SOME FAMILIES OF ANALYTIC FUNCTIONS RELATED TO THE ERDELY-KOBER INTEGRAL OPERATOR | ||
| Journal of Fractional Calculus and Applications | ||
| Volume 16, Issue 1, 2025, Pages 1-10 PDF (388.06 K) | ||
| Document Type: Regular research papers | ||
| DOI: 10.21608/jfca.2024.290640.1102 | ||
| Authors | ||
| Aditya Lagad* 1; Rajkumar Ingle2; Dr.Thirupathi Reddy Reddy pinninti3 | ||
| 1N.E.S SCIENCE COLLEGE,NANDED | ||
| 2Department of Mathematics, Bahirji Smarak Mahavidyalay, Bashmathnagar - 431 512, Maharashtra, India | ||
| 3Department of Mathematics, DRK Institute of Science and Technology, Bowarmpet-500 043, Hyderabad, Telangana, India. | ||
| Abstract | ||
| The Erdelyi-Kober integral operator, named after mathematicians Arthur Erdelyi and Hans Kober, finds applications in various areas of mathematics, physics, engineering, and other fields. Some of the key applications include: Integral Equations, Differential Equations, Potential Theory, Fractional Calculus, Special Functions, Probability Theory and Analytic Number Theory. It serves as a bridge between different mathematical concepts and provides a common framework for tackling complex problems. Furthermore, the Erdelyi-Kober operator continues to inspire research and innovation, as mathematicians and scientists explore new applications, extensions, and connections with other areas of mathematics and physics. The Erdelyi-Kober integral operator is a specific integral transform used in mathematical analysis, particularly in connection with solving certain differential equations and studying properties of functions. The study of analytic functions in connection with the Erdelyi-Kober integral operator involves analyzing how the operator affects the analytic properties of functions, ensuring convergence, and understanding the behavior near singularities. These properties are crucial for applications in various branches of mathematics, including differential equations, harmonic analysis, and integral transforms. This paper aims to explore a novel category of regular mapping characterized by negative coefficients in connection with the Erdely-Kober integral operator within the unit disk. We will establish fundamental properties such as coefficient inequalities, extreme points, integral means inequalities and subordination results for this class | ||
| Keywords | ||
| convex; starlike; integral operator; coefficient estimates; subordination | ||
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