In this work, by considering a general subclass of univalent functions and using the Chebyshev polynomials, we obtain coefficient expansions for functions in this class.

In this work, by considering a general subclass of univalent functions and using the Chebyshev polynomials, we obtain coefficient expansions for functions in this class.

In this paper, we obtain lower and upper bounds on the number of parity check digits of a linear code that corrects $e$ or less errors within a sub-block. An example of such a code is provided. We introduce blockwise-tensor product of matrices and using this, we propose classes of error locating codes (or EL-codes) that can detect $e$ or less errors within a sub-block and locate several such corrupted sub-blocks.

Let $G$ be a finite group and let $X$ be a conjugacy class of $G.$ The rank of $X$ in $G,$ denoted by $rank(G{:}X)$ is defined to be the minimal number of elements of $X$ generating $G.$ In this paper we review the basic results on generation of finite simple groups and we survey the recent developments on computing the ranks of finite simple groups.

In the present paper we introduce and study some generalized $I$-convergent sequence spaces of interval numbers defined by an infinite matrix and a Musielak-Orlicz function. We also make an effort to study some topological and algebraic properties of these spaces.

We consider a more general class than the class of Schur multipliers namely the Abel-Schur multipliers, which in turn coincide with the bounded linear operators on $\ell_{2}$ preserving the diagonals. We extend to the matrix framework Theorem 2.4 (a) of a paper of Anderson, Clunie, and Pommerenke published in 1974, and as an application of this theorem we obtain a new proof of the necessity of an old theorem of Hardy and Littlewood in 1941.

Let $\mathbb{T}$ be a periodic time scale. We use a fixed point theorem due to Krasnoselskii to show that the nonlinear neutral dynamic equation with infinite delay \[ x^{\Delta}(t)=-a(t)x^{\sigma}(t)+\left( Q(t,x(t-g(t))))\right) ^{\Delta }+\int_{-\infty}^{t}D\left( t,u\right) f\left( x(u)\right) \Delta u,\ t\in\mathbb{T}, \] has a periodic solution. Under a slightly more stringent inequality we show that the periodic solution is unique using the contraction mapping principle. Also, by the aid of the contraction mapping principle we study the asymptotic stability of the zero solution provided that $Q(t,0)=f(0)=0$. The results obtained here extend the work of Althubiti, Makhzoum and Raffoul [1].

In this paper, we present certain new $L_p$ inequalities for $\mathcal B_{n}$-operators which include some known polynomial inequalities as special cases.

The aim of this paper is that of discussing closed graph theorems for bornological vector spaces in a self-contained way, hoping to make the subject more accessible to non-experts. We will see how to easily adapt classical arguments of functional analysis over $\mathbb R$ and $\mathbb C$ to deduce closed graph theorems for bornological vector spaces over any complete, non-trivially valued field, hence encompassing the non-Archimedean case too. We will end this survey by discussing some applications. In particular, we will prove De Wilde's Theorem for non-Archimedean locally convex spaces and then deduce some results about the automatic boundedness of algebra morphisms for a class of bornological algebras of interest in analytic geometry, both Archimedean (complex analytic geometry) and non-Archimedean.