3rd-Order Differential Subordination and Superordination Results for Univalent Analytic Functions Associated with Zeta-Riemann Fractional Differential Operator

Authors

  • Ahmed Shexo Department of Mathematics, College of Computer Science and Mathematics, University of Mosul, Mosul, Iraq
  • Waggas Galib Atshan Department of Mathematics, College of Science, University of Al-Qadisiyah, Diwaniya, Iraq
  • Abdulghfoor Jasim Salim Department of Mathematics, College of Computer Science and Mathematics, University of Mosul, Mosul, Iraq

DOI:

https://doi.org/10.29304/jqcsm.2024.16.31649

Keywords:

Differential subordination, Analytic function, Fractional operators, Sandwich theorem, Third-Order

Abstract

Using the results of 3rd order differential subordination, we introduce certain families of admissible functions and discuss some applications of 3rd order differential subordination for normalized analytic functions associated with novel fractional operator namely Zeta-Riemann Fractional differential operator. Some new results on differential subordination and superordination with some sandwich theorems are obtained. Moreover, several particular cases are also noted.

Downloads

Download data is not yet available.

References

J. A. Antonino, S. S. Miller, Third-order differential inequalities and subordination in the complex plane, Complex Var. Elliptic Equ., 56(2011), 439-454.

W. G. Atshan and A. A. R. Ali, On some sandwich theorems of analytic functions involving Noor- Sãlãgean operator, Advances in Mathematics: Scientific Journal, 9(10) (2020), 8455-8467.

W. G. Atshan, A. H. Battor and A. F. Abaas, On third-order differential subordination results for univalent analytic functions involving an operator, Journal of Physics: Conference Series, 1664 (2020) 012044, 1-19.

P. Agarwal, A. A. Hyder and M. Zakarya, Well-Posedness of Stochastic Modified Kawahara Equation. Adv. Differ. Equ., 1(2020), 1–10.

G. AlNemer, M. Zakarya, H. A. A. El-Hamid, M. R. Kenawy and H. M. Rezk, Dynamic Hardy-Type Inequalities with Non-Conjugate Parameters. Alex. Eng. J., 59(2020), 4523–4532.

W. G. Atshan and A. A. R. Ali, On sandwich theorems results for certain univalent functions defined by generalized operators, Iraqi Journal of Science, 62(7) (2021), pp: 2376-2383.

W. G. Atshan and S. R. Kulkarni, On application of differential subordination for certain subclass of meromorphically p-valent functions with positive coefficients defined by linear operator, Journal of Inequalities in Pure and Applied Mathematics, 10(2) (2009), Article 53, 11pp.

W. G. Atshan, A. H. Battor and A. F. Abaas, Some sandwich theorems for meromorphic univalent functions defined by new integral operator, Journal of Interdisciplinary Mathematics, 24(3) (2021), 579-591.

W. G. Atshan, R. A. Hiress and S. Altinkaya, On third-order differential subordination and superordination properties of analytic functions defined by a generalized operator, Symmetry, 14 (2) (2022), 418, 1-17.

A.A. Attiya, T.M. Seoudy and A. Albaid, Third-Order Differential Subordination for Meromorphic Functions Associated with Generalized Mittag-Leffler Function. Fractal Fract. 2023, 7, 175.

S. D. Bernardi, “ Convex and Starlike Univalent Functions”, Transaction of American Mathematical Society, 1969, 135, 429-449.

S. R. Bakheet, W. G. Atshan, Third-order sandwich results for analytic univalent functions defined by integral operator. Adv. Mech., 10(2022), 1178-1197.

A. M. Darweesh, W. G. Atshan, A. H. Battor and A. A. Lupas, Third-order differential subordination results for analytic functions associated with a certain differential operator, Symmetry, 14(1) (2022), 99, 1-15.

M. P. Jeyaraman and T. K. Suresh, Third-order differential subordination of analytic functions, Acta Univ. Apulensis Math. Inform., 35 (2013), 187–202.

Saliu A, Jabeen K, Ravichandran V. Differential subordination for certain strongly starlike functions. Rendiconti del Circolo Matematico di Palermo Series 2. 2024 Feb;73(1):1-8.

S. S. Miller and P. T. Mocanu and M. O. Reade, Subordination-preserving integral operators. Trans. Amer. Math. Soc., 283(1984), 605–615.

M. Sharma, NK. Jain and S. Kumar , Starlikeness of analytic functions using special functions and subordination. Boletín de la Sociedad Matemática Mexicana. 2024 Jul;30(2):55.

S. S. Miller and P. T. Mocanu, Subordinants of differential superordinations, Complex Var. Elliptic Equ., 48 (2003), 815-826.

S. S. Miller and P. T. Mocanu, Differential Subordination: Theory and Applications; Series on Monographs and Textbooks in Pure and Applied Mathematics; Marcel Dekker Incorporated: New York, NY, USA, 2000; Volume 225.

S. Ponnusamy and O. P. Juneja, Third-order differential inequalities in the complex plane, in Current Topics in Analytic Function Theory, World Scientific Publishing Company, Singapore, New Jersey, London and Hong Kong, (1992).

D. Ra ̆ducanu, Third order differential subordinations for analytic functions associated with generalized Mittag-Leffler functions, Mediterr. J. Math., 14 (4) (2017), Article ID 167, 1–18.

H. M. Rezk, G. AlNemer, H. A. Abd El-Hamid, A. H. Abdel-Aty, K. S. Nisar and M. Zakarya, Hilbert-Type Inequalities for Time Scale Nabla Calculus. Adv. Differ. Equ., 1(2020), 1–21.

H. M. Srivastava, S. Owa, “ Univalent Functions, Fractional Calculus, and Their Applications”, Wiley: New York, NY, USA, 1989.

T. M. Seoudy, Some applications of third-order differential subordination for analytic functions involving k-Ruscheweyh derivative operator. Afrika Matematika. 2023 Jun;34(2):29.

Q. A. Shakir W. G. Atshan. "On Sandwich Results of Univalent Functions Defined by Generalized Abbas-Atshan Operator." Journal of Al-Qadisiyah for Computer Science and Mathematics 15.4 (2023): 11-20.‏

A.S. Tayyah and W. G. Atshan, New Results on r,k,μ-Riemann–Liouville Fractional Operators in Complex Domain with Applications, Fractal and Fractional, 8(3)(2024), 165,1-17.

H. Tang, H. M. Srivastava, E. Deniz and S. Li, Third-order differential superordination involving the generalized Bessel functions, Bull. Malays. Math. Sci. Soc., 38 (2015), 1669–1688.

H. Tang, H. M. Srivastava, S. Li and L. Ma, Third order differential subordination and superordination results for meromorphically multivalent functions associated with the Liu-Srivastava operator, Abstr. App. Anal. , 2014 (2014), Article ID 792175, 1-11.

H. Tang and E. Deniz, Third-order differential subordination results for analytic functions involving the generalized Bessel functions, Acta Math. Sci. Ser. B Engl. Ed.,34 (2014),1707-1719.

Downloads

Published

2024-09-30

How to Cite

Shexo, A., Galib Atshan, W., & Jasim Salim, A. (2024). 3rd-Order Differential Subordination and Superordination Results for Univalent Analytic Functions Associated with Zeta-Riemann Fractional Differential Operator. Journal of Al-Qadisiyah for Computer Science and Mathematics, 16(3), Math. 1–25. https://doi.org/10.29304/jqcsm.2024.16.31649

Issue

Section

Math Articles

Most read articles by the same author(s)

1 2 3 > >>