Asian-European Journal of Mathematics

We aim to estimate coefficient inequalities for some new subfamilies of close-to-convex functions, which are here, defined by generalized differential operator and Cauchy–Euler type non-homogeneous differential equation. The results presented here would extend, unify and improve some recent results in literature.

Let $R$ be a ring and $M$ be a right $R$-module. In this paper, we introduce the set $Z_R(M)=\{r\in R|Nr=0,$ for some essential submodule $N$ of $M\}$ of singular elements of$R$ with respect to$M$ , and we investigate the properties of it. For example, it is shown that $Z_R(M)$ is an ideal of $R$ and $Z_R(M)={\bigcup }_{N{\le }_{e}M}{\mathrm{\text{ann}}}_r^R(N)$. Also if $R$ is a semiprime right Goldie ring, then $Z_R(R_R)=Z(R_R)=0$, where $Z(R_R)$ is the right singular ideal of $R$. We prove that if $M$ is a semisimple module or a prime module, then $Z_R(M)={\mathrm{\text{ann}}}_r^R(M)$. For any submodule $N$ of $M$, we have $Z_R(M)\subseteq Z_R(N)$ and if $N{\le }_{e}M$, then $Z_R(M)=Z_R(N)$. We show that $Z_{R[X]}(R[X])=(Z_R(R))[X]$ and $Z_{M_n(R)}(M_n(R))=M_n(Z_R(R))$. In the end, the singular elements of some rings with respect to the formal triangular matrix ring are investigated.

In this paper, we discuss the validity of the result of Khuangsatung and Kangtunyakarn [Existence and convergence theorem for fixed point problem of various nonlinear mappings and variational inequality problems without some assumptions, Filomat 32(1) (2018) 305–309].

Let $k$ be a number field and $k_2^{(1)}$ (respectively, $k_2^{(2)}$) its first (respectively, second) Hilbert $2$-class field. Let $G=\mathrm{\text{Gal}}(k_2^{(2)}/k)$ be the Galois group of $k_2^{(2)}/k$. The purpose of this note is to determine the structure of $G$ for some special Dirichlet fields $k=\mathbb{Q}(\sqrt{d},\sqrt{-1})$.

For a simple and connected graph $G$ with $n$ vertices and the minimum degree two, we show that $H(G)\ge 4+\frac{1}{n-1}-\frac{12}{n+1}$ by a technique based on linear programming, where $H(G)$ is the harmonic index of a graph $G$, defined as the sum of the weights $\frac{2}{d_u+d_v}$ of all edges $uv$ of $G$, $d_u$ denotes the degree of a vertex $u$, and characterize the graph with the minimum value.

Let $L$ be a Lie algebra crossed module. In this paper, we shall introduce a chain of crossed modules of $\mathrm{\text{Act}}(L)$ and show that if $M$ and $L$ are two isoclinic crossed modules, then ${\mathrm{\text{ID}}}^{\ast }\mathrm{\text{Act}}(L)\cong {\mathrm{\text{ID}}}^{\ast }\mathrm{\text{Act}}(M)$.

Hypergroup is the generalized concept of group introduced first by Marty. Since then, the study of it and its applications has been of great importance. This paper deals with representations of the hypergroup associated to the braid group $B_n$. First, we define our hypergroup $(B_n,\star )$ and our semihyperring $(P,\oplus ,\odot )$ over the set of non-negative integers. Next, we construct non-trivial matrix representations of $B_n$ of degree $k$, for all $k\in \mathbb{N}$. Finally, we find all matrix representations of $(B_n,\star )$ with degree less than $3$ and classify them according to irreducibility and unitarizability.

In any network, the diameter is often taken as a measure of efficiency, as it measures the maximum communication delay. The fact that addition or deletion of edges changes the diameter gives rise to the concept of diameter variability. Its study becomes important as it determines the communication efficiency when an addition or deletion of a link occurs in a network. Two other important graph parameters considered as a measure of reliability and efficiency of networks are wide diameter and fault diameter. In this paper, we study these diameter notions of the Fibonacci cubes.

In this paper, we establish existence and uniform asymptotic stability of unique positive almost periodic solutions for three-species Lotka–Volterra competitive system on time scales by using Lyapunov functional method.

Nonlinear conjugate gradient (CG) methods are widely used for solving large scale unconstrained optimization problems. Many studies have been devoted to develop and improve these methods. In this paper, we aim to study the global convergence of the BBB conjugate gradient method with exact line search.

In this paper, we introduce the notion of ∗-$K$-operator frame as a generalization of the notion of $K$-operator frame and we study the corresponding frame operator. It is completed by a result on the frame operator of the tensor product of two frame operators.

The composition $F(f(x))$ of a distribution $F(x)$ and a locally summable function $f(x)$ is defined as the neutrix limit of the regular sequence $\{F_n(f(x))\}.$ In this paper, we prove that the neutrix composition of the distributions $x_{-}^{\lambda }{ln}^s{x}_{-}$ and $x_{+}^{-r/\lambda }$ exists and equals

Let $k$ be a fixed integer, we define the multiplicative function $D_k(n)=\frac{d_k(n)}{d_k^{\ast }(n)}$, where $d_k(n)$ is the Piltz divisor function and $d_k^{\ast }$ is the unitary analogue function of $d_k$. The main purpose of this paper to use elementary methods to study the mean value of the function $D_k(n)$.

We introduce $\alpha$-coupled fixed point for $𝜃$-contractions in the space of bounded functions on a set $S$. As an application of our result, we prove the existence and uniqueness of solutions for a class of systems of functional equations arising in dynamic programming.

In 2012, Sulaiman [Reverses of Minkowski’s, Hölder’s, and Hardy’s integral inequalities, Int. J. Mod. Math. Sci. 1(1) (2012) 14–24] proved integral inequalities concerning reverses of Minkowski’s and Hardy’s inequalities. In 2013, Banyat Sroysang obtained a generalization of the reverse Minkowski’s inequality [More on reverses of Minkowski’s integral inequality, Math. Aeterna 3(7) (2013) 597–600] and the reverse Hardy’s integral inequality [A generalization of some integral inequalities similar to Hardy’s inequality, Math. Aeterna 3(7) (2013) 593–596]. In this article, two results are given. First one is further improvement of the reverse Minkowski inequality and second is further generalization of the integral Hardy inequality.

A module which is invariant under automorphisms of its injective envelope is called an automorphism-invariant module. The class of automorphism-invariant modules was introduced and investigated by Lee and Zhou in 2013. In this paper, we study the class of modules which are invariant under all nilpotent endomorphisms of their injective envelopes of index two, such as modules are called 2-nilpotent-invariant. Many basic properties are obtained. For instance, it is proved that a nonsingular module $M$ is a weak duo 2-nilpotent-invariant module if and only if $\mathrm{\text{End}}(E(M))$ is a strongly regular ring. For the ring $R$ satisfying every cyclic right $R$-module is 2-nilpotent-invariant, we prove that $R\cong R_1\times R_2$, where $R_1,R_2$ are rings which satisfy $R_1$ is a semi-simple Artinian ring and $R_2$ is square-free as a right $R_2$-module and all idempotents of $R_2$ is central.

The (W.C.C) condition was developed by K.P.R. Rao et al. in 2013 which established common fixed point results in partial metric spaces. By using Hausdorff metric-like space, we obtain Suzuki type common fixed point theorems for hybrid pair of maps in metric-like spaces. We observe different conditions about maps to obtain a fixed point. In addition, as consequence of our main result, we study the existence of a common solution for a class of functional equations originating in dynamic programming.

In this paper, we consider an optimization model for solving the nonmonotone affine variational inequalities problem (AVI). It is formulated as a DC (Difference of Convex functions) program for which DCA (DC Algorithms) are applied. The resulting DCA are simple: it consists of solving successive convex quadratic program. Numerical experiments on several test problems illustrate the efficiency of the proposed approach in terms of the quality of the obtained solutions and the speed of convergence.