Riesz Dunford integral and operators on Hilbert space based on univalent functions with fixed residue

Document Type : Research Paper

Authors

Department of Mathematics, Payame Noor University, Tehran, Iran

Abstract

In the present paper, we introduce and investigate a new class of meromorphic functions analytic in the open unit disk and applying a $q-$derivative and $q-$differential integral operator associated with quantum calculus. Furthermore, by using the familiar Riesz-Dunford integral of a linear operator on Hilbert space H, a new class of univalent functions with a fixed point is introduced. Coefficient estimate, distortion bound and extreme points are obtained.

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References

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[3] Gasper, G., & Rahman, M. (2011). Basic Hypergeometric Series, Vol. 96. Cambridge University Press.
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[5] Jakson, FH. (1909). On q􀀀functions and a certain di erence operator, Trans. Royal Soc. Edinburg, 46(2), 253-281. http://dx.doi.org/10.1017/S0080456800002751.
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[7] Saleh, ZM, & Mustafa, AO. (2022). Class of meromorphic univalent functions with  xed second positive coecients de ned by q􀀀di erence operator, Proc. Pak. Acad. Sci., A. Physical and Computational Sciences 59(1), 29-36. https://doi.org/10.53560/PPASA(59-1)640. 

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History

  • Receive Date: 04 June 2025
  • Revise Date: 15 January 2026
  • Accept Date: 02 February 2026

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