Research Article
BibTex RIS Cite
Year 2020, Volume: 4 Issue: 4, 459 - 482, 30.12.2020
https://doi.org/10.31197/atnaa.825204

Abstract

References

  • [1] K. Al-Shaqsi and M. Darus, On certain subclasses of analytic functions defined by a multiplier transformation with two parameters, Appl. Math. Sci 3(36) (2009), 1799-1810.
  • [2] S. D. Bernardi, Convex and starlike univalent functions, Trans. Am. Math. Soc. 135(1969), 429-446.
  • [3] N.E. Cho and K.I. Noor, Inclusion properties for certain classes of meromorphic functions associated with the Choi-Saigo- Srivastava operator, J. Math. Anal. Appl. 320(2) (2006), 779-786.
  • [4] J.H. Choi, M. Saigo and H.M. Srivastava, Some inclusion properties of a certain family of integral operators, J. Math. Anal. Appl. 276(1) (2002), 432-445.
  • [5] R. Diaz and E. Pariguan, On hypergeometric functions and Pochhammer k-symbol, Divulgaciones Matemtcas 15(2) (2007), 179-192.
  • [6] P. Eenigenburg, S. Miller, P. Mocanu and M. Reade, On a Briot-Bouquet differential subordination, Revue Roumaine de Math. Pures Appl. 29(7) (1984), 567-573.
  • [7] C.Y. Gao, S.-M. Yuan and H.M. Srivastava, Some functional inequalities and inclusion relationships associated with certain families of integral operators, Comput. Math. Appl. 49(11-12) (2005), 1787-1795.
  • [8] I.B. Jung, Y.C. Kim and H.M. Srivastava, The Hardy space of analytic functions associated with certain one-parameter families of integral operators, J. Math. Anal. Appl. 176(1) (1993), 138-147.
  • [9] W. Ma and D. Minda, A unified treatment of some special classes of univalent functions, Proceeding of the Conference on Complex Analysis, Z. Li, F. Ren, L. Yang and S. Zhang (Eds), Int. Press (1994), 157-169.
  • [10] S.S. Miller and P.T. Mocanu, Differential subordinations: theory and applications, CRC Press (2000).
  • [11] S.S. Miller and P.T. Mocanu , Differential subordinations and univalent functions., Mich. Math. J. 28(2) (1981), 157-172.
  • [12] G. Murugusundaramoorthy and N. Magesh, On certain subclasses of analytic functions associated with hypergeometric functions, Appl. Math. Lett. 24(4) (2011), 494-500.
  • [13] K.I. Noor, On quasi-convex functions and related topics, Int. J. Math. Math. Sci. 10(2) (1987), 241- 258.
  • [14] S. Porwal and K. K. Dixit, An application of generalized Bessel functions on certain analytic functions, Acta Univ. M. Belii Ser. Math. (2013), 51-57.
  • [15] E.D. Rainville, Special functions, Chelsea (1971).
  • [16] Z.G. Wang, C.Y. Gao and S.M. Yuan, On certain subclasses of close-to-convex and quasi-convex functions with respect to k-symmetric points, J. Math. Anal. Appl. 322(1) (2006), 97-106.

Some Properties for Certain Subclasses of Analytic Functions Associated with $k-$Integral Operators

Year 2020, Volume: 4 Issue: 4, 459 - 482, 30.12.2020
https://doi.org/10.31197/atnaa.825204

Abstract

In this paper, the k-integral operators for analytic functions dened in the open unit disc
U = fz 2 C : jzj < 1g are introduced. Several new subclasses of analytic functions satisfying certain
relations involving these operators are also introduced. Further, we establish the inclusion relation for
these subclasses. Next, the integral preserving properties of a k-integral operator satised by these newly
introduced subclasses are obtained. Some applications of the results are discussed. Concluding remarks
are also given.

References

  • [1] K. Al-Shaqsi and M. Darus, On certain subclasses of analytic functions defined by a multiplier transformation with two parameters, Appl. Math. Sci 3(36) (2009), 1799-1810.
  • [2] S. D. Bernardi, Convex and starlike univalent functions, Trans. Am. Math. Soc. 135(1969), 429-446.
  • [3] N.E. Cho and K.I. Noor, Inclusion properties for certain classes of meromorphic functions associated with the Choi-Saigo- Srivastava operator, J. Math. Anal. Appl. 320(2) (2006), 779-786.
  • [4] J.H. Choi, M. Saigo and H.M. Srivastava, Some inclusion properties of a certain family of integral operators, J. Math. Anal. Appl. 276(1) (2002), 432-445.
  • [5] R. Diaz and E. Pariguan, On hypergeometric functions and Pochhammer k-symbol, Divulgaciones Matemtcas 15(2) (2007), 179-192.
  • [6] P. Eenigenburg, S. Miller, P. Mocanu and M. Reade, On a Briot-Bouquet differential subordination, Revue Roumaine de Math. Pures Appl. 29(7) (1984), 567-573.
  • [7] C.Y. Gao, S.-M. Yuan and H.M. Srivastava, Some functional inequalities and inclusion relationships associated with certain families of integral operators, Comput. Math. Appl. 49(11-12) (2005), 1787-1795.
  • [8] I.B. Jung, Y.C. Kim and H.M. Srivastava, The Hardy space of analytic functions associated with certain one-parameter families of integral operators, J. Math. Anal. Appl. 176(1) (1993), 138-147.
  • [9] W. Ma and D. Minda, A unified treatment of some special classes of univalent functions, Proceeding of the Conference on Complex Analysis, Z. Li, F. Ren, L. Yang and S. Zhang (Eds), Int. Press (1994), 157-169.
  • [10] S.S. Miller and P.T. Mocanu, Differential subordinations: theory and applications, CRC Press (2000).
  • [11] S.S. Miller and P.T. Mocanu , Differential subordinations and univalent functions., Mich. Math. J. 28(2) (1981), 157-172.
  • [12] G. Murugusundaramoorthy and N. Magesh, On certain subclasses of analytic functions associated with hypergeometric functions, Appl. Math. Lett. 24(4) (2011), 494-500.
  • [13] K.I. Noor, On quasi-convex functions and related topics, Int. J. Math. Math. Sci. 10(2) (1987), 241- 258.
  • [14] S. Porwal and K. K. Dixit, An application of generalized Bessel functions on certain analytic functions, Acta Univ. M. Belii Ser. Math. (2013), 51-57.
  • [15] E.D. Rainville, Special functions, Chelsea (1971).
  • [16] Z.G. Wang, C.Y. Gao and S.M. Yuan, On certain subclasses of close-to-convex and quasi-convex functions with respect to k-symmetric points, J. Math. Anal. Appl. 322(1) (2006), 97-106.
There are 16 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Eman Abujarad This is me 0000-0003-0715-1293

Mohammed H Abujarad 0000-0001-7995-1025

Thabet Abdeljawad 0000-0002-8889-3768

Fahd Jarad 0000-0002-3303-0623

Publication Date December 30, 2020
Published in Issue Year 2020 Volume: 4 Issue: 4

Cite