Certain Subclass of Harmonic Univalent Functions Associated With Fractional Calculus Operator

Authors

  • Puneet Shukla Department of Mathematics, Brahmanand P.G. College, C.S.J.M. University, Kanpur-208004, Uttar Pradesh, India Author
  • A. L. Pathak Department of Mathematics, Brahmanand P.G. College, C.S.J.M. University, Kanpur-208004, Uttar Pradesh, India Author

DOI:

https://doi.org/10.32628/IJSRST24114322

Keywords:

Harmonic functions, Univalent functions, Fractional Calculus Operator

Abstract

In this paper, a class of complex-valued harmonic univalent functions f (z) in the open disk U is defined by fractional calculus operator. We obtained coefficient bounds, distortion inequalities, convex combination, extreme points and convolution conditions for this class.

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References

Altinkaya S. and Yalcin S., On a class of harmonic univalent functions defined by using a new differential operator, Th. Appl. of Math. And Comp. Sci., 6(2)(2016), 125-133.

Avci Y. and Zlotkiewicz E., On harmonic univalent mappings, Ann. Univ. Mariae Curie-Sklodowska Sect. A. 44(1990), 1-7.

Bucur R., Andrei L. and Danial D., Coefficient bounds and Fekete-Szego problem for a class of analytic functions defined by using a new differential operator, Appl. Math. Sci. 9(2015), 1355-1368. DOI: https://doi.org/10.12988/ams.2015.511

Clunie J. and Sheil-Small T., Harmonic univalent functions, Ann. Acad. Sci. Fenn. Ser. A I Math., 9(1984), 3-25. DOI: https://doi.org/10.5186/aasfm.1984.0905

Dorff M., Minimal graphs in R3 over convex domain, Proc. Am. Math. Soc., 132(2003), 491-498. DOI: https://doi.org/10.1090/S0002-9939-03-07109-0

Duren P. L., Harmonic mappings in the plane, Cambridge University Press, (2004). DOI: https://doi.org/10.1017/CBO9780511546600

Jahangiri J. M. and Silverman H., Meromorphic univalent harmonic functions with negative coefficients, Bull. Korean Math. Soc. 36(1999), 763-770.

Metkari A. N., Sangle N. D. and Hande S.P., A new class of univalent harmonic meromorphic functions of complex order, Our Heritage., 68(30)(2020), 5506-5518.

Owa S., On the distortion theorem I, Kyungpook Math. J., 18(1978), 53-59.

Salagean G. S., Subclasses of univalent functions, Complex analysis-fifth Romanin Finish Seminar, Bucharest, 1(1983), pp. 362-372.

Salagean G. S., Subclasses of univalent functions, Lecture Notes in Math. Springer-Verlag Heidelberg, 1013(1983), 362-372. DOI: https://doi.org/10.1007/BFb0066543

Sangle N.D., Metkari A.N. and Hande S.P., On a subclass of harmonic univalent functions defined by using a new differential operator, IJSSSR., Vol-1, Issue-3(2023), pp. 27-37.

Silverman H., Harmonic univalent functions with negative coefficients, J. Math. Anal. Appl., 220(1998), 283-289. DOI: https://doi.org/10.1006/jmaa.1997.5882

Silverman H., Subclasses of harmonic univalent functions, Physical Review A, 28(1999), 275-284.

Srivastava H.M. and Owa S., An application of the fractional derivative, Math. Japon., 29(1984), 383-389.

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Published

12-12-2024

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Research Articles