Geometric properties of holomorphic functions involving generalized distribution with bell number

S. Santhiya; K. Thilagavathi; S. Santhiya; K. Thilagavathi

doi:10.3934/math.2023405

AIMS Mathematics

2023, Volume 8, Issue 4: 8018-8026. doi: 10.3934/math.2023405

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Research article

Geometric properties of holomorphic functions involving generalized distribution with bell number

S. Santhiya ,
K. Thilagavathi ^,

School of Advanced Sciences, Vellore Institute of Technology, Vellore 632014, Tamil Nadu, India

Received: 04 November 2022 Revised: 12 December 2022 Accepted: 20 December 2022 Published: 31 January 2023
MSC : 30C80, 30C45

One of the statistical tools used in geometric function theory is the generalized distribution which has recently gained popularity due to its use in solving practical issues. In this work, we obtained a new subclass of holomorphic functions, which defined by the convolution of generalized distribution and incomplete beta function associated with subordination in terms of the bell number. Further, we estimate the coefficient inequality and upper bound for a subclass of holomorphic functions. Our findings show a clear relationship between statistical theory and geometric function theory.
- holomorphic functions,
- generalized distribution,
- bell number,
- incomplete beta functions
Citation: S. Santhiya, K. Thilagavathi. Geometric properties of holomorphic functions involving generalized distribution with bell number[J]. AIMS Mathematics, 2023, 8(4): 8018-8026. doi: 10.3934/math.2023405

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Abstract

One of the statistical tools used in geometric function theory is the generalized distribution which has recently gained popularity due to its use in solving practical issues. In this work, we obtained a new subclass of holomorphic functions, which defined by the convolution of generalized distribution and incomplete beta function associated with subordination in terms of the bell number. Further, we estimate the coefficient inequality and upper bound for a subclass of holomorphic functions. Our findings show a clear relationship between statistical theory and geometric function theory.

References

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