Ramanpreet Kaur

• University of Delhi

For a transcendental entire function with sufficiently small growth, Baker raised the question whether it has no unbounded Fatou components. We have shown that if the function is of order strictly less than half, minimal type, then it has no unbounded Fatou components. This, in particular gives a partial answer to Baker's question. In addition, we...

For a transcendental entire function, a partial affirmative answer to Baker's question on the boundedness of its Fatou components is given. In addition, we have addressed Wang's question on Fej\'er gaps. Certain results about functions with Fabry gaps and of infinite order have also been generalized.

Given two permutable entire functions f and g, we establish vital relationship between escaping sets of entire functions f, g and their composition. We provide some families of transcendental entire functions for which Eremenko’s conjecture holds. In addition, we investigate the dynamical properties of the mapping \(f(z)=z+1+e^{-z}.\)

In this paper, we have explored some of the basic properties of the Bungee set of a transcendental entire function. We have provided a class of permutable entire functions for which their Bungee sets are equal. Moreover, we have given a class of permutable entire functions for which the escaping set of the composite entire function equals the union...

The notion of nearly abelian rational semigroup was introduced by Hinkannen and Martin. In this paper, we have introduced the notion of nearly abelian transcendental semigroup. We have extended the results of nearly abelian rational semigroups to the best possible class of nearly abelian transcendental semigroups. We have given a class of functions...