The objective of this paper is to obtain sharp upper bound for the function f for the second Hankel determinant |a2a4 − a 2 3 |, when it belongs to the class of functions whose derivative has a positive real part of order α (0 ≤ α < 1), denoted by RT (α). Further, an upper bound for the inverse function of f for the nonlinear functional (also called the second Hankel functional), denoted by |t2t4 − t 2 3 |, was determined when it belongs to the same class of functions, using Toeplitz determinants.