1 citations · 1 across the 9 of their papers we have counts for
9 papers
An equation in nonlinear combination of iterates
Chaitanya Gopalakrishna, Weinian Zhang
In this paper we deal with an equation in nonlinear combination of iterates. Although it can be reduced by the logarithm conjugacy to a form for application of Schauder's or Banach…
A note on iterated maps of the unit sphere
Chaitanya Gopalakrishna
Let denote the set of continuous maps from the unit sphere in into itself endowed with the supremum norm. We prove that the set $\{f…
Iterative Roots of Multifunctions
B. V. Rajarama Bhat, Chaitanya Gopalakrishna
Some easily verifiable sufficient conditions for the nonexistence of iterative roots for multifunctions on arbitrary nonempty sets are presented. Typically if the graph of the mult…
The non-iterates are dense in the space of continuous self-maps
B. V. Rajarama Bhat, Chaitanya Gopalakrishna
In this paper we develop a tool to identify functions which have no iterative roots of any order. Using this, we prove that when is , or , every no…
A note on Fredholm integral equation
Chaitanya Gopalakrishna
This note gives results on the existence of semi-continuous solutions of a Fredholm integral equation of the second kind using Tarski's fixed point theorem.
Differentiable solutions of an equation with product of iterates
Chaitanya Gopalakrishna
In the previous work [2] (i.e., arXiv:2105.03385), we considered continuous solutions of an iterative equation involving the multiplication of iterates. In this paper, we continue…
Continuous solutions of an iterative equation with multiplication
Chaitanya Gopalakrishna, Murugan Veerapazham, Suyun Wang +1
Iterative equation is an equality with an unknown function and its iterates. There were not found a result on iterative equations with multiplication of iterates of the unknown fun…
Iteration and iterative equation on lattices
Chaitanya Gopalakrishna, Weinian Zhang
In this paper we investigate iteration of maps on lattices and the corresponding polynomial-like iterative equation. Since a lattice need not have a metric space structure, neither…
Iterative square roots of functions
B V Rajarama Bhat, Chaitanya Gopalakrishna
An iterative square root of a function is a function such that . We obtain new characterizations for detecting the non-existence of such square roots…