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In this paper, we introduce a new concept of q-bounded radius rotation and define the class R* m (q), m ≥ 2, q ∈ (0, 1). The class R*2(q) coincides with S* q which consists of q-starlike functions defined in the open unit disc. Distortion theorems, coefficient result and radius problem are studied. Relevant connections to various known results are pointed out.
) = 0 and | w ( z )| < 1, and such that f ( z ) = g ( w ( z )). If g is univalent, then f ≺ g if and only if f (0) = g (0) and f (𝔻) ⊂ g (𝔻). The class of starlike functions consists of all those functions f ∈ 𝒜 such that the domain
References [1] Bello , R ., and Opoola , T . Upper bounds for fekete-szego functions and the second hankel determinant for a class of starlike functions . IOSR Journal of Mathematics 12 , 2 ( 2017 ), 34 – 39 . [2] Duren , P. L . Univalent
Abstract
We present some relations for inequalities involving certain differential-integral operators.
Let L(f, r) denote the length of the closed curve which is the image of |z| = r < 1 under the mapping w = f(z). We establish some sufficient conditions for L(f, r) to be bounded and for f(z) to in the classes of strongly close-to-convex function of order α and to be strongly Bazilevič function of type β of order α. Moreover, we prove an inequality connected with the Fejér-Riesz's inequality.
] G oodman , A. W. , On uniformly starlike functions , Journal of Mathematical Analysis and Applications , 155 ( 1991 ), 364 – 370 . [10] H ohlov , Y u . E
