Mathematics and Statistics Vol. 12(5), pp. 465 - 474
DOI: 10.13189/ms.2024.120508
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Certain Subclass of Analytic Functions Defined By q−analogue Differential Operator

G. Sujatha ¹, K. K. Viswanathan ^2,*, B. Venkateswarlu ¹, H. Niranjan ³, P. Thirupathi Reddy ^4
1 Department of Mathematics, GSS, GITAM University, Doddaballapur - 562 163, Bengaluru Rural, Karnataka, India
² Department of Mathematical Modeling, Faculty of Mathematics, Samarkand State University,15, University Bulevard, 140104 Samarkand, Uzbekistan
³ Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore-632014, Tamil Nadu, India
⁴ Department of Mathematics, D.R.K. Institute of Science & Technology, Bowrampet, 500043, Hyderabad, Telangana, India

ABSTRACT

The quantum (or q-) calculus is a vital area of study in the field of traditional mathematical analysis. This paper explores the innovative use of the q - q-derivative concept to develop specific differential operators, extending the class of Salagean operators to include univalent functions. By leveraging this new operator, we define a novel subclass of analytic functions within the open unit disc . Our primary objective is to establish a subclass of uniformly starlike functions corresponding to uniformly convex functions through the q-analog of the generalized differential operator. This research delves deeply into the intricate properties of this newly defined class of functions. We systematically analyze various aspects, such as coefficient estimates, which provide critical insights into the behavior of the functions within this class. Additionally, we examine neighborhoods, elucidating the local behavior and interaction of these functions within the region. Our study of partial sums offers a detailed understanding of the series representations and their properties. Furthermore, we investigate integral means inequalities, which are essential in understanding these functions' average growth and value distribution. The radii of close-to-convexity and star likeness are also rigorously evaluated, shedding light on the geometric properties that characterize the boundaries within which these functions maintain their specific starlike or convex nature.

KEYWORDS
Analytic Functions, Univalent Functions, Starlike Functions, Symmetric Points, Uniformly Convex Functions, Uniformly Starlike Functions, Sǎlǎgean Derivative, q−derivative

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] G. Sujatha , K. K. Viswanathan , B. Venkateswarlu , H. Niranjan , P. Thirupathi Reddy , "Certain Subclass of Analytic Functions Defined By q−analogue Differential Operator," Mathematics and Statistics, Vol. 12, No. 5, pp. 465 - 474, 2024. DOI: 10.13189/ms.2024.120508.

(b). APA Format:
G. Sujatha , K. K. Viswanathan , B. Venkateswarlu , H. Niranjan , P. Thirupathi Reddy (2024). Certain Subclass of Analytic Functions Defined By q−analogue Differential Operator. Mathematics and Statistics, 12(5), 465 - 474. DOI: 10.13189/ms.2024.120508.