Asian-European Journal of Mathematics

In this work, we obtain an upper bound estimate for the second Hankel determinant of a subclass ${{𝒩}}_{\sigma }^{\mu }(\lambda ,t)$ of analytic bi-univalent function class $\sigma$ which is associated with Chebyshev polynomials in the open unit disk.

The aim of this work is to present the $k$-Pell, the $k$-Pell–Lucas and the Modified $k$-Pell sedenions and we give some properties involving these sequences, including the Binet-style formulae and the ordinary generating functions.

The area of $q$-calculus has attracted the serious attention of researchers. This great interest is due its application in various branches of mathematics and physics. The application of $q$-calculus was initiated by Jackson [Jackson, On $q$-definite integrals, Quart. J. Pure Appl. Math. 41 (1910) 193–203; On $q$-functions and a certain difference operator, Trans. Roy. Soc. Edinburgh 46 (1908) 253–281.], who was the first to develop $q$-integral and $q$-derivative in a systematic way. In this paper, we make use of the concept of $q$-calculus in the theory of univalent functions, to obtain the bounds for certain coefficient functional problems of $q$-starlike and $q$-convex functions. Further, we also obtain similar type of inequalities related to lemniscate of Bernoulli. The authors sincerely hope that this paper will revive this concept and encourage other researchers to work in this $q$-calculus in the near-future in the area of complex function theory. Also, we present a direct and shortened proof for the estimates of $|a_3-\mu a_2^2|$ found in [Mishra and Gochhayat, Fekete–Szego problem for $k$-uniformly convex functions and for a class defined by Owa–Srivastava operator, J. Math. Anal. Appl. 347(2) (2008) 563–572] for $f\in k-{𝒰}{𝒞}{𝒱}$, $0\le k<\infty$.

This paper continues the study of finite summation formulas of multivariable hypergeometric functions. Earlier, Wang and Chen [Finite summation formulas of double hypergeometric functions, Int. Transf. Spec. Funct. 28(3) (2016) 239–253] established finite summation formulas of double hypergeometric functions by using some well-known summation theorems. We present here finite summation formulas for Srivastava’s general triple hypergeometric function. Certain particular cases leading to finite summation formulas for Lauricella functions and Srivastava’s triple hypergeometric functions are also presented.

In this paper, we present a construction of hidden variable bivariate fractal interpolation functions (HVBFIFs) with function vertical scaling factors and estimate errors of HVBFIFs on perturbation of the function vertical scaling factor. We construct HVBFIFs on the basis of the iterated function system (IFS) with function vertical scaling factors. The perturbation of the function vertical scaling factors in the IFS causes a change in the HVBFIF. An upper estimation of the errors between the original HVBFIF and the perturbed HVBFIF is given.

The purpose of this paper is to present some new fixed point theorems for multifunctions, obtained by combining the methods of Suzuki and Samet and by using different conditions for generalized contractive multifunctions. Some examples are also considered.

The main purpose of the paper is to consider two Morita equivalent semirings $R$ and $S$ via Morita context $〈R,S{,}_R{P}_S{,}_S{Q}_R,𝜃,\varphi 〉$ instead of considering them via the equivalence of the resulting semimodule categories and then to investigate various Morita invariants related to each of the pairs $R,S$; $R,P$; $R,Q$; $S,Q$, etc.

Let $R$ be a commutative ring with identity and $𝔸(R)$ be the set of ideals of $R$ with nonzero annihilator. The annihilator-ideal graph of $R$, denoted by $A_{{ℐ}}(R)$, is a simple graph with the vertex set $𝔸{(R)}^{\ast }:=𝔸(R)\backslash \{(0)\}$, and two distinct vertices $I$ and $J$ are adjacent if and only if ${\mathrm{\text{Ann}}}_R(IJ)\ne {\mathrm{\text{Ann}}}_R(I)\cup {\mathrm{\text{Ann}}}_R(J)$. In this paper, we present some results on the bipartite, complete bipartite, outer planar and unicyclic of the annihilator-ideal graphs of a commutative ring. Among other results, bipartite annihilator-ideal graphs of rings are characterized. Also, we investigate planarity of the annihilator-ideal graph and classify rings whose annihilator-ideal graph is planar.

We discuss self-dual codes over the ring $R_{u,v}={𝔽}_2+u{𝔽}_2+v{𝔽}_2+uv{𝔽}_2,u^2=0,v^2=0,uv=vu$. We characterize the structure of self-dual, Type I codes and Type II codes over $R_{u,v}$ with given generator matrix in terms of the structure of their Torsion and Residue codes. We construct self-dual, Type I and Type II codes over $R_{u,v}$ for different lengths.

Recently, several authors used linear codes to construct secret sharing schemes. It is known that if each nonzero codeword of a code $C$ is minimal, then the dual code $C^{\perp }$ is suitable for secret sharing. To seek such codes Ashikhmin–Barg give a sufficient condition from weights; in ${[n,k,d]}_q$ code $C$, let $w_{min}$ and $w_{max}$ be the minimum and maximum nonzero weights, respectively. If

This paper gives lower and upper bounds on the covering radius of codes over ${\mathbb{Z}}_{p^2}$ with respect to Lee distance. We also determine the covering radius of various repetition codes over ${\mathbb{Z}}_{p^2}.$

Let $(I,A)$ be a pair of $n$-Lie algebras. Then, we introduce the concept of Schur multiplier of the pair $(I,A)$, denoted by ${ℳ}(I,A)$, and some inequalities for the dimension of ${ℳ}(I,A)$ are given. We also determine a necessary and sufficient condition, for which the Schur multiplier of a pair of $n$-Lie algebras can be embedded into the Schur multipliers of their $n$-Lie algebra factors. Moreover, some inequalities for the Schur multiplier of a pair of finite-dimensional nilpotent $n$-Lie algebras are acquired.

A bounded operator $T$ in a Banach space $X$ is said to satisfy the descent spectrum equality, if the descent spectrum of $T$ as an operator on $X$ coincides with the descent spectrum of $T$ as an element of the algebra $B(X)$ of all bounded linear operators on $X$. In this paper, we give some conditions under which the equality ${\sigma }_{\mathrm{\text{desc}}}(T)={\sigma }_{\mathrm{\text{desc}}}(T,B(X))$ holds for a single operator $T$.

In this paper, we are dealing with $\mathrm{\Gamma }$-semihypergroups which are a generalization of a semigroup, $\mathrm{\Gamma }$-semigroup and a semihypergroup. We introduce the notion of generalized quasi-$\mathrm{\Gamma }$-hyperideal i.e. of $(m,n)$-quasi-$\mathrm{\Gamma }$-hyperideal, $n$-right $\mathrm{\Gamma }$-hyperideal and $m$-left $\mathrm{\Gamma }$-hyperideal in $\mathrm{\Gamma }$-semihypergroups and different properties of them and relations between them are studied.

This paper introduces the concept of lattice vector space and establishes many important results. Also, this paper deals with linear transformations on lattice vector spaces and discusses their elementary properties. We prove that every finite dimensional lattice vector space is isomorphic to $V_n(L)$ and show that the set of all columns (or the set of all rows) of an invertible matrix over $L$ is a basis for $V_n(L)$.

We show that every complemented modular lattice can be converted into a left residuated lattice where the binary operations of multiplication and residuum are term operations. The concept of an operator left residuated poset was introduced by the authors recently. We show that every strongly modular poset with complementation as well as every strictly modular poset with complementation can be organized into an operator left residuated poset in such a way that the corresponding operators $M(x,y)$ and $R(x,y)$ can be expressed by means of the operators $L$ and $U$ in posets. We describe connections between the operator left residuation in these posets and the residuation in their lattice completion. We also present examples of strongly modular and strictly modular posets.

The authors consider generalized norms for different systems of infinite and noncyclic subgroups in nonperiodic groups. Relations between these norms are established. The conditions under which the given norms are Dedekind, in particular, central, are studied.