New Subclasses of Harmonic Starlike and Convex Functions

. The purpose of the present paper is to establish some interesting results in-volving coecient conditions, extreme points, distortion bounds and covering theoremsfor the classes V H (β) and U H (β). Further, various inclusion relations are also obtainedfor these classes. We also discuss a class preserving integral operator and show that theseclasses are closed under convolution and convex combinations. 1. IntroductionA continuous complex-valued function f = u + iv is said to be harmonic ina simply connected domain D if both u and v are real harmonic in D. In anysimply connected domain we can write f = h + g , where h and g are analytic inD. We call h the analytic part and g the co-analytic part of f. A necessary andsucient condition for f to be locally univalent and sense-preserving in D is that h 0 (z) ,z> g 0 ∈ D. See Clunie and Sheil-Small [3], for more basic results onharmonic functions one may refer to the following standard introductory text bookby Duren [7], see also Ahuja [1] and Ponnusamy and Rasila ([9], [10]).Let S