AbstractIn this paper we introduce the subclass K(μ, γ, η, α, β) of β-uniformly convex and β-uniformly starlike functions which are analytic and multivalent with negative coefficients defined by using fractional calculus operators. Characterization property exhibited by the functions in the class and the results of modified Hadamard product are discussed. Connections with the popular subclasses...

In this paper we introduce a class of strongly starlike functions of order α and type β with respect to symmetric points and investigate the neighborhoods and coefficients bounds of such functions.

For analytic functions f(z) in the open unit disk U with f(0) = 0 and f ′(0) = 1, S. S. Miller, P. T. Mocanu and M. O. Reade (Proc. Amer. Math. Soc. 37(1973)) have introduced α-convex functions in U with some condition, and Z. Lewandowski, S. S. Miller and E. Zl /otkiewicz (Ann. Univ. Marie-Curie Skl /odowska 27(1974)) have discussed γ-starlike functions in U with some condition. The object of ...

let $p$ be an analytic function defined on the open unit disc $mathbb{d}$ with $p(0)=1.$ the conditions on $alpha$ and $beta$ are derived for $p(z)$ to be subordinate to $1+4z/3+2z^{2}/3=:varphi_{c}(z)$ when $(1-alpha)p(z)+alpha p^{2}(z)+beta zp'(z)/p(z)$ is subordinate to $e^{z}$. similar problems were investigated for $p(z)$ to lie in a region bounded by lemniscate of bernoulli $|w^{2}-1...

In this paper we consider the classes of starlike functions, starlike functions of order α, convex functions, convex functions of order α and the classes of the univalent functions denoted by SH (β), SP and SP (α, β). On these classes we study the convexity and αorder convexity for a general integral operator.

In this paper we study functions which are strongly starlike, with the method of differential inequalities. We also give a generalization of the results obtained by the authors Milutin Obradovic and Santosh B. Joshi (1998) with new class of functions defined by q order ordinary differential operator.

Abstract Sharp bounds are given for the second Hankel determinant of logarithmic coefficients strongly starlike and convex functions.