PreprintCC BY 4.0arXiv
Monotonicity and bounded variation for harmonic mappings with applications to special functions
Abstract
We investigate sufficient conditions for the close-to-convexity and univalence of planar harmonic mappings. First, we establish a unified monotonicity criterion for harmonic mappings that incorporates the ordinary and odd harmonic cases. We then develop a criterion based on the total variation of successive coefficient differences. Unlike conventional monotonicity conditions, this approach allows the coefficient sequences to exhibit non-monotone behavior. Several previously established criteria for harmonic close-to-convexity are recovered as particular consequences. Applications are developed for harmonic mappings associated with Gaussian hypergeometric functions and Legendre polynomials, with explicit restrictions on their parameters.
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BibTeX
@misc{prajapat2026monotonicity,
title = {{Monotonicity and bounded variation for harmonic mappings with applications to special functions}},
author = {Jugal Kishore Prajapat},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02290},
eprint = {2611.02290},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02290},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Monotonicity and bounded variation for harmonic mappings with applications to special functions
AU - Jugal Kishore Prajapat
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.02290
UR - https://arxiv.org/abs/2611.02290
AB - We investigate sufficient conditions for the close-to-convexity and univalence of planar harmonic mappings. First, we establish a unified monotonicity criterion for harmonic mappings that incorporates the ordinary and odd harmonic cases. We then develop a criterion based on the total variation of successive coefficient differences. Unlike conventional monotonicity conditions, this approach allows the coefficient sequences to exhibit non-monotone behavior. Several previously established criteria for harmonic close-to-convexity are recovered as particular consequences. Applications are developed for harmonic mappings associated with Gaussian hypergeometric functions and Legendre polynomials, with explicit restrictions on their parameters.
ER -