Results

**1 - 3**of**3**### COEFFICIENTS BOUNDS IN SOME SUBCLASS OF ANALYTIC FUNCTIONS

"... Abstract. In this paper we consider a class of analytic functions introduced by Mishra and Gochhayat, Fekete-Szegö problem for a class defined by an integral operator, Kodai Math. J., 33(2010) 310–328, which is connected with k-starlike functions through Noor operator. We find inclusion relations an ..."

Abstract
- Add to MetaCart

(Show Context)
Abstract. In this paper we consider a class of analytic functions introduced by Mishra and Gochhayat, Fekete-Szegö problem for a class defined by an integral operator, Kodai Math. J., 33(2010) 310–328, which is connected with k-starlike functions through Noor operator. We find inclusion relations and coefficients bounds in this class. 1.

### © Hindawi Publishing Corp. TECHNIQUES OF THE DIFFERENTIAL SUBORDINATION FOR DOMAINS BOUNDED BY CONIC SECTIONS

, 2003

"... We solve the problem of finding the largest domain D for which, under given ψ and q, the differential subordination ψ(p(z),zp ′(z)) ∈ D ⇒ p(z) ≺ q(z), where D and q(�) are regions bounded by conic sections, is satisfied. The shape of the domain D is described by the shape of q(�). Also, we find th ..."

Abstract
- Add to MetaCart

(Show Context)
We solve the problem of finding the largest domain D for which, under given ψ and q, the differential subordination ψ(p(z),zp ′(z)) ∈ D ⇒ p(z) ≺ q(z), where D and q(�) are regions bounded by conic sections, is satisfied. The shape of the domain D is described by the shape of q(�). Also, we find the best dominant of the differential subordination p(z)+ (zp′(z)/(βp(z)+γ)) ≺ pk(z), when the function pk (k ∈ [0,∞)) maps the unit disk onto a conical domain contained in a right half-plane. Various applications in the theory of univalent functions are also given.

### THE FEKETE-SZEGÖ PROBLEM FOR A CLASS DEFINED BY THE HOHLOV OPERATOR

"... Abstract. Let A be the class of analytic functions in the open unit disk U. be the operator defined on A by For complex numbers a, b and c (c = 0, −1, −2,....), let I a,b c (I a,b c (f))(z) = z2F1(a, b; c; z) ∗ f(z) where 2F1(a, b; c; z) is the Gaussian hypergeometric function. The function f in ..."

Abstract
- Add to MetaCart

(Show Context)
Abstract. Let A be the class of analytic functions in the open unit disk U. be the operator defined on A by For complex numbers a, b and c (c = 0, −1, −2,....), let I a,b c (I a,b c (f))(z) = z2F1(a, b; c; z) ∗ f(z) where 2F1(a, b; c; z) is the Gaussian hypergeometric function. The function f in A is said to be in the class k − SP a,b c if I a,b c (f) is a k-parabolic starlike function. For this class the Fekete-Szegö problem is settled in the present paper. 2000 Mathematics Subject Classification: 30C45, 33C15. 1. Introduction and