Abstract
Making use of the Cho-Kwon-Srivastava operator, we introduce and study a certain SCn (j, p, λ, α, δ) of p-valently analytic functions with negative coefficients. In this paper, we obtain coefficient estimates, distortion theorem, radii of close-to-convexity, starlikeness and convexity and modified Hadamard products of functions belonging to the class SCn (j, p, λ, α, δ). Finally, several applications investigate an integral operator, and certain fractional calculus operators also considered.
Highlights
Let T j, p denote the class of functions of the form: which are analytic and p-valent in the open unit disc Re zf f z z z U;0 p; p N (1.2) We denote by T jp, the class of all p-valently starlike functions of order
Making use of the Cho-Kwon-Srivastava operator, we introduce and study a certain SCn (j, p, λ, α, δ) of p-valently analytic functions with negative coefficients
We obtain coefficient estimates, distortion theorem, radii of close-to-convexity, starlikeness, convexity and modified Hadamard products of functions belonging to the class SCn (j, p, λ, α, δ)
Summary
Let T j, p denote the class of functions of the form:. p, the class of all p-valently starlike functions of order. Let T j, p denote the class of functions of the form:. P, the class of all p-valently starlike functions of order. T j, p is said to be p-valently convex of order if it satisfies the inequality: U;. We denote by C j p, the class of all p-valently convex functions of order. We note that (see for example Duren [1] and Goodman [2]). P,1 a, a D p 1 f z p , where D p 1 is the well-known Ruscheweyh derivative of p 1 -th order. P which is the class of starlike functions of order studied by Owa [3] and Yamakawa [6].
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