A Study on Some Subclasses of Univalent Analytic Functions in the Unit Disc

Abstract

In recent years, various interesting properties and characteristics of newlinemany different subclasses of univalent analytic functions have been newlinesystematically investigated. newlineThe properties of functions in the class S, and its subclasses such as newlineStarlike, Strongly starlike, Convex, Uniformly Convex, Uniformly Starlike, newlineMeromarphically Uniformly Convex, Meromarphiclaly Starlike functions newlinehave been widely investigated by various researchers in the past three newlinedecades. In the other direction new subclass of functions which are defined newlineinvolving operators were introduced. Differential operators are powerful newlinemathematical tools that find new subclasses of S. One of the famous newlinedifferential operators is Salagean Operator. newlineIn the Present work some new subclasses of Univalent Analytic newlineFunctions are introduced and their coefficient estimates, growth and newlinedistortion theorems, radius of starlikeness and convexity are obtained. newlineApplications of differential subordination are also obtained for these classes newline2) OBJECTIVES: newlineThe main objectives of the study carried out are as follows: newline1. To study and understand the various subclasses of Univalent Analytic newlinefunctions such as Starlike, Convex, Close to Convex, newlinemeromorphically starlike, etc. newline7 newline2. To study and understand various differential operators, integral newlineoperators to investigate some new subclasses of univalent analytic newlinefunctions in the unit disc. newline3. To investigate and introduce some new subclasses of univalent newlineanalytic functions. newline4. To discuss some interesting properties of certain subclasses of newlineunivalent analytic functions in the unit disc. newline5. To find coefficient estimates, extreme points, radius of starlike and newlineradius of convexity for our new subclasses. newline3) PROPOSED CONTENTS AND BRIEF DESCRIPTION OF THE newlineTHESIS: newlineThe thesis entitled A STUDY ON SOME SUBCLASSES OF newlineUNIVALENT ANALYTIC FUNCTIONS IN THE UNIT DISC has newlineseven chapters is divided into section and subsections. The chapter wise newlinescheme of the thesis is as follows. The present work is devoted to the study newlineof certain subclasses of un