Studies on certain subclasses of univalent and multivalent functions in the unit disc

Abstract

The present work is devoted to the study of STUDIES ON newlineCERTAIN SUBCLASSES OF UNIVALENT AND MULTIVALENT newlineFUNCTIONS IN THE UNIT DISC This work consists of six chapters and newlinereferences newlineChapter 1 forms a general introduction of the subject matter of the newlinethesis Also it consists basic definitions and notions like univalence newlineconvexity starlikeness and related concepts Well known and important newlineproperties of several subclasses of functions relevant to the present work are newlinestated in the form of theorems without proof newlineIn Chapter 2 we employed the DziokSrivastava operator to obtain newlinethe differential sandwich results The mixture of differential subordination newlineand superordination The applications of our results in this chapter are newlineimproving the results discussed by Magesh et al 2010 Shanmugam et al newline2006a 2008 Aouf et al 2005 Further future works mentioned following newlinethe concluding section newlineIn Chapter 3 a new subclass of starlike and convex functions of newlinecomplex order is defined based on convolution technique and the coefficient newlinebound extreme points radii of close to convexity starlikeness and convexity newlinefor aforementioned class are investigated Further a unified class of functions newlineof complex order involving generalized fractional calculus operator is defined newlineto derive coefficient bounds for the function class we establish distortion newlinebounds inclusion relationship involving the neighborhoods of analytic newline valent functions belonging to this subclass It is interest to note that there newlineare some applications in fluid dynamics those will be considering as newlineproblems for future work newlineIn Chapter 4 a new subclass of multivalent functions associated with newlinea Dziok Srivastava operator is defined Characterization property exhibited newlineby the functions in the class and radius of starlikeness and convexity are newlinediscussed Results on growth and distortion theorems closure property newlineextreme points class preserving integral operators region of valency and newlineother interesting properties of the class are also included newlineIn Chapter 5 a unified subclass of meromorphic fu