@article{Ahmed2024, 
author = {Ahmed M. Ahmed and Ahmed I. Saied and Mohammed Zakarya and Amirah Ayidh I Al-Thaqfan and Maha Ali and Haytham M. Rezk},
title = {Advanced Hardy-type inequalities with negative parameters involving monotone functions in delta calculus on time scales},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {11},
pages = {31926-31946},
keywords = {Hardy's inequality, negative parameter, monotone functions, Hölder's inequality, weighted inequalities, delta calculus, time scales},
url = {https://www.sciopen.com/article/10.3934/math.20241534},
doi = {10.3934/math.20241534},
abstract = {In this study, we introduced several novel Hardy-type inequalities with negative parameters for monotone functions within the framework of delta calculus on time scales  T. As an application, when  T=N0, we derived discrete inequalities with negative parameters for monotone sequences, offering fundamentally new results. When  T=R, we established continuous analogues of inequalities that have appeared in previous literature. Additionally, we presented inequalities for other time scales, such as  T=qN0 for  q>1, which, to the best of the authors' knowledge, represented largely novel contributions.}
}