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Majorization property for certain classes of analytic functions associated with general operator

Year 2024, Volume: 73 Issue: 1, 122 - 130, 16.03.2024
https://doi.org/10.31801/cfsuasmas.1275521

Abstract

In this study, we introduce two new classes $S_{k}[E, F;\mu; \gamma]$ and $T_{k}(\theta,\,\mu,\,\gamma)$ of analytic functions using the general integral operator. For these two classes, we study the majorization properties. Some applications of the results are discussed in the form of corollaries.

References

  • Altintas, O., Özkan, Ö., Srivastava, H. M., Majorization by starlike functions of complex order, Complex Var. Elliptic Equ., (46)(3) (2001), 207–218. https://doi.org/10.1080/17476930108815409
  • Attiya, A. A., Bulboaca, T., A general theorem associated with the Briot-Bouquet differential subordination, J. Comput. Anal. Appl., 16(4) (2014), 722–730.
  • Bulboaca, T., Classes of first-order differential subordinations, Demonstr. Math., 35 (2) (2002), 287–292. https://doi.org/10.4236/am.2011.27114
  • Flett, T. M., The dual of an inequality of Hardy and Littlewood and some related inequalities, J. Math. Anal. Appl., 38(3) (1972), 746–765. https://doi.org/10.1016/0022-247X(72)90081-9
  • Fournier, R., Ruscheweyh, S., On two extremal problems related to univalent functions, Rocky Mt. J. Math., 24 (1994), 529–538. https://doi.org/10.1216/rmjm/1181072416
  • Goswami, P., Sharma B., Bulboac˘a, T., Majorization for certain classes of analytic functions using multiplier transformation, Appl. Math. Lett., 23(5) (2010), 633–637. https://doi.org/10.1016/j.aml.2010.01.029
  • Goswami, P., Aouf, M. K., Majorization properties for certain classes of analytic functions using the Salagean operator, Appl. Math. Lett., 23(11) (2010), 1351–1354. https://doi.org/10.1016/j.aml.2010.06.030
  • Gour, M. M., Goswami, P., Frasin B A., Althobaithi S., Majorization for certain classes of analytic functions defined by Fournier-Ruscheweyh integral operator, Journal of Mathematics, 2022 (2022), Article ID: 6580700. https://doi.org/10.1155/2022/6580700
  • Goyal, S. P., Goswami, P., Majorization for certain classes of meromorphic functions defined by integral operator, Ann. Univ. Mariae Curie-Sk lodowska, Sect. A, 66(2) (2012), 57-62. https://doi.org/10.2478/v10062-012-0013-1
  • Goyal, S. P., Goswami, P., Majorization for certain classes of analytic functions defined by fractional derivatives, Appl. Math. Lett., 22(12) (2009), 1855-1858. https://doi.org/10.1016/j.aml.2009.07.009
  • Jung, I. B., Kim, Y. C., Srivastava, H. M., The Hardy space of analytic functions associated with certain one-parameter families of integral operators, J. Math. Anal. Appl., 176(1) (1993), 138-147. https://doi.org/10.1006/jmaa.1993.1204
  • Kutbi, M. A., Attiya, A. A., Differential subordination result with the Srivastava-Attiya integral operator, J. Inequal. Appl., 2010 (2010), 1-10. https://doi.org/10.1155/2010/618523
  • Li, J. L., Srivastava, H. M., Starlikeness of functions in the range of a class of integral operators, Integral Transforms Spec. Funct., 15(2) (2004), 129-136. https://doi.org/10.1080/10652460310001600708
  • Li, J. L., Srivastava, H. M., Some questions and conjectures in the theory of univalent functions, Rocky Mt. J. Math., 28 (1998), 1035-1041. http://hdl.handle.net/1828/1649
  • Li, J. L., Notes on Jung-Kim-Srivastava integral operator, J. Math. Anal. Appl., 294(1) (2004), 96-103. https://doi.org/10.1016/j.jmaa.2004.01.040
  • Liu, J. L., Noor, K. I., Some properties of Noor integral operator, J. Nat. Geom., 21(1-2) (2002), 81–90. https://doi.org/10.1016/S0022-247X(03)00270-1
  • MacGreogor, T. H., Majorization by univalent functions, Duke Math. J., 34 (1967), 95-102. https://doi.org/10.1215/S0012-7094-67-03411-4
  • Nehari Z., Conformal Mapping, MacGraw-Hill Book Company, New York, Toronto, London, 1955.
  • Roberston M.S., Quasi-subordination and coefficient conjectures, Bull. Am. Math. Soc., 76 (1970), 1-9.
  • Srivastava, H. M., Attiya, A. A., An integral operator associated with the Hurwitz-Lerch Zeta function and differential subordination, Integral Transforms Spec. Funct., 18(3) (2007), 207-216. https://doi.org/10.1080/10652460701208577
  • Tang, H., Aouf, M. K., Deng, G. T., Majorization problems for certain subclasses of meromorphic multivalent functions associated with the Liu-Srivastava operator, Filomat, 29(4) (2015), 763-772. https://doi.org/10.2298/FIL1504763T
  • Tang, H., Deng, G., Majorization problems for two subclasses of analytic functions connected with the Liu-Owa integral operator and exponential function, J. Inequal. Appl., 277 (2018), 1-11. https://doi.org/10.1186/s13660-018-1865-x
Year 2024, Volume: 73 Issue: 1, 122 - 130, 16.03.2024
https://doi.org/10.31801/cfsuasmas.1275521

Abstract

References

  • Altintas, O., Özkan, Ö., Srivastava, H. M., Majorization by starlike functions of complex order, Complex Var. Elliptic Equ., (46)(3) (2001), 207–218. https://doi.org/10.1080/17476930108815409
  • Attiya, A. A., Bulboaca, T., A general theorem associated with the Briot-Bouquet differential subordination, J. Comput. Anal. Appl., 16(4) (2014), 722–730.
  • Bulboaca, T., Classes of first-order differential subordinations, Demonstr. Math., 35 (2) (2002), 287–292. https://doi.org/10.4236/am.2011.27114
  • Flett, T. M., The dual of an inequality of Hardy and Littlewood and some related inequalities, J. Math. Anal. Appl., 38(3) (1972), 746–765. https://doi.org/10.1016/0022-247X(72)90081-9
  • Fournier, R., Ruscheweyh, S., On two extremal problems related to univalent functions, Rocky Mt. J. Math., 24 (1994), 529–538. https://doi.org/10.1216/rmjm/1181072416
  • Goswami, P., Sharma B., Bulboac˘a, T., Majorization for certain classes of analytic functions using multiplier transformation, Appl. Math. Lett., 23(5) (2010), 633–637. https://doi.org/10.1016/j.aml.2010.01.029
  • Goswami, P., Aouf, M. K., Majorization properties for certain classes of analytic functions using the Salagean operator, Appl. Math. Lett., 23(11) (2010), 1351–1354. https://doi.org/10.1016/j.aml.2010.06.030
  • Gour, M. M., Goswami, P., Frasin B A., Althobaithi S., Majorization for certain classes of analytic functions defined by Fournier-Ruscheweyh integral operator, Journal of Mathematics, 2022 (2022), Article ID: 6580700. https://doi.org/10.1155/2022/6580700
  • Goyal, S. P., Goswami, P., Majorization for certain classes of meromorphic functions defined by integral operator, Ann. Univ. Mariae Curie-Sk lodowska, Sect. A, 66(2) (2012), 57-62. https://doi.org/10.2478/v10062-012-0013-1
  • Goyal, S. P., Goswami, P., Majorization for certain classes of analytic functions defined by fractional derivatives, Appl. Math. Lett., 22(12) (2009), 1855-1858. https://doi.org/10.1016/j.aml.2009.07.009
  • Jung, I. B., Kim, Y. C., Srivastava, H. M., The Hardy space of analytic functions associated with certain one-parameter families of integral operators, J. Math. Anal. Appl., 176(1) (1993), 138-147. https://doi.org/10.1006/jmaa.1993.1204
  • Kutbi, M. A., Attiya, A. A., Differential subordination result with the Srivastava-Attiya integral operator, J. Inequal. Appl., 2010 (2010), 1-10. https://doi.org/10.1155/2010/618523
  • Li, J. L., Srivastava, H. M., Starlikeness of functions in the range of a class of integral operators, Integral Transforms Spec. Funct., 15(2) (2004), 129-136. https://doi.org/10.1080/10652460310001600708
  • Li, J. L., Srivastava, H. M., Some questions and conjectures in the theory of univalent functions, Rocky Mt. J. Math., 28 (1998), 1035-1041. http://hdl.handle.net/1828/1649
  • Li, J. L., Notes on Jung-Kim-Srivastava integral operator, J. Math. Anal. Appl., 294(1) (2004), 96-103. https://doi.org/10.1016/j.jmaa.2004.01.040
  • Liu, J. L., Noor, K. I., Some properties of Noor integral operator, J. Nat. Geom., 21(1-2) (2002), 81–90. https://doi.org/10.1016/S0022-247X(03)00270-1
  • MacGreogor, T. H., Majorization by univalent functions, Duke Math. J., 34 (1967), 95-102. https://doi.org/10.1215/S0012-7094-67-03411-4
  • Nehari Z., Conformal Mapping, MacGraw-Hill Book Company, New York, Toronto, London, 1955.
  • Roberston M.S., Quasi-subordination and coefficient conjectures, Bull. Am. Math. Soc., 76 (1970), 1-9.
  • Srivastava, H. M., Attiya, A. A., An integral operator associated with the Hurwitz-Lerch Zeta function and differential subordination, Integral Transforms Spec. Funct., 18(3) (2007), 207-216. https://doi.org/10.1080/10652460701208577
  • Tang, H., Aouf, M. K., Deng, G. T., Majorization problems for certain subclasses of meromorphic multivalent functions associated with the Liu-Srivastava operator, Filomat, 29(4) (2015), 763-772. https://doi.org/10.2298/FIL1504763T
  • Tang, H., Deng, G., Majorization problems for two subclasses of analytic functions connected with the Liu-Owa integral operator and exponential function, J. Inequal. Appl., 277 (2018), 1-11. https://doi.org/10.1186/s13660-018-1865-x
There are 22 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Pranay Goswamı 0000-0003-1205-1975

Murli Manohar Gour 0000-0003-2907-8226

Som Prakash Goyal 0009-0007-9016-9529

Lokesh Kumar Yadav 0000-0003-0896-5723

Publication Date March 16, 2024
Submission Date April 2, 2023
Acceptance Date October 6, 2023
Published in Issue Year 2024 Volume: 73 Issue: 1

Cite

APA Goswamı, P., Gour, M. M., Goyal, S. P., Yadav, L. K. (2024). Majorization property for certain classes of analytic functions associated with general operator. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 73(1), 122-130. https://doi.org/10.31801/cfsuasmas.1275521
AMA Goswamı P, Gour MM, Goyal SP, Yadav LK. Majorization property for certain classes of analytic functions associated with general operator. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. March 2024;73(1):122-130. doi:10.31801/cfsuasmas.1275521
Chicago Goswamı, Pranay, Murli Manohar Gour, Som Prakash Goyal, and Lokesh Kumar Yadav. “Majorization Property for Certain Classes of Analytic Functions Associated With General Operator”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73, no. 1 (March 2024): 122-30. https://doi.org/10.31801/cfsuasmas.1275521.
EndNote Goswamı P, Gour MM, Goyal SP, Yadav LK (March 1, 2024) Majorization property for certain classes of analytic functions associated with general operator. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73 1 122–130.
IEEE P. Goswamı, M. M. Gour, S. P. Goyal, and L. K. Yadav, “Majorization property for certain classes of analytic functions associated with general operator”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 73, no. 1, pp. 122–130, 2024, doi: 10.31801/cfsuasmas.1275521.
ISNAD Goswamı, Pranay et al. “Majorization Property for Certain Classes of Analytic Functions Associated With General Operator”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73/1 (March 2024), 122-130. https://doi.org/10.31801/cfsuasmas.1275521.
JAMA Goswamı P, Gour MM, Goyal SP, Yadav LK. Majorization property for certain classes of analytic functions associated with general operator. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2024;73:122–130.
MLA Goswamı, Pranay et al. “Majorization Property for Certain Classes of Analytic Functions Associated With General Operator”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 73, no. 1, 2024, pp. 122-30, doi:10.31801/cfsuasmas.1275521.
Vancouver Goswamı P, Gour MM, Goyal SP, Yadav LK. Majorization property for certain classes of analytic functions associated with general operator. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2024;73(1):122-30.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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