Document Type : Regular research papers
Authors
1
N.E.S SCIENCE COLLEGE,NANDED
2
Department of Mathematics, Bahirji Smarak Mahavidyalay, Bashmathnagar - 431 512, Maharashtra, India
3
Department 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
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