Making use of fractional q-calculus operators, we introduce a new subclass ℳq(λ,γ,k) of starlike functions and determine the coefficient estimate, extreme points, closure theorem, and distortion bounds for functions in ℳq(λ,γ,k). Furthermore we discuss neighborhood results, subordination theorem, partial sums, and integral means inequalities for functions in ℳq(λ,γ,k).
In this paper, we introduce two new subclasses of the function class Σ of bi-univalent functions defined in the open unit disc based on Hohlov Operator. Furthermore, we find estimates on the coefficients |a 2 | and |a 3 | for functions in these new subclasses. Also consequences of the results are pointed out.
Abstract. For functions of the form f (z) = z p + ∞ n=1 ap+nz p+n we obtain sharp bounds for some coefficients functionals in certain subclasses of starlike functions. Certain applications of our main results are also given. In particular, Fekete-Szegö-like inequality for classes of functions defined through extended fractional differintegrals are obtained.
Introduction.Let A p denote the class of all functions of the formwhich are analytic in the open disk = {z ∈ C : |z| < 1} and let A = A 1 . For f (z) given by (1.1) and g(z) given by g(z) = z p + ∞ n=1 b p+n z p+n , their convolution (or Hadamard product), denoted by f * g, is defined asGiven two functions f and g, which are analytic in , the function f is said to be subordinate to g in , written f ≺ g or f (z) ≺ g(z), if there exists a Schwarz function w(z), analytic in with w(0) = 0 and |w(z)| < 1 such that f (z) = g(w(z)), z ∈ . In particular, if the function g is univalent in, the above subordination is equivalent to f (0) = g(0) and f ( ) ⊂ g( ).2000 Mathematics Subject Classification. 30C45.
By considering a p−valent Bazilevič function in the open unit disk △ which maps △ onto the strip domain w with pα < ℜ w < pβ, we estimate bounds of coefficients and solve Fekete-Szegö problem for functions in this class.
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