1}{2N}\}$, we have proved that, if $\varphi \in L^2(ℝ)$ generates an MRA with dilation factor $N$, then $\alpha =\frac{1}{N}$. Also, for $\alpha =\frac{1}{N},N=2,3,4$, we have proved existence of a continuous $\varphi \in L^2(ℝ)$ which generates an MRA with dilation factor $N$. We have also constructed the corresponding orthonormal $N$-wavelet.

The aim of this paper is to introduce the concept of minimum independent dominating energy of a graph, compute it for some classes of graphs and to study its bounds.