Sharp Coefficient Bounds for Certain p-Valent Functions.

The main aim of this manuscript is to investigate sharp bound on the functional |ap+1ap+2-ap+3| for functions f(z)=zp+ap+1zp+1+ap+2zp+2+ap+3zp+3+⋯ belonging to the class Rp(α) associated with the right half-plane. Also sharp bounds on the initial coefficients, bounds on |ap+1ap+2-ap+3|, and |ap+1ap+3-ap+22| for functions in the class RLp(α), related to the lemniscate of Bernoulli, are also derived. Further, these estimates are used to derive a bound on the third Hankel determinant. [ABSTRACT FROM AUTHOR]