Coefficient Bounds for Some Families of Starlike and Convex Functions of Reciprocal Order

The aim of the present paper is to investigate coefficient estimates, Fekete-Szegő inequality, and upper bound of third Hankel determinant for some families of starlike and convex functions of reciprocal order

Fekete-Szegö Problem of Functions Associated with Hyperbolic Domains

In the field of Geometric Function Theory, one can not deny the importance of analytic and univalent functions. The characteristics of these functions including their taylor series expansion, their coefficients in these representations as well as their associated functional inequalities have always attracted the researchers. In particular, Fekete-Szegö inequality is one of such vastly studied and investigated functional inequality. Our main focus in this article is to investigate the Fekete-Szegö functional for the class of analytic functions associated with hyperbolic regions. Tofurther enhance the worth of our work, we include similar problems for the inverse functions of these discussed analytic functions

Differential subordination related with exponential functions

In this article, we study some first-order differential subordinations. We determine the conditions on β  such that 1 + β zp′(z) ≺ √1+cz) and 1 + β zp′(z) ≺ 1 + √(2z+ 1/2 z2  implies p(z) ≺ ez. Similarly, some results are also obtained for the expressions 1 + β zp′ (z)/p(z) and 1 + β zp′(z) / p2(z). We also give applications of these results to obtain some sufficient conditions for a function to be starlike related to exponential functions.&nbsp