Abstract
In this paper we introduce and investigate three new subclasses of \(p\)-valent analytic functions by using the linear operator \(D_{\lambda,p}^m(f*g)(z)\). The various results obtained here for each of these function classes include coefficient bounds, distortion inequalities and associated inclusion relations for \((n,\theta)\)-neighborhoods of subclasses of analytic and multivalent functions with negative coefficients, which are defined by means of a non-homogenous differential equation.
Highlights
Let Ap(n) denote the class of functions of the form (1.1) ∞f (z) = zp + akzk (n > p; p, n ∈ N = {1, 2, . . .}), k=n which are analytic and p-valent in the open unit disk U = {z : |z| < 1}
For a given function g(z) ∈ Ap(n) defined by g(z) = zp + bkzk, k=n we introduce a new subclass Cγq(g(z); n, m, p, λ, β, b) of the class Tp(n) of p-valently analytic functions, which consists of functions f (z) ∈ Tp(n) satisfying the inequality
Suppose that f ∈ Nnθ,p k(q), we find from the definition (4.1) that δ(k, q)k |ak − ck| ≤ θ, k=n which implies the coefficient inequality
Summary
Let Ap(n) denote the class of functions of the form For a given function g(z) ∈ Ap(n) defined by g(z) = zp + bkzk (bk > 0; n > p; p, n ∈ N), k=n we introduce a new subclass Cγq(g(z); n, m, p, λ, β, b) of the class Tp(n) of p-valently analytic functions, which consists of functions f (z) ∈ Tp(n) satisfying the inequality 2. Basic properties of the classes Cγq(g(z); n, m, p, λ, β, b) and Rγq (g(z); n, m, p, λ, β, b).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
