Properties of neighborhood for certain classes associated with complex order and m‑q‑p‑valent functions with higher order

Document Type : Original Article

Abstract

In this paper, by using q-calculus (Jackson’s q-derivative) Dq,p we defined new operator
Dn
,q,pf (m)(z) . After that, we used this operator to introduce two new subclasses of multivalent
analytic functions with complex order. Also, we obtained coefficients estimates
and consequent inclusion relationships involving the Np,q
j,,m(f )-neighborhood of these
classesIn this paper, by using q-calculus (Jackson’s q-derivative) Dq,p we defined new operator
Dn ,q,pf (m)(z) . After that, we used this operator to introduce two new subclasses of multivalent
analytic functions with complex order. Also, we obtained coefficients estimates and consequent inclusion relationships involving the Np,q j,,m(f )-neighborhood of these classes

Keywords