Geometric function theory combines geometric tools and their applications for information communication analysis. It is also successfully used in the field of advanced signals, image processing, machine learning, speech sound recognition. Various new subclasses analytic functions have been defined using quantum calculus to investigate many interesting properties these subclasses. This article d...

It is clear that 0∈ h(Δ). Moreover, (i) if 0 ∈ h(Δ), then h is called spirallike (resp., starlike) with respect to an interior point; (ii) if 0 ∈ h(Δ), then h is called spirallike (resp., starlike) with respect to a boundary point. In this case, there is a boundary point (say, z = 1) such that h(1) := ∠ limz→1h(z)= 0 (see, e.g., [1, 6]); by symbol∠ lim, we denote the angular (nontangential) lim...

The sharp bounds for the third and fourth coefficients of Ma-Minda starlike functions having fixed second coefficient are determined. These results are proved by using certain constraint coefficient problem for functions with positive real part whose coefficients are real and the first coefficient is kept fixed. Analogous results are obtained for a general class of close-to-convex functions