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1 Introduction and preliminary concepts 1.1 Introduction 1.2 Preliminary results and definitions 1.2 1 Starlike functions 1.2 2 Convex functions 1.2 3 Close.to.convex functions 1.2.4 Multivalent functions 1.2.5 Certain classes of meromohic functions 1.2.6 Hadamard product/Convolution 1.2.7 ClassP of flmctionswithpositive real part 1.2.8 Differential subordination and superordination 1.2.9 Strong dim_rential subordination and superordination 1.2.10 Fractional operators 1.3 Summary 1.4 Glossary 1.5 List of publications 2 Certain New Classes of Analytic Functions 2.1 Introduction and preliminaries 2.2 Main inclusion relationship 2.3 Coefficmestimate 3 Certain Subclasses of p.Valent Alytinlncti 3.1 Introduction and preliminaries 3.2 Main inclusion relationships 3.3 Integral operator 4 A subclass of Close.to.convex Functions with Fekete.Szego Problem 4.1 Introduction and preliminariest 4.2 Properties of starlike functions 4.3 Inclusion relationships 4.4 Coefficm estimates 4.5 Covering theorem 46 Distortion theorem 4.7 Fekete¡ªSzego problem 5 Certain Subclasses of Meromorphic Close.to.convex Functions 5.1 Introduction 5.2 The classes Jt4£¯C(A£¬B)and MK(t£¬A£¬B) 5.2.1 Properties ofmeromorphic starlike fuuctions 5.2.2 CoeÎécient estimates 5.2.3 Distortion theorem 5.3 The class MK(i£¬A£¬B) 5.3.1 Properties ofthe class MS(¦Á£¬¦Â) 6 Differential Subordination and Superordination results for pvalent An alytic Functions 6.1 Introduction and preliminaries 6.2 Main results 6.3 Superordination results 7 Strong Differential Subordination and Superordination 7.1 Introduction and definitions 7.2 Main results 7.3 Superordination resultsforthe operatorIep ±à¼­ÊÖ¼Ç