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

Abstract

Abstract In this paper, by using q-calculus (Jackson’s q-derivative) $$D_{q,p}$$ D q , p we defined new operator $$D_{\lambda ,q,p}^{n}f^{(m)}(z)$$ D λ , q , p n f ( 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 $$N_{j,\delta ,m}^{p,q}(f)$$ N j , δ , m p , q ( f ) -neighborhood of these classes

Keywords

• Complex order
• Coefficient estimates
• Neighborhood
• p-valent