Asian-European Journal of Mathematics

In this paper, we have introduced and studied two-dimensional $(P,Q)$-Mellin transform which extends the known results of two-dimensional $Q$-Mellin transform. We provide its several basic properties, the appropriate convolution, the inversion formula and the Parseval-type relations. Some applications of $(P,Q)$-Mellin transform have been pointed out in solving integral equations. Finally, a Titchmarsh-type theorem has been proved.

In this paper, we study split generalized mixed equilibrium problem and fixed point problem in real Hilbert spaces with a view to analyze an iterative method for approximating a common solution of split generalized mixed equilibrium problem and fixed point problem of an infinite family of a quasi-nonexpansive multi-valued mappings. The iterative algorithm introduced in this paper is designed in such a way that it does not require the knowledge of the operator norm. We state and prove a strong convergence result of the aforementioned problems and also give application of our main result to split variational inequality problem. Our result complements and extends some related results in literature.

A set $S\subseteq V(G)$ of a graph $G$ is an $open$ $packing$ $set$ of $G$ if no two vertices of $S$ have a common neighbor in $G$. An open packing set $S$ is called an outer-connected open packing set (ocop-set) if either $S=V(G)$ or $〈V-S〉$ is connected. The minimum and maximum cardinalities of an ocop-set are called the lower outer-connected open packing number and the outer-connected open packing number, respectively, and are denoted by ${\rho }_{\mathrm{\text{loc}}}^o$ and ${\rho }_{\mathrm{\text{oc}}}^o$, respectively. In this paper, we initiate a study on these parameters.

In this paper, we study characteristic polynomials, determinants, inverses and Hadamard inverses of the Max and Min matrices with the hyper-Fibonacci numbers.

In this research paper, we generalized the results of Ignacy in the multivariate case in order to characterize the complex Wishart distribution.

The aim of paper is to find the condition under which a Fréchet-valued function $f\in C^{\infty }(\{0\})$ admitting meromorphic extension along some pencil of complex lines can be meromorphically extended to a neighborhood of $0\in {ℂ}^N.$ Some auxiliary results concerning the domains of existence for Fréchet-valued meromorphic functions, Rothstein’s theorem, Levi extension theorem for meromorphic functions with values in a locally complete space, convergence of formal power series of Fréchet-valued homogeneous polynomials are also proved in this work.

In this paper, we deal with the periodicity of solutions of the following general system rational of difference equations:

In 2016, the second and third authors introduced the notion of 2-Engelizer of an element $x$ in a given group $G$ and the set of all such $2$-Engelizers in $G$ denoted by $E^2(G)$. In this paper, among other results, we construct some upper and lower bounds for the probability of randomly chosen a pair of elements of a finite group to be $2$-Engel.

Ma–Minda class (of starlike functions) consists of normalized analytic functions $f$ defined on the unit disk for which the image of the function $z{f}^{\prime }(z)/f(z)$ is contained in some starlike region lying in the right-half plane. In this paper, we obtain the best possible bounds on some initial coefficients for the inverse functions of Ma–Minda starlike functions. Further, the bounds on the Fekete–Szegö functional and the second Hankel determinant are computed for such functions. In addition, some sharp radius estimates are also determined.

Let $G$ be a group given by a free presentation $G\cong F/R$. The 2-nilpotent multiplier of $G$ is the abelian group ${𝕄}^{(2)}(G)=(R\cap {\gamma }_3(F))/{\gamma }_3(R,F)$ which is invariant of $G$ [R. Baer, Representations of groups as quotient groups, I, II, and III, Trans. Amer. Math. Soc. 58 (1945) 295–419]. An effective approach to compute the 2-nilpotent multiplier of groups has been proposed by Burns and Ellis [On the nilpotent multipliers of a group, Math. Z. 226 (1997) 405–428], which is based on the nonabelian tensor product. We use this method to determine the explicit structure of ${𝕄}^{(2)}(G)$, when $G$ is a finite (generalized) extra special $p$-group. Moreover, the descriptions of the triple tensor product ${\otimes }^{3}G$, and the triple exterior product ${\wedge }^{3}G$ are given.

We introduce the concept of essentiality in a lattice $L$ with respect to an element $\delta \in L$. We define notions such as $\delta$-essential, $\delta$-uniform elements and obtain some of their properties. Examples of lattices are given wherein essentiality can be retained with respect to an arbitrary element (specifically, there are elements in $L$ which are $\delta$-essential but not essential). We prove Goldie analogue results in terms of $\delta$-uniform elements and $\delta$-∨-independent sets. Furthermore, we define a graph with respect to $\delta$-essential element in a lattice and study its properties.

This work deals with the mathematical inspection of a hybrid family of the degenerate polynomials of the Apostol-type. The inclusion of the derivation of few series expansion formulas, explicit representations and difference equations for this hybrid family brings a novelty to the existing literature. Moreover, certain connection formulas and several novel identities for these polynomials are established and investigated. The graphical representations of certain degenerate polynomials are explored and several new interesting pattern of the zeros are observed.

Interval interpolation formulae play a significant role to find the value of an unknown function at some points under interval uncertainty. The objective of this paper is to establish Newton’s divided interpolation formula for interval-valued functions using generalized Hukuhara difference of intervals. For this purpose, arithmetic of intervals, Hukuhara difference and its some properties and concept of interval-valued function have been discussed briefly. Using Hukuhara difference of intervals, the definition of Newton’s divided gH-difference for interval-valued function has been introduced. Then Newton’s divided gH-differences interpolation formula has been derived. Finally, with the help of some numerical examples, the proposed interpolation formula has been illustrated.

Let $R$ be a commutative ring with nonzero identity. The comaximal graph of $R$, denoted by $\mathrm{\Gamma }(R)$, is a simple graph with vertex set $R$, and two distinct vertices $a$ and $b$ are adjacent if and only if $Ra+Rb=R$. Let ${\mathrm{\Gamma }}_2(R)$ be an induced subgraph of $\mathrm{\Gamma }(R)$ with nonunit elements of $R$ as vertices. In this paper, we describe the normalized Laplacian spectrum of $\mathrm{\Gamma }({\mathbb{Z}}_n)$, and we determine it for some values of $n$, where ${\mathbb{Z}}_n$ is the ring of integers modulo $n$. Moreover, we investigate the normalized Laplacian energy and general Randic index of ${\mathrm{\Gamma }}_2({\mathbb{Z}}_n)$.

In this paper, we use the genus properties in critical point theory to prove the existence of infinitely many solutions for fractional $p$-Laplacian equations of Schrödinger-Kirchhoff type.

In this paper, we describe the structure of finite groups whose element orders or proper (abelian) subgroup orders form an arithmetic progression of ratio $r\ge 2$. This extends the case $r=1$ studied in previous papers [R. Brandl and W. Shi, Finite groups whose element orders are consecutive integers, J. Algebra 143 (1991) 388–400; Y. Feng, Finite groups whose abelian subgroup orders are consecutive integers, J. Math. Res. Exp. 18 (1998) 503–506; W. Shi, Finite groups whose proper subgroup orders are consecutive integers, J. Math. Res. Exp. 14 (1994) 165–166].

Bandelt and Petrich [Subdirect products of rings and distributive lattices, Proc. Edinburgh Math. Soc. (2) 25(2) (1982) 155–171] characterized a class of additive inverse semirings which are subdirect products of a distributive lattice and a ring. The aim of this paper is to characterize a class of additively regular semirings which are subdirect products of an idempotent semiring and a $b$-lattice of skew-rings.

In this paper, we present a method for constructing a Jacobi matrix $J\in {ℝ}^{n\times n}$ using $n$ known eigenvalues ${\lambda }_1,{\lambda }_2,\dots ,{\lambda }_n$. Some conditions are also given under which the constructed matrix is nonnegative and its diagonal entries are specified. Finally, we present a technique for constructing symmetric and nonsymmetric nonnegative matrices by their eigenvalues.

In this paper, we investigate certain subclass of  analytic functions on the open unit disc. This class generalizes the well-known class of $\alpha$-convex functions with respect to n-symmetric points. Some interesting properties such as subordination results, containment relations, integral preserving properties, and the integral representation for functions in this class are obtained.

The main purpose of this paper is to find upper bounds for the second and third Taylor–Maclaurin coefficients for two families of holomorphic and bi-univalent functions associated with Wanas operator. Further, we point out certain special cases for our results.

In this work, we define a new type of Eisenstein-like series by using Pell-Lucas numbers and call them the Pell-Lucas–Eisenstein Series. First, we show that the Pell-Lucas–Eisenstein series are convergent on their domain. Afterwards we prove that they satisfy some certain functional equations. Proofs follows from some on calculations on Pell-Lucas numbers.