For a given p-valent analytic function g with positive coefficients in the open unit disk ∆, we study a class of functions f(z) = z + ∑∞ n=m anz , an ≥ 0 satisfying 1 p < ( z(f ∗ g)′(z) (f ∗ g)(z) ) < α ( z ∈ ∆; 1 < α < m+ p 2p ) . Coefficient inequalities, distortion and covering theorems, as well as closure theorems are determined. The results obtained extend several known results as special ...

Making use of a certain operator of fractional derivative, a new subclass Fλ(n, p, α, μ) of analytic and p-valent functions with negative coefficients is introduced and studied here rather systematically. Coefficient estimates, a distortion theorem and radii of p-valently closeto-convexity, starlikeness and convexity are given. Finally several applications involving an integral operator and a c...

By means of the generalized fractional calculus operator, we introduce and investigate a subclass of p−valent functions with negative coefficients. We obtain the coefficient estimates, distortion bounds for the class. Furthermore, we discuss inclusion relationship involving the neighborhood result of the same. Mathematics Subject Classification: 30C45

In this paper, a new operator Dsf, with s real number, is defined considering functions that belong to the known class of p-valent analytic in open unit disk U. Applying operator, subclass p-valently introduced and some interesting subordination- coefficient-related properties are discussed. It also shown for certain values given parameters involved definition class, starlike convex orders can ...

This paper investigates various new subordination results for certain p -valent analytic functions involving a generalized multiplier transformation operator Jm p (λ , l),m ∈ Z, defined recently by J. K. Prajapat [Math. Comput. Modelling, 55 (2012), 1456–1465]. Several lines of approach are followed to obtain the subordination results. We also consider some simpler and precise forms of the deri...

The objective of this paper is to obtain an upper bound to the second Hankel determinant |ap+1ap+3 − ap+2| for p-valent starlike and convex functions of order α, using Toeplitz determinants. AMS Mathematics Subject Classification (2010): 30C45, 30C50