Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 16 (2021), 223 -- 236

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This work is licensed under a Creative Commons Attribution 4.0 International License.

AN APPLICATION OF GENERALIZED DISTRIBUTION SERIES ON CERTAIN CLASSES OF UNIVALENT FUNCTIONS ASSOCIATED WITH CONIC DOMAINS

Saurabh Porwal and G. Murugusundaramoorthy

Abstract. The purpose of the present paper is to obtain some necessary and sufficient conditions for generalized distribution series belonging to the classes UCV(α, β), SP(α, β), UCV(β), C(λ), S*(λ) and obtain some inclusion relation between the classes Rτ(A, B) and UCV(α, β), UCV(β), C(λ). Finally, we attain some necessary and sufficient conditions of integral operator associated with the generalized distribution series for the classes UCV(α, β), UCV(β) and C(λ). Some particular cases of our main results are briefly indicated.

2020 Mathematics Subject Classification: 30C45.
Keywords: generalized distribution, analytic, univalent functions, uniformly convex function and uniformly starlike functions.

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Saurabh Porwal
Department of Mathematics,
Ram Sahai Government Degree College,
Bairi Shivrajpur-Kanpur-209205, (U.P.), India.
e-mail: saurabhjcb@rediffmail.com


G. Murugusundaramoorthy
School of Advanced Sciences, Vellore Institute of Technology,
Vellore-632014, Tamilnadu, India.
e-mail: gmsmoorthy@yahoo.com

http://www.utgjiu.ro/math/sma