Sumit Nagpal

A subclass of starlike functions associated with left-half of the lemniscate of Bernoulli

Let

A subclass of close-to-convex harmonic mappings

\mathcal{S}_{RL}^{*}

Applications of the theory of differential subordination for functions with fixed initial coefficient to univalent functions

denote the class of all analytic functions f in the open unit disk with the normalizations f(0) = f′(0) - 1 = 0 such that zf′(z)/f(z) lies in the interior of the left-half of the shifted lemniscate of Bernoulli

CONSTRUCTION OF SUBCLASSES OF UNIVALENT HARMONIC MAPPINGS

((x-\sqrt{2})^2+y^2)^2-2((x-\sqrt{2})^2-y^2) = 0

Univalence and convexity in one direction of the convolution of harmonic mappings

. In this paper, we investigate the geometric properties of functions in this class and compute the

Radius Constants for Functions with the Prescribed Coefficient Bounds

\mathcal{S}_{RL}^*

Radii of Starlikeness and Convexity for Analytic Functions with Fixed Second Coefficient Satisfying Certain Coefficient Inequalities

-radius for functions belonging to several interesting classes.

Convolution properties of the harmonic Koebe function and its connection with 2-starlike mappings

A subclass of complex-valued close-to-convex harmonic functions that are univalent and sense-preserving in the open unit disc is investigated. The coefficient estimates, growth results, area theorem, boundary behaviour, convolution and convex combination properties for the above family of harmonic functions are obtained.

Second-Order Differential Superordination for Analytic Functions With Fixed Initial Coefficient

By using the theory of first-order differential subordination for functions with fixed initial coefficient, several well-known results for subclasses of univalent functions are improved by restricting the functions to have fixed second coefficient. The influence of the second coefficient of univalent functions is evident in the results obtained.

Fully starlike and fully convex harmonic mappings of order α

Complex-valued harmonic functions that are univalent and sense-preserving in the open unit disk are widely studied. A new methodology is employed to construct subclasses of univalent harmonic mappings from a given subfamily of univalent analytic functions. The notion of harmonic Alexander integral operator is introduced. Also, the radius of convexity for certain families of harmonic functions is determined.