Coefficient Bounds on Subclasses of Bi Univalent Sakaguchi Type Functions Associated with Special Functions

Abstract

The current work is dedicated to the study of Coefficient Bounds on Subclasses of Bi- newlineUnivalent Sakaguchi Type Functions Associated with Special Functions . In Geometric newlineFunction Theory, there are enormous absorbing properties and characteristics of various newlinesubclasses of holomorphic univalent functions were investigated. newlineIn this present work the subclasses S_;_ newline_m(t), S_;_ newline_m(t), C_;_ newline_m(t) and C_;_ newline_m(t) of m-fold biunivalent newlineSakaguchi kind holomorphic functions are presented in the open unit disk U newlineand intial coefficient bounds ja1+mj, ja1+2mj are estimated. newlineThe work also consists of subclass SLB_;_;t (p_(_)) of bi-univalent Sakaguchi kind newlineholomorphic functions are elucidate in the open unit disk U, which is subordinated by newlinespecial caratheodory function p_(_), for which Fibonacci numbers are building blocks. newlineInitial coefficeint bounds ja2j, ja3j are estimated and also Fekete-Szeg¨o problem is newlinediscussed for the subclass. newlineThere after, the subclass HB_;_;t f_(_; _)g of bi-univalent Sakaguchi kind holomorphic newlinefunctions are defined in the open unit disk U. This class is characterized by application newlineof Horadam polynomial hn(_) with subordination condition. Initial coefficeint bounds newlineja2j, ja3j are estimated and also Fekete-Szeg¨o problem is discussed for the subclass. newlineFurther more, the subclass Hq(_; _; _; t) of Sakaguchi kind holomorphic functions are newlinedefined in the open unit disk U. It is defined using new linear operator, which is the newlineresult of Hadamard product of holomorphic univalent function and hypergeometric newlinefunction. Sufficient conditions are also provided with additional restrictions for the newlinesubclass. Coefficeint bounds janj; 8 n 2 N and bound for ja3and#1048576;_a22 newlinej are also estimated. newlineFurther the Subordination properties of the subclass are also discussed. newlineAdditionally, the subclasses K_ newline_ (_; t), L_(_; t) and SJ _ newline_ (t) of Sakaguchi kind of newlinefunctions are confined in U, whose radii are calculated and provided the sufficient newlinecondition for the above mentioned subclasses. newline