Geometric properties of certain families of Meromorphic functions

Abstract

Inthis thesis various geometric properties meromorphic functions are discussed. Some subfamiliesofmeromorphicmultivalentfunctionsMC q (;;L;M) andMS q (;;L;M) associated with Janowski functions are introduced in q analogue using a new operator. The su¢ ciency criteria, Growth results, Distorsion problem and Radii problem for these functions in these new subclasses are discussed. Furthermore inclusion relationship for the functions belonging to these subclasses are investigated along with some convolution properties. A subfamily MKq (;;;L;M) of meromorphic close-to-convex functions are dened and studied in q-analogue in association with generalized Janowski functions in q-analogue. Some results like the coe¢ cient bounds, Growth and Distortion theorems are proved for these functions. Also the radii in the functured open unit disc where these functions behave like meromorphic starlike and meromorphic convex with some order are evaluated. Furthermore, thesubclassesMP;Q (;;L;M) ofmeromorphicfunctionsinPostQuantum analogue are introduced along with some of its geometric properties. Certain important results like radius of starlikeness, radius of convexity and distortion problems are discussed. A class of meromorphic functions in association with the Lemniscate of bernouli functions is introduced in meromorphic p-valent functions. This class MSL ;q is discussed with the help of some su¢ cient conditions. Some results for are evaluated so that 1 + z+1@qf(z) [;q] ;1 + z@qf(z) [;q]f(z);1 + z1@qf(z) [;q](f(z))2 and 1 + z@qf(z) [;q](f(z))3 are associated with Janowski functions and then fuctions are conditionally been shown to belong toMSL ;q: