SUBCLASS OF UNIFORMLY CONVEX FUNCTIONS ASSOCIATED WITH BOREL DISTRIBUTION SERIES | ||||
| Electronic Journal of Mathematical Analysis and Applications | ||||
| Volume 12, Issue 2, 2024, Page 1-12 PDF (471.8 K) | ||||
| Document Type: Regular research papers | ||||
| DOI: 10.21608/ejmaa.2024.294588.1217 | ||||
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| Authors | ||||
SONALI JADHAV1; P.G. JADHAV2; Thirupathi Reddy Pinninti   3
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| 1Department of Mathematics, New Arts, Commerce and Science College, Ahmednagar-414 001, Maharashtra,, India. | ||||
| 2Department of Mathematics, Balasaheb Jadhav Arts, Commerce and Science College, Pune-412 411, Maharashtra, India | ||||
| 3Department of Mathematics,DRKIST. Hyderabad | ||||
| Abstract | ||||
| The study of operators plays an important role in Geometric Function Theory. Many differential and integral operators can be written in terms of the convolution of certain analytic functions. It is observed that this formalism makes further mathematical exploration easier, and also improves the understanding of the geometric and symmetric properties of such operators. The Borel distribution series has applications in geometric function theory, particularly in the study of univalent functions, coefficient problems, and growth and distortion theorems. The Borel distribution series can be used to analyze the behavior of these functions, particularly in determining the distribution of their coefficients.It helps in understanding the probabilistic distribution of these coefficients, providing insights into their expected magnitude and variance.The Borel distribution series is used in modeling random holomorphic functions, which are of interest in various areas of mathematical physics and probability theory. This approach provides insights into the typical behavior of such functions, which can then be applied to specific problems in geometric function theory. In some cases, the Borel distribution series is applied to study the analytic continuation of functions. This involves understanding how functions defined by a power series can be extended beyond their radius of convergence, a topic closely related to the geometric properties of these functions. we obtain geometric properties like Coefficient inequalities, closure theorem, extreme points and radius of starlikeness and covexity of functions belonging to the subclass. | ||||
| Keywords | ||||
| analytic function; partial sums Convolution; Coefficient Estimate; Borel Distribution | ||||
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