This article proposes a new type of analytic function called Mtan and introduces a new geometric structure that blends exponential and trigonometric properties. In addition, it obtains exact bounds for all second- and third-order Hankel determinants and establishes extremal results for the Fekete–Szegö and Zalcman functionals. Moreover, it discusses the validity of the Krushkal inequality. Furthermore, it applies the developed methodology to improve the contrast and quality of color images and demonstrates that the proposed enhancement filters yield notable improvements in contrast and quality compared to other filters, based on the PSNR, SSIM, MSE, RMSE, PCC, and MAE metrics. This article demonstrates its dual nature, namely advances in geometric function theory and practical advantages in digital image processing.
El-Ityan et al. (Sun,) studied this question.