in this paper, we introduce new classes $sum_{k,p,n}(alpha ,m,lambda ,l,rho )$ and $mathcal{t}_{k,p,n}(alpha ,m,lambda ,l,rho )$ of p-valent meromorphic functions defined by using the extended multiplier transformation operator. we use a strong convolution technique and derive inclusion results. a radius problem and some other interesting properties of these classes are discussed.

Abstract Let $E$ be an elliptic curve defined over a number field $K$, let $\alpha \in E(K)$ point of infinite order, and $N^{-1}\alpha $ the set $N$-division points in $E(\overline {K})$. We prove strong effective uniform results for degrees Kummer extensions $[K(E[N],N^{-1}\alpha ): K(E[N])]$. When $K=\mathbb Q$, under minimal (necessary) assumption on $, we show that inequality $[\mathbb Q(E...

Considering singular Sturm--Liouville differential expressions of the type \[ \tau_{\alpha} = -(d/dx)x^{\alpha}(d/dx) + q(x), \quad x \in (0,b), \; \alpha \mathbb{R}, \] we employ some Sturm comparison-type results in spirit Kurss to derive criteria for $\tau_{\alpha}$ be limit point and circle case at $x=0$. More precisely, if $\alpha \mathbb{R}$ $0 0$ such that $0<x$ sufficiently small, \begi...

The Three Gap Theorem states that for any $\alpha \in \mathbb{R}$ and $N \mathbb{N}$, the fractional parts of $\{ 0\alpha, 1\alpha, \dots, (N - 1)\alpha \}$ partition unit circle into gaps at most three distinct lengths. We prove a result about symmetries in order with which sizes appear on circle.

This paper deals with the study of global analysis following $(1,2)-$type system non-linear difference equations:\[ u_{n+1}=\frac{\alpha v_{n-1}}{\beta +\gamma v_{n}^{p}v_{n-2}^{q}},\ \ v_{n+1}=\frac{\alpha _{1}u_{n-1}}{\beta _{1}+\gamma _{1}u_{n}^{p}u_{n-2}^{q}},\ n=0,1,... \] where parameters $\alpha ,\beta ,\gamma ,\alpha _{1},\beta _{1},\gamma _{1,}p,q$ and initial conditions $u_{i},v_{i},$...

The main result of this paper refers to the boundedness orthogonal projection $$P_{\alpha }:L^{2}({\mathbb {R}}^{n},d\mu _{\alpha })\rightarrow {\mathcal {H}}_{\alpha }^{2}, n\ge 2 $$ associated harmonic Fock space $${\mathcal }^{2},$$ where $$d\mu }(x)=(\pi \alpha )^{-n/2}e^{-\frac{|x|^2}{\alpha }}dx.$$ We prove that operator }$$ is not bounded on $$L^{p}({\mathbb _{\beta })$$ when $$0<p< 1$$ ...

The aim of this paper is to present the new and interesting notionof ascending family of  $alpha $−n-norms corresponding to an intuitionistic fuzzy nnormedlinear space. The notion of best aproximation sets in an  $alpha $−n-normedspace corresponding to an intuitionistic fuzzy n-normed linear space is alsodefined and several related results are obtained.

Densities of particles on $${{{\textbf{R}}}^n}$$ which interact pairwise through an attractive-repulsive power-law potential $$W_{\alpha ,\beta }(x) = |x|^\alpha /\alpha -|x|^\beta /\beta $$ have often been used to explain patterns produced by biological and physical systems. In the mildly repulsive regime $$\alpha > \beta \ge 2$$ with $$n , we show there exists a decreasing homeomorphism _{\De...

Let $f\colon \mathbb N \rightarrow C $ be an arithmetic function and consider the Beatty set $\mathcal{B} (\alpha ) = \{ \lfloor {n\alpha }\rfloor : n\in \}$ associated to a real number $\alpha $, where $\lfloor {\xi }\rfloor$ denote