Geometric convolution characteristics of $ q $-Janowski type functions related to $ (j, k) $-symmetrical functions

Faizah D Alanazi; Fuad Alsarari; Faizah D Alanazi; Fuad Alsarari

doi:10.3934/math.2025304

AIMS Mathematics

2025, Volume 10, Issue 3: 6652-6663. doi: 10.3934/math.2025304

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Geometric convolution characteristics of $ q $-Janowski type functions related to $ (j, k) $-symmetrical functions

Faizah D Alanazi ¹,
Fuad Alsarari ^{2
,
,}

1.
Department of Mathematics, College of Science, Northern Border University, Arar, Saudi Arabia
2.
Department of Mathematics and statistics, College of Science, Yanbu, Taibah University, Saudi Arabia

Received: 17 January 2025 Revised: 04 March 2025 Accepted: 11 March 2025 Published: 25 March 2025
MSC : 30C45, 30C50

In this paper, we investigate the properties of functions belonging to the classes $ \psi(\eta)\in\mathcal{\overline{T}}^{j, k}_q(A, B) $ and $ \psi(\eta)\in\mathcal{\overline{K}}^{j, k}_q(A, B) $, these functions are defined within the context of $ q $-calculus and $ (j, k) $-symmetrical functions. We employ convolution techniques and quantum calculus to explore the convolution conditions, which will serve as foundational results for further studies in our work Furthermore, we establish conditions for membership in $ \psi(\eta)\in\mathcal{\overline{T}}^{j, k}_q(A, B) $ and present an example demonstrating the application of these results to rational functions.
- quantum calculus,
- analytic functions,
- Hadamard product,
- $ q $-starlike functions,
- $ (x, y) $-symmetrical functions,
- $ q $-convex functions
Citation: Faizah D Alanazi, Fuad Alsarari. Geometric convolution characteristics of $ q $-Janowski type functions related to $ (j, k) $-symmetrical functions[J]. AIMS Mathematics, 2025, 10(3): 6652-6663. doi: 10.3934/math.2025304

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Abstract

In this paper, we investigate the properties of functions belonging to the classes $ \psi(\eta)\in\mathcal{\overline{T}}^{j, k}_q(A, B) $ and $ \psi(\eta)\in\mathcal{\overline{K}}^{j, k}_q(A, B) $, these functions are defined within the context of $ q $-calculus and $ (j, k) $-symmetrical functions. We employ convolution techniques and quantum calculus to explore the convolution conditions, which will serve as foundational results for further studies in our work Furthermore, we establish conditions for membership in $ \psi(\eta)\in\mathcal{\overline{T}}^{j, k}_q(A, B) $ and present an example demonstrating the application of these results to rational functions.

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