DIFFERENTIAL SUBORDINATIONS, COEFFICIENTS ESTIMATE AND RADIUS CONSTANTS OF CERTAIN ANALYTIC FUNCTIONS

Abstract

In this thesis, we have derived di erential subordination, superordination and sandwich type results and also determined several coe cient estimates for certain classes of analytic functions. Further, we have investigated various radius problems associated with analytic functions with positive real part. The thesis comprises of seven chapters, which includes a chapter on introduction. In Chapter 2, we have obtained conditions on certain parameters so that the given di erential subordination implication holds. In Chapter 3, we have discussed the properties of a class of linear operators which satisfy a common recurrence relation. Several su cient conditions for Janowski, Sok o l-Stankiewicz and strongly starlikeness are also determined. In addition to that we have given alternate proofs of certain results proved in [17]. In Chapter 4, we have considered a class of linear operators de ned in terms of convolution which can be expressed as convex combination of two operators. For this class of operators, we have established the di erential sandwich theorems. Several applications of these results are also discussed. In Chapter 5, we have derived estimate on the Fekete-Szeg o functional for ceratin classes of functions and various special cases of our results are also pointed out. In Chapter 6, estimate on the initial coe cients of certain subclasses of bi-univalent functions are established. Further some of our results improve the known estimates, which are pointed out here along with some special cases to our results. In Chapter 7, radius of starlikeness such as starlikeness of order , parabolic starlikeness and Sok o l-Stankiewicz starlikeness for functions with xed second coe cient are investigated when they satisfy certain conditions on the ratio f=g, where g is either starlike or convex function with xed second coe cient