201321

Code: 201321

Some Convolution and Inclusion Properties for Subclasses of Meromorphic p-Valent Functions Involving Integral Operator

R. M. El-Ashawah

 

Abstracts

Making use of the linear operator <img height="39" border="0" style="vertical-align:bottom" width="291" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0252960213601204-si1.gif">${ℒ}_p^m\left(\lambda ,\mathcal{l}\right)f\left(z\right)=\frac{1}{z^p}+\sum _{k=1}^{\infty }{\left[\frac{\mathcal{l}}{\mathcal{l}+\lambda k}\right]}^m{a}_k{z}^{k-p,}$ where l>0,λ>0,p∈ℕ,m∈ℕ₀=ℕ∪{0},z∈U*$\mathcal{l}>0,\lambda >0,p\in \text{ℕ},m\in {\text{ℕ}}_0=\text{ℕ}\cup \left\{0\right\},z\in U*$ and f(z)∈Σp,$f\left(z\right)\in {\Sigma }_{\text{p}},$ we introduce two subclasses of meromorphic p-valent analytic functions and investigate convolution and inclusion properties for these classes

 

 

201316

Code: 201316

Properties of the Convolution with Prestarlike Functions 

Jacek Dziok

 

Abstracts

In the paper we investigate convolution properties related to the prestarlike functions and various inclusion relationships between defined classes of functions. Interesting applications involving the well-known classes of functions defined by linear operators are also considered