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