New Concept on Fourth-Order Differential Subordination and Superordination with Some Results for Multivalent Analytic Functions
DOI:
https://doi.org/10.29304/jqcm.2020.12.1.681Keywords:
Differential subordination, Differential superordination, Multivalent function, Admissible function, Fourth-OrderAbstract
In this paper, we introduce new concept that is fourth-order differential subordination and superordination associated with differential linear operator in open unit disk. Also, we obtain some new results.
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References
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[6] M. K. Aouf and T. M. Seoudy , Subordination and superordination of a certain integral operator on merormorphic functions, Comput. Math. Appl, 59 (2010), 3669-3678.
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[8] W. G. Atshan and E. I. Badawi, On sandwich theorems for certain univalent functions defined by a new operator, Journal of Al-Qadisiyah for Computer Science and Mathematics, 11(2)(2019) ,72–80.
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[10] W.G. Atshan and S. A. A. Jawad, On differential sandwich results for analytic functions, Journal of Al-Qadisiyah for Computer Science and Mathematics, 11(1)(2019) ,96–101.
[11] A. A. Attiya, O. S. Kwon, P. J. Hang and N. E. Cho, An Integro-differential operator for meromorphic functions associated with the Hurwitz - Lerch Zeta function ,Filomat, 30, 7 (2016), 2045-2057.
[12] R. W. Ibrahim, M. Z. Ahmad and H. F. Al-Janaby, Third-order differential subordination and superordination involving a fractional operator, Open Math., 2015, 13: 706-728.
[13] S. Kavitha, S. Sivasubramanian and R. Jayasankar, Differential subordination and superordination results for Cho-Kwon-Srivastava operator, Comput. Math. Appl., 64(2012),1789-1803.
[14] S. S. Miller and P. T. Mocanu, Differential subordinations: Theory and Applications ,Series on Monographs and Textbooks in Pure and Applied Mathematics, No. 225, Marcel Dekker Incorporated, New York and Basel, (2000).
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[16] T. N. Shanmugam, S. Sivasubramanian and H. M. Srivastava, Differential sandwich theorems for certain subclasses of analytic functions involving multiplier transformations, Integral Transforms Spec. Funct. ,17 (2006), 889-899.
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[18] H. Tang, H. M. Srivastava, E. Deniz and S. Li, Third-order differential superordination involving the generalized Bessel functions, Bull. Malays. Math. Sci. Soc., (2014), 1-22.
[19] 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, Abstract and Applied Analysis, (2014), Article ID 792175, 1-11 .
[2] R. M. Ali, V. Ravichandran and N. Seenivasagan, Differential subordination and superordination of analytic functions defined by the multiplier transformation, Math. Inequal. Appl. ,12 (2009), 123-139.
[3] R. M. Ali, V. Ravichandran and N. Seenivasagan, On subordination and superordination of the multiplier transformation for meromorphic functions, Bull. Malays. Math. Sci. Soc. ,33 (2010), 311-324.
[4] J. A. Antonino and S. S. Miller, Third-order differential inequalities and subordinations in the complex plane, Complex Var. Elliptic Equ. ,56 (2011), 439-454.
[5] J. S. Abdul Rahman, A. H. S. Mushtaq and Al. H. F. Mohammed, Third-order differential subordination and superordination results for meromorphically univalent functions involving linear operator, European Jorunal of Scientific Research, (EJSR) , 132(1)(2015) ,57-65.
[6] M. K. Aouf and T. M. Seoudy , Subordination and superordination of a certain integral operator on merormorphic functions, Comput. Math. Appl, 59 (2010), 3669-3678.
[7] W. G. Atshan and I. A. Abbas, A study of Differential Subordination and Superordination Results in Geometric Function Theory, M.Sc. Thesis, University of Al-Qadisiyah, Diwaniyah ,(2017).
[8] W. G. Atshan and E. I. Badawi, On sandwich theorems for certain univalent functions defined by a new operator, Journal of Al-Qadisiyah for Computer Science and Mathematics, 11(2)(2019) ,72–80.
[9] W. G. Atshan and A. A. Husien, Some results of second order differential subordination for fractional integral of Dziok-Srivastava operator , Analele Universitatii Oradea Fasc. Matematica , Tom XXI(2014), Issue No. 1 ,145-152.
[10] W.G. Atshan and S. A. A. Jawad, On differential sandwich results for analytic functions, Journal of Al-Qadisiyah for Computer Science and Mathematics, 11(1)(2019) ,96–101.
[11] A. A. Attiya, O. S. Kwon, P. J. Hang and N. E. Cho, An Integro-differential operator for meromorphic functions associated with the Hurwitz - Lerch Zeta function ,Filomat, 30, 7 (2016), 2045-2057.
[12] R. W. Ibrahim, M. Z. Ahmad and H. F. Al-Janaby, Third-order differential subordination and superordination involving a fractional operator, Open Math., 2015, 13: 706-728.
[13] S. Kavitha, S. Sivasubramanian and R. Jayasankar, Differential subordination and superordination results for Cho-Kwon-Srivastava operator, Comput. Math. Appl., 64(2012),1789-1803.
[14] S. S. Miller and P. T. Mocanu, Differential subordinations: Theory and Applications ,Series on Monographs and Textbooks in Pure and Applied Mathematics, No. 225, Marcel Dekker Incorporated, New York and Basel, (2000).
[15] S. S. Miller and P. T. Mocanu, Subordinations of differential superordinations, Complex Var. Theory Appl. 48 (2003), 815-826.
[16] T. N. Shanmugam, S. Sivasubramanian and H. M. Srivastava, Differential sandwich theorems for certain subclasses of analytic functions involving multiplier transformations, Integral Transforms Spec. Funct. ,17 (2006), 889-899.
[17] H. Tang and E. Deniz, Third-order differential subordination results for analytic functions involving the generalized Bessel functions, Acta Math. Sci., (2014), 34B(6), 1707-1719.
[18] H. Tang, H. M. Srivastava, E. Deniz and S. Li, Third-order differential superordination involving the generalized Bessel functions, Bull. Malays. Math. Sci. Soc., (2014), 1-22.
[19] 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, Abstract and Applied Analysis, (2014), Article ID 792175, 1-11 .
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Published
2020-03-18
How to Cite
Atshan, W. G., Abbas, I. A., & Yalcin, S. (2020). New Concept on Fourth-Order Differential Subordination and Superordination with Some Results for Multivalent Analytic Functions. Journal of Al-Qadisiyah for Computer Science and Mathematics, 12(1), Math Page 96–107. https://doi.org/10.29304/jqcm.2020.12.1.681
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Math Articles
