Some class of analytic functions related to conic domains

For q ∈ (0, 1) let the q-difference operator be defined as follows ∂ q f(z) = f(qz) - f(z) z(q - 1) (z ∈ U), where U denotes the open unit disk in a complex plane. Making use of the above operator the extended Ruscheweyh differential operator R qλ f is defined. Applying R qλ f a subfamily of analytic functions is defined. Several interesting properties of a defined family of functions are investigated.