arXiv subjects

Omendra Mishra

Publications and source records attributed to Omendra Mishra.

2 recordsLinked to original sources

arXiv2026

Note on the Coefficient Conjecture of Clunie and Sheil-Small on the univalent harmonic mapping

In this article, we construct generalized harmonic univalent mappings and find its coefficients bounds. We present the counterexample to validate the coefficient conjecture proposed by Clunie and Sheil-Small for the class of functions $f=h+\overline{g}\in \mathcal{S}_{\mathcal{H}}$ with the help of these examples we improve the conjecture bounds of class $\mathcal{S}_{\mathcal{H}}$.

math.CV↗

arXiv2021

Quantum approach on linear combination of harmonic univalent mappings

In this paper using $q$ calculus operator we obtain some sufficient conditions on $f_1$ and $f_2$ so that their linear combination $% f=tf_{1}+(1-t)f_{2},\ t\in \left[ 0,1\right] $, is univalent and convex in the direction of the real axis. Some examples are also illustrated to support our main results.

math.CV↗