Estimation of Hankel inequalities of symmetric starlike functions in crescent-shaped domains and their application in image processing.

This study explores some geometric properties of the class of symmetric starlike functions associated with a Crescent-shaped domain denoted by [Formula: see text]. Initially, we establish key coefficient inequalities and investigate upper bounds for the 2nd and 3rd order Hankel determinants. All the obtained results are sharp. These bounds provide deeper insights into the structural behavior of this class and contribute to a broader understanding of Geometric Function Theory. In addition to the theoretical findings, the practical implications of the results obtained are demonstrated in the domain of image processing. We used our estimated sharp Hankel determinants to develop a novel algorithm for image enhancement. The performance of the algorithm is evaluated on different image datasets of varying dimensions, with key quality metrics such as PSNR, SSIM, PCC, and MAE. Our experimental results indicate a significant improvement over conventional image enhancement techniques, particularly in retaining structural integrity and reducing distortions. In addition, a comparative study highlights the effectiveness of the proposed algorithm compared to existing methods reported in the literature, demonstrating its potential to enhance image quality in practical applications.