A class of harmonic univalent functions associated with modified q−Cătaș operator

Authors

DOI:

https://doi.org/10.24193/subbmath.2024.4.02

Keywords:

Harmonic functions, modified q−Cătaș operator, coefficients estimate, extreme points

Abstract

Using the modified q−Cătaș operator, we define a class of harmonic univalent functions and obtain various properties for functions in this class.

 Mathematics Subject Classification (2010): 30C45.

References

1. Al-Oboudi, F.M., On univalent functions defined by a generalized Salagean operator, Internat. J. Math. Math. Sci., 27(2004), 1429-1436.

2. Annby, M.H., Mansour, Z.S., q−Fractional Calculus Equations, Lecture Notes in Math., 2056, Springer-Verlag Berlin Heidelberg, 2012.

3. Aouf, M.K., A subclass of Salagean-type harmonic univalent functions, Acta Univ. Apulensis Math. Inform., (2011), no. 25, 263-275.

4. Aouf, M.K. Darwish, H.E., Salagean, G.S., On a generalization of starlike functions with negative coefficients, Math. Tome 43, 66(2001), no. 1, 3-10.

5. Aouf, M.K., Madian, S.M., Neighborhoods properties for certain multivalent analytic functions associated with q − p−valent Cătaș operator, J. Taibah Univ. for Science, 14(2020), no. 1, 1226-1232.

6. Aouf, M.K., Mostafa, A.O., Some properties of a subclass of uniformly convex function with negative coefficients, Demonstr. Math., 41(2008), no. 2, 1-18.

7. Aouf, M.K., Mostafa, A.O., Subordination results for analytic functions associated with fractional q-calculus operators with complex order, Afr. Mat. 31(2020), 1387–1396.

8. Aouf, M.K., Mostafa, A.O., Adwan, E.A., Subclass of multivalent harmonic functions defined by Wright generalized hypergeometric functions, J. Complex Anal. Volume 2013, Article ID 397428, 1-7.

9. Aouf, M.K., Mostafa, A.O., Al-Quhali, F.Y., A class of β−uniformly univalent functions defined by Salagean type q−difference operator, Acta Univ. Apulensis Math. Inform., (2019), no. 60. 19-35.

10. Aouf, M.K., Mostafa, A.O., Shamandy, A., Adwan, E.A., Subclass of harmonic univalent functions defined by Dziok-Srivastafa operator, LE Matimatiche, 68(2013), no. 1, 165– 177.

11. Aouf, M.K., Mostafa, A.O., Shamandy, A., Wagdy, A.K., A study on certain class of harmonic functions of complex order associated with convolution, LE Matimatiche, 67(2012), no. 2, 169–183.

12. Aouf, M.K., Seoudy, T.M., Convolution properties for classes of bounded analytic functions with complex order defined by q−derivative operator, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math., 113(2019), no. 2, 1279-1288.

13. Aral, A, Gupta, V., Agarwal, R.P., Applications of q−Calculus in Operator Theory, Springer, New York, USA, 2013.

14. Cătaș, A., Oros, G.I., Oros, G., Differential subordinations associated with multiplier transformations, Abstract Appl. Anal., 2008(2008), ID 845724, 1-11.

15. Cho, N.E., Kim, T.H., Multiplier transformations and strongly close-to-convex functions, Bull. Korean Math. Soc., 40 (2003), no. 3, 399-410.

16. Cho, N.E., Srivastava, H.M., Argument estimates of certain analytic functions defined by a class of multiplier transformations, Math. Comput. Modelling, 37(2003), no. 1-2, 39-49.

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

18. Dixit, K.K., Porwal, S., A subclass of harmonic univalent functions with positive coefficients, Tamkang J. Math., 41(3) (2010), 261-269.

19. Frasin, B.A., Murugusundaramoorthy, G., A subordination results for a class of analytic functions defined by q-differential operator, Ann. Univ. Paedagog. Crac. Stud. Math., 19(2020), 53-64.

20. Gasper, G., Rahman, M., Basic Hypergeometric Series, Cambridge Univ. Press, Cambridge, U. K., 1990.

21. Govindaraj, M., Sivasubramanian, S., On a class of analytic function related to conic domains involving q−calculus, Anal. Math., 43(3)(2017), no. 5, 475-487.

22. Jackson, F.H., On q-functions and a certain difference operator, Trans. Royal. Soc. Edinburgh, 46(1908), 253-281.

23. Jahangiri, J.M., Murugusundaramoorthy, G., Vijaya, K., Salagean-type harmonic univalent functions, Southwest J. Pure Appl. Math., 2(2002), 77-82.

24. Mostafa, A.O., Aouf, M.K., Shamandy, A., Adwan, E.A., Subclass of harmonic univalent functions defined by modified Cătaș operator, Acta Univ. Apulensis Math. Inform., (2012), no. 32, 1-12.

25. Porwal, S., On a new subclass of harmonic univalent functions defined by multiplier transformation, Mathematica Moravica, 19-2(2015), 75-87.

26. Porwal, S., Dixit, K.K., New subclasses of harmonic starlike and convex functions, Kyungpook Math. J., 53(2013), 467-478.

27. Porwal, S., Dixit, K.K., On a new subclass of Salagean-type harmonic univalent functions, Indian J. Math., 54(2)(2012), 199-210.

28. Ramachandran, C., Soupramanien, T., Frasin, B.A., New subclasses of analytic function associated with q−difference operator, Eur. J. Pure Appl. Math, 10(2017), no. 2, 348-362.

29. Sălăgean, G., Subclasses of univalent functions, Lect. Notes in Math., (Springer Verlag), 1013(1983), 362-372.

30. Seoudy, T.M., Aouf, M.K., Coefficient estimates of new classes of q−starlike and q−convex functions of complex order, J. Math. Ineq., 10(2016), no. 1, 135-145.

31. Srivastava, H.M., Aouf, M.K., Mostafa, A.O., Some properties of analytic functions associated with fractional q− calculus operators, Miskolc Math. Notes, 20(2019), no. 2, 1245–1260.

32. Srivastava, H.M., Mostafa, A.O., Aouf, M.K., Zayed, H.M., Basic and fractional q−calculus and associated Fekete-Szego problem for p−valently q−starlike functions and p−valently q−convex functions of complex order, Miskolc Math. Notes, 20(2019), no. 1, 489-509.

33. Uralegaddi, B.A., Somanatha, C., Certain Classes of Univalent Functions, in Current Topics in Analytic Function Theory, 371-374, World Sci. Publishing, River Edge, New Jersey, London, Hong Kong, 1992, 371-374.

Downloads

Published

2024-12-13

How to Cite

MOSTAFA, A. O., & AOUF, M. K. (2024). A class of harmonic univalent functions associated with modified q−Cătaș operator. Studia Universitatis Babeș-Bolyai Mathematica, 69(4), 735–748. https://doi.org/10.24193/subbmath.2024.4.02

Issue

Section

Articles

Similar Articles

<< < 23 24 25 26 27 28 29 30 31 32 > >> 

You may also start an advanced similarity search for this article.