Majorization in Analytic Functions Among Distinct Classes Defined by Modified Tremblay Fractional Operator

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-22-2024-119
Published: Jul 19, 2024
Cite as:
Indushree Mohan, Madhu Venkataraman, Majorization in Analytic Functions Among Distinct Classes Defined by Modified Tremblay Fractional Operator, Int. J. Anal. Appl., 22 (2024), 119.

Main Article Content

Indushree Mohan, Madhu Venkataraman

Abstract

This paper presents and investigates three distinct kinds of analytic functions described by the Modified Tremblay Fractional Operator: IΥ[A,B], QΥ[A,B], and PΥ[A,B]. We give a detailed knowledge of these unique categories features by exploring majorization difficulties within them. By means of a careful analysis of majorization phenomena, we present a range of novel findings that demonstrate the significance of parameter specialisation in these classes. This work greatly expands our understanding of analytic functions and improves the field of mathematical analysis as a whole. To sum up, this study offers a comprehensive investigation of new analytic function classes, clarifies certain aspects of majorization, and makes significant contributions that broaden our understanding of complex analysis and geometric function theory.

Article Details

References

  1. O. Altinta¸s, Ö. Özkan, H.M. Srivastava, Majorization by Starlike Functions of Complex Order, Complex Var. Theory Appl.: Int. J. 46 (2001), 207–218. https://doi.org/10.1080/17476930108815409.
  2. M. Arif, M. Ul-Haq, O. Barukab, et al. Majorization results for certain subfamilies of analytic functions, J. Function Spaces 2021 (2021), 5548785. https://doi.org/10.1155/2021/5548785.
  3. S. Bulut, E. A. Adegani, T. Bulboaca, Majorization Results for a General Subclass of Meromorphic Multivalent Functions, U.P.B. Sci. Bull., Ser. A, 83 (2021), 121–128.
  4. A. Çetinkaya, Majorization Problems for Subclasses of Univalent Functions Involving the Jung-Kim-Srivastava Integral Operator, Conf. Proc. Sci. Technol. 4 (2021), 238–241.
  5. Z. Esa, A. Kilicman, R.W. Ibrahim, M.R. Ismail, S.K.S. Husain, Application of Modified Complex Tremblay Operator, AIP Conf. Proc. 1739 (2016), 020059. https://doi.org/10.1063/1.4952539.
  6. S.P. Goyal, P. Goswami, Majorization for Certain Classes of Analytic Functions Defined by Fractional Derivatives, Appl. Math. Lett. 22 (2009), 1855–1858. https://doi.org/10.1016/j.aml.2009.07.009.
  7. P. Goswami, B. Sharma, T. Bulboac ˘a, Majorization for Certain Classes of Analytic Functions Using Multiplier Transformation, Appl. Math. Lett. 23 (2010), 633–637. https://doi.org/10.1016/j.aml.2010.01.029.
  8. P. Goswami, M.K. Aouf, Majorization Properties for Certain Classes of Analytic Functions Using the S ˘al ˘agean Operator, Appl. Math. Lett. 23 (2010), 1351–1354. https://doi.org/10.1016/j.aml.2010.06.030.
  9. S.P. Goyal, P. Goswami, Majorization for certain classes of meromorphic functions defined by integral operator, Ann. Univ. Mariae Curie-Sklodowska Sect. A Math. 66 (2012), 57–62. https://doi.org/10.2478/v10062-012-0013-1.
  10. M.M. Gour, P. Goswami, B.A. Frasin, S. Althobaiti, Majorization for Certain Classes of Analytic Functions Defined by Fournier-Ruscheweyh Integral Operator, J. Math. 2022 (2022), 6580700. https://doi.org/10.1155/2022/6580700.
  11. R.W. Ibrahim, J.M. Jahangiri, Boundary Fractional Differential Equation in a Complex Domain, Bound Value Probl. 2014 (2014), 66. https://doi.org/10.1186/1687-2770-2014-66.
  12. T.H. MacGregor, Majorization by Univalent Functions, Duke Math. J. 34 (1967), 95–102. https://doi.org/10.1215/s0012-7094-67-03411-4.
  13. Z. Nehari, Conformal Mapping, McGraw-Hill, New York, 1955.
  14. M. S. Roberston, Quasi-Subordination and Coefficient Conjectures, Bull. Amer. Math. Soc. 76 (1970), 1–9.
  15. H. Tang, M. Aouf, G. Deng, Majorization Problems for Certain Subclasses of Meromorphic Multivalent Functions Associated With the Liu-Srivastava Operator, Filomat, 29 (2015), 763–772.
  16. H. Tang, G. Deng, Majorization problems for two subclasses of analytic functions connected with the Liu–Owa integral operator and exponential function, J. Inequal. Appl. 2018 (2018), 277. https://doi.org/10.1186/s13660-018-1865-x.
  17. R. Tremblay, Une Contribution a la Theorie de la Derivee Fractionnaire, Ph.D. Thesis, Laval University, Qu`ebec, 1974.