Research Areas

Differential Subordination

The differential subordination is the complex analog of the differential inequality in the real line. We have developed the theory of differential subordination for the functions whose images lie inside the region bounded by the exponential function. This new theory has several interesting applications in univalent function theory.

Special Functions

Special functions are particular mathematical functions that have more or less established names and notations due to their importance in mathematical analysis, functional analysis, geometry, physics, or other applications. For example, confluent hypergeometric function, Bessel function, Wright function, etc. Geometric properties of such functions have been studied associated with the exponential function.

Radius Problems

 A convex function is necessarily starlike but not conversely. However, the starlike functions map a smaller disk into convex domains. The largest radius with this property is known as the radius of convexity of starlike functions. For any two geometric regions, one can talk about radius problems. We have investigated several radii problems associated with the exponential function.