Results on spirallike <em>p</em>-valent functions

p -Valent strongly starlike and strongly convex functions connected with linear differential Borel operator

“…Let A p denote the class of functions of the form: The class S * (p, β) was introduced and studied by Patel and Thakare [19] (see also [3,11,12]). Also, we note that S * (p, 0) = S * p , where S * p is the class of p-valently starlike functions (see [8]).…”

“…The class C (p, β) was introduced and studied by Owa [18] ( see also [11,22]). Also, we note that C (p, 0) = C p , where C p is the class of p-valently convex functions (see [8]).…”

Some results on two new subclasses of p-valent spirallike and convexlike functions

“…Let A (p), p = 1, 2, 3, ... be the class of p−valent analytic functions f (z) = z p + ∞ ∑ k=1 a p+k z p+k (1) defined in the open unit disc U = {z ∈ C : |z| < 1}.We write A (1) = A. A function f ∈ A (p) is said to be p−valently starlike of order α in U, if it satisfies the inequality…”

“…for some real β and 0 < α < 1, where f ( p) (z) is the pth derivative of f (z). The classes S β (α, p) and C β (α, p)is introduced and studied by N.Khan et al, [1]. They given the following Theorem 2 and Theorem 3.…”

Some applications of higher-order derivatives involving certain subclass of analytic and multivalent functions

“…The above-defined function classes U S T (p, α, β ) and U C V (p, α, β ) were introduced recently by Khairnar and More [5]. Various analogous classes of analytic and multivalent functions were defined and studied by many other authors (see, for example, [1,6,7,9]).…”