GEOMETRIC PROPERTIES ON (j, k)-SYMMETRIC FUNCTIONS RELATED TO STARLIKE AND CONVEX FUNCTION

GEOMETRIC PROPERTIES ON (j, k)-SYMMETRIC FUNCTIONS RELATED TO STARLIKE AND CONVEX FUNCTION

For j = 0, 1, 2,&#x2026;, k - 1; k &#x2265; 2; and - 1 &#x2264; B < A &#x2264; 1, we have introduced the functions classes denoted by ST_[j,k](A, B) and K_[j,k](A, B), respectively, called the generalized (j, k)-symmetric starlike and convex functions. We first proved the sharp bounds on |f(z)| and |f'(z)|. Various radii related problems, such as radius of (j, k)-symmetric starlikeness, convexity, strongly starlikeness and parabolic starlikeness are determined. The quantity |a²₃ - a₅|, which provide the initial bound on Zalcman functional is obtained for the functions in the family ST_[j,k]. Furthermore, the sharp pre-Schwarzian norm is also established for the case when f is a member of K_[j,k](&#x03B1;) for all 0 &#x2264; &#x03B1; < 1.