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.

Downloads

Download data is not yet available.

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.

Clunie J. and Sheil-Small T., Harmonic univalent functions, Ann. Acad. Sci. Fenn. Ser. A I Math., 9(1984), 3-25.

Dorff M., Minimal graphs in R3 over convex domain, Proc. Am. Math. Soc., 132(2003), 491-498.

Duren P. L., Harmonic mappings in the plane, Cambridge University Press, (2004).

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.

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.

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.

International Journal of Scientific Research in Science and Technology

Downloads

Published

12-12-2024

Issue

Vol. 11 No. 6 (2024): November-December

Section

Research Articles

License

Copyright (c) 2024 International Journal of Scientific Research in Science and Technology

Creative Commons License

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