Application of $ q $-starlike and $ q $-convex functions under $ (u, v) $-symmetrical constraints

Hanen Louati; Afrah Al-Rezami; Erhan Deniz; Abdulbasit Darem; Robert Szasz; Hanen Louati; Afrah Al-Rezami; Erhan Deniz; Abdulbasit Darem; Robert Szasz

doi:10.3934/math.20241591

AIMS Mathematics

2024, Volume 9, Issue 12: 33353-33364. doi: 10.3934/math.20241591

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Research article Special Issues

Application of $ q $-starlike and $ q $-convex functions under $ (u, v) $-symmetrical constraints

1.
Department of Mathematics, College of Science, Northeren Border University, P.O. Box 1321, Arar, 73222, KSA
2.
Laboratory of PDEs and Applications (LR03ES04), Faculty of Science of Tunis, University of Tunis El Manar, Tunis, Tunisia
3.
Mathematics Department, Prince Sattam Bin Abdulaziz University, Al-Kharj 16278, Saudi Arabia
4.
Department of Statistics and Information, Sana'a University, Sana'a 1247, Yemen
5.
Department of Mathematics, Faculty of Science and Letters, Kafkas University, Campus, 36100, Kars-T$ \ddot{u} $rkiye
6.
Department of Computer Science at college of Science, Northern Border University, Arar, Saudi Arabia
7.
Department of Mathematics and Informatics, Sapientia Hungarian University of Transylvania, T$ \hat{a} $rgu-Mures, Romania

Received: 14 August 2024 Revised: 17 October 2024 Accepted: 28 October 2024 Published: 25 November 2024
MSC : 30C45, 30C50

This research paper addressed a significant knowledge gap in the field of complex analysis by introducing a pioneering category of $ q $-starlike and $ q $-convex functions intricately interconnected with $ (u, v) $-symmetrical functions. Recognizing the limited exploration of these relationships in existing literature, the authors delved into the new classes $ \mathcal{S}_q(\alpha, u, v) $ and $ \mathcal{T}_q(\alpha, u, v) $. The main contribution of this work was the establishment of a framework that amalgamates $ q $-starlikeness and $ q $-convexity with the symmetry conditions imposed by $ (u, v) $-symmetrical functions. This comprehensive study include coefficient estimates, convolution conditions, and the properties underpinning the $ (\rho, q) $-neighborhood, thereby enriching the understanding of these novel function classes.
- analytic functions,
- $ q $-calculus,
- $ (u, v) $-symmetrical functions $ (\rho, q) $-neighborhood,
- coefficient inequality
Citation: Hanen Louati, Afrah Al-Rezami, Erhan Deniz, Abdulbasit Darem, Robert Szasz. Application of $ q $-starlike and $ q $-convex functions under $ (u, v) $-symmetrical constraints[J]. AIMS Mathematics, 2024, 9(12): 33353-33364. doi: 10.3934/math.20241591

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Abstract

This research paper addressed a significant knowledge gap in the field of complex analysis by introducing a pioneering category of $ q $-starlike and $ q $-convex functions intricately interconnected with $ (u, v) $-symmetrical functions. Recognizing the limited exploration of these relationships in existing literature, the authors delved into the new classes $ \mathcal{S}_q(\alpha, u, v) $ and $ \mathcal{T}_q(\alpha, u, v) $. The main contribution of this work was the establishment of a framework that amalgamates $ q $-starlikeness and $ q $-convexity with the symmetry conditions imposed by $ (u, v) $-symmetrical functions. This comprehensive study include coefficient estimates, convolution conditions, and the properties underpinning the $ (\rho, q) $-neighborhood, thereby enriching the understanding of these novel function classes.

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