Asian-European Journal of Mathematics

Let $R$ be a commutative semiring with identity $1\ne 0$. In this paper weakly $n$-absorbing ideal of $R$ which is a generalization of weakly prime ideal of $R$ is introduced and some related results are obtained.

Several subclasses of starlike functions are associated with regions in the right half plane of the complex plane, like half-plane, disks, sectors, parabolas and lemniscate of Bernoulli. For a normalized analytic function $f$ defined on the open unit disk $𝔻$ belonging to certain well-known classes of functions associated with the above regions, we investigate the radius $\rho$ such that, for the function $F(z)=f(\rho z)/\rho$, $z{F}^{\prime }(z)/F(z)$ lies in the lune defined by $\{w\in ℂ:|w^2-1|<2|w|\}$ for all $z\in 𝔻$.

In this paper, we introduce the concept of set-valued Prešić–Reich type contractive condition in ultrametric spaces and establish the existence and uniqueness of coincidence and common fixed point of a set-valued and a single-valued mapping besides furnishing illustrative examples to highlight the realized improvements in the context of ultrametric spaces. Our results generalize and extend some known results in the literature.

By using a linear operator associated with the Hurwitz–Lerch zeta function, which is defined here by means of the Hadamard product (or convolution), the authors introduce and investigate certain inclusion relationships of certain subclass of univalent meromorphic functions defined in the punctured unit disc.

In this paper, we study CR-warped product submanifolds of $T$-manifolds. We prove that the CR-warped product submanifolds with invariant fiber are trivial warped products and provide a characterization theorem of CR-warped products with anti-invariant fiber of $T$-manifolds. Moreover, we develop an inequality of CR-warped product submanifolds for the second fundamental form in terms of warping function and the equality cases are considered. Also, we find a necessary and sufficient condition for compact oriented CR-warped products turning into CR-products of $T$-space forms.

Let $A$ be a unital prime Banach algebra over complex field $ℂ$ with unity and $g$ be a nonzero continuous linear generalized derivation associated with a nonzero continuous linear derivation $d$. In this paper, we investigate the commutativity of $A$. In particular, we prove that a unital prime Banach algebra $A$ is commutative if one of the following holds; (i) either $g({(xy)}^n)+\mu d(x^n)d(y^n)+\nu [x^n,y^n]=0$ or $g({(xy)}^n)+\mu d(y^n)d(x^n)+\nu [y^n,x^n]=0$, (ii) either $g({(xy)}^n)+\mu [d(x^n),d(y^n)]+\nu [x^n,y^n]=0$ or $g({(xy)}^n)+\mu [d(y^n),d(x^n)]+\nu [y^n,x^n]=0$, for sufficiently many $x,y$, for any complex numbers $\mu ,\nu$ and an integer $n=n(x,y)>1$.

In this paper, we propose a new primal-dual path-following interior-point method for semidefinite optimization based on a new reformulation of the nonlinear equation of the system which defines the central path. The proposed algorithm takes only full Nesterov and Todd steps and therefore no line-searches are needed for generating the new iterations. The convergence of the algorithm is established and the complexity result coincides with the best-known iteration bound for semidefinite optimization problems.

In this paper, an approximate solution for solving weakly singular kernel partial integro-differential equations with time fractional order is proposed. The method is based on using a second-order time difference approximation followed by applying the fractional integral operator and piecewise linear interpolation to compute the singularity of the kernel that appear in the discretization process. The stability of the method is also considered in the sense of von Neumann analysis. Numerical examples are solved to demonstrate the validity and applicability of the presented technique.

In this paper, we study a $n$th-order impulsive eigenvalue problem with an advanced argument. We shall establish several criteria for the optimal intervals of the parameter $\lambda$ so as to ensure existence of single or many positive solutions. Our methods are based on transformation technique, Hölder’s inequality and the eigenvalue theory.

In this paper, we generalize Nadler’s result by establishing the existence and uniqueness of coincidence and common fixed points of Nadler’s type set-valued mappings in ultrametric spaces. Examples are given to illustrate the results. As an application, well-posedness of a common fixed point problem is proved. The presented results generalize many known results in literature in the framework of ultrametric spaces.

Let $R$ be an associative ring with identity. A ring $R$ is called reversible if $ab=0$, then $ba=0$ for $a,b\in R$. The total graph of unfaithful submodules of a module $M$ over a reversible ring $R$, denoted by ${\mathrm{\Gamma }}_R(M)$, is a graph whose vertices are all nonzero unfaithful submodules of $M$ and two distinct vertices $A$ and $B$ are adjacent if $A+B$ is unfaithful. In this paper, we determine the diameter and girth of ${\mathrm{\Gamma }}_R(M)$. Also, we study some combinatorial properties of ${\mathrm{\Gamma }}_R(M)$ such as independence number and clique number. Moreover, we study the case that the degree of a vertex of ${\mathrm{\Gamma }}_R(M)$ is finite.

In this work, we introduce some properties of a complex fractional differential operator. The boundedness and some other properties are studied in view of geometric function theory.

Let $L$ be a non-abelian nilpotent Lie algebra of dimension $n$ and put $s(L)=\frac{1}{2}(n-1)(n-2)+1-\mathrm{\text{dim}}{ℳ}(L)$, where ${ℳ}(L)$ denotes the Schur multiplier of $L$. Niroomand and Russo in 2011 proved that $s(L)\ge 0$ and that $s(L)=0$ if and only if $L\cong H(1)\oplus F(n-3)$, in which $H(1)$ is the Heisenberg algebra of dimension $3$ and $F(n-3)$ is the abelian $(n-3)$-dimensional Lie algebra. In the same year, they also classified all nilpotent Lie algebras $L$ satisfying $s(L)=1$ or $2$. In this paper, we obtain all nilpotent Lie algebras $L$ provided that $s(L)=3$.

In this paper, we construct Kantorovich type Szász–Mirakjan operators generated by Dunkl generalization of the exponential function via $q$-integers. We obtain some approximation results via well-known Korovkin’s type theorem for these operators and study convergence properties by using the modulus of continuity. Furthermore, we obtain the rate of convergence in terms of the classical, second-order, and weighted modulus of continuity.

In this paper, we introduce the concept of quasi-convex functions by considering a subclass ${{𝒞}}_p^{\ast }(\lambda ,\beta )$ of normalized analytic functions in the unit disk $𝕌$ for some convex function $g(z)$ with fixed second coefficient of order $\lambda$, such that

The set of all pairs of positive integers is considered as a directed set under the direction: $(m,n)\le (i,j)$ if and only if $m\le i$ and $n\le j$. This directed set is used for Pringsheim-type convergence of double sequences. Consequences of uniform boundedness principle through double sequences are derived in this paper.

The method of transformation of a linear system of evolution equations into the system of Riccati-type equations is elaborated. It is shown that the system of generalized Riccati equations is governed by the characteristic polynomial of $n$-order generator matrix of the linear system of evolution equations. Solutions of the generalized Riccati equations are presented by roots of the polynomial function, whose coefficients constitute the solutions of the linear system of evolution equations. An inverse mapping from the solutions of generalized Riccati equations onto the solutions of the linear evolution equations is constructed.

The fractional derivative operator is an extension of the usual derivative operator $D^n$ to an arbitrary (integer, rational, irrational or complex) values of $n$. In this paper, weighted fractional differentiation composition operators from mixed-norm spaces to Zygmund spaces are characterized in terms of boundedness and compactness.

Given a group $G$, we study right and left zeros, idempotents, the minimal ideal, left cancelable and right cancelable elements of the semigroup $N_k(G)$ of $k$-linked upfamilies and characterize groups $G$ whose extensions $N_k(G)$ are commutative. We finish the paper with the complete description of the structure of the semigroups $N_k(G)$ for all groups $G$ of cardinality $\left|G\right|\le 4$.

The current note is devoted to investigate the trees, which maximize or minimize the reduced second Zagreb index among all $n$-vertex trees with fixed number of segments. This note also involves development of some results, which may be used to characterize the extremal trees with respect to the aforementioned index among all $n$-vertex trees having fixed number of branching vertices.