On Certain New Classes of Analytic Functions Associated with Generalized Bounded Mocanu Variation

Abstract

“On Certain New Classes of Analytic Functions Associated with Generalized Bounded Mocanu Variation” “ Geometric function theory is the branch of Complex analysis that deals with the ge ometric characterization of analytic functions. As a result of the geometric properties of the image domains, analytic functions are being categorized into subclasses. To this end, subclasses of normalized analytic functions having some nice geometrical structures are investigated in this thesis. Essentially, Bessel functions are used to initiate the classes of analytic functions, which are starlike and convex with respect to symmetrical points. The techniques of differential subordination and that of the classical approach are used to ob tain various geometrical properties of these classes. Furthermore, subclasses of functions which are related to crescent domains are presented and properties such as coefficients estimate, subordination conditions, distortion results and many related properties are deter mined. Also, we examined the subfamilies of functions which are connected with limaçon domains. Coefficients bounds, Fekete Szego inequalities and the bounds of the third Han- ¨ kel determinants are derived. Additionally, the sharp radius for which the classes are linked to each other and the notable subclasses of univalent functions are found. Further, the idea of subordination is utilized to obtain some results for functions belonging to these”classes. Moreover,“ the concept of close-to-convex functions is generalized in different forms. New results that include necessary condition, arc length, rate of growth of coefficients and Hankel determinant, and some radius results are established in this direction. Besides, a linear operator is initiated and used to introduce a class of analytic functions which are related to the class of bounded Mocanu variation. Both the Fekete Szego and third Han- ¨ kel determinant’s bounds are found for this novel class. In like manner, the concept of q−calculus is used to introduce some classes of analytic functions which also generalized the class of bounded Mocanu variation. In this way, we obtain sufficient conditions, Fekete Szego inequality, covering results for these classes. ¨ ” “Overall, many remarkable particular cases are also presented.”