On Subclass of Meromorphic Analytic Functions Defined by a Differential Operator

In this work, using the differential operator and the concept of meromorephic analytic functions we introduce and investigate the class ${{\rm{\Sigma }}}_{\beta,\lambda }^{\alpha,m}(A,B,Y,\beta )$, of functions of the form $f(z)={z}^{-1}+\sum _{n=1}^{{\rm{\infty }}}{a}_{n}{z}^{n},{a}_{n}\ge 0$, which are analytic and meromorphic univalent in the punctured unit disk ${U}^{* }=\{z\in C:0\lt |z|\lt 1\}$, satisfying $|\frac{A[\gamma {z}^{2}{({{\mathfrak{D}}}_{\beta,\lambda }^{\alpha,m}f(z))}^{{\rm{^{\prime} }}{\rm{^{\prime} }}{\rm{^{\prime} }}}+z(3{\rm{{\Upsilon }}}+\beta ){({{\mathfrak{D}}}_{\beta,\lambda }^{\alpha,m}f(z))}^{{\rm{^{\prime} }}{\rm{^{\prime} }}}+({\rm{{\Upsilon }}}+\beta ){({{\mathfrak{D}}}_{\beta,\lambda }^{\alpha,m}f(z))}^{{\rm{^{\prime} }}}]}{B[{\rm{{\Upsilon }}}z{({{\mathfrak{D}}}_{\beta,\lambda }^{\alpha,m}f(z))}^{{\rm{^{\prime} }}{\rm{^{\prime} }}}+({\rm{{\Upsilon }}}+\beta ){({D}_{\beta,\lambda }^{\alpha,m}f(z))}^{{\rm{^{\prime} }}}]}|\lt 1$. Further, coefficient bounds, Hadamard product, radius of close to-convexity, inclusive properties and neighbourhoods of functions in our class are obtain.