Differential Sandwich Theorems for Mittag-Leffler Function Associated with Fractional Integral Defined by Convolution Structure
Abstract
In this work, we use fractional integral and Mittag-Leffler function to obtain some results related to differential subordination and superordination defined by Hadamard product for univalent analytic functions defined in the open unit disk. These results are applied to obtain differential sandwich results. Our results extend corresponding previously known results.
References
Al-Dohiman, A. A., Frasin, B. A., Tasar, N., & Sakar, F. M. (2023). Classes of harmonic functions related to Mittag-Leffler function. Axioms, 12, 714. https://doi.org/10.3390/axioms12070714
Aydogan, M., Bshouty, D. Miller, S. S., & Sakar, F. M. (2021). Differential subordinations in harmonic mapping, New Directions in Function Theory: From Complex to Hypercomplex to Non-Commutative: Chapman University, 19-27.
Attiya, A. A. (2016). Some applications of Mittag-Leffler function in the unit disk. Filomat, 30(7), 2075-2081. https://doi.org/10.2298/FIL1607075A
Attiya, A. A., & Yassen, M. F. (2017). Some subordination and superordination results associated with generalized Srivastava-Attiya operator. Filomat, 31(1), 53-60. https://doi.org/10.2298/FIL1701053A
Bulboacă, T. (2002). Classes of first order differential superordinations. Demonstratio Mathematica, 35(2), 287-292. https://doi.org/10.1515/dema-2002-0209
Garg, M., Manoha, P., & Kalla, S. L. (2013). A Mittag-Leffler-type function of two variables. Integral Transforms and Special Functions, 24(11), 934-944. https://doi.org/10.1080/10652469.2013.789872
Kiryakova, V. (2010). The multi-index Mittag-Leffler functions as an important class of special functions of fractional calculus. Computers & Mathematics with Applications, 59(5), 1885-1895. https://doi.org/10.1016/j.camwa.2009.08.025
Miller, S. S., & Mocanu, P. T. (2000). Differential subordinations: Theory and applications. Marcel Dekker Inc. https://doi.org/10.1201/9781482289817
Mittag-Leffler, G. M. (1903). Sur la nouvelle function. Comptes Rendus de l’Académie des Sciences, Paris, 137, 554-558.
Mittag-Leffler, G. M. (1905). Sur la representation analytique d’une function monogene (cinquieme note). Acta Mathematica, 29, 101-181. https://doi.org/10.1007/BF02403200
Prajapati, J. C., Jana, R. K., Saxena, R. K., & Shukla, A. K. (2013). Some results on the generalized Mittag-Leffler function operator. Journal of Inequalities and Applications, 2013, 1-6. https://doi.org/10.1186/1029-242X-2013-33
Rahrovi, S. (2015). Subordination and superordination properties for convolution operator. International Journal of Nonlinear Analysis and Applications, 6(2), 137-147.
Sakar, F. M., & Canbulat, A. (2021). Quasi-subordinations for a subfamily of bi-univalent functions associated with k-analogue of Bessel function. Journal of Mathematical Analysis, 12(1), 1-12.
Seoudy, T. M. (2017). Subordination and superordination results of p-valent analytic functions involving a linear operator. Boletim da Sociedade Paranaense de Matemática, 35(2), 223-234. https://doi.org/10.5269/bspm.v35i2.21993
Shukla, A. K., & Prajapati, J. C. (2007). On a generalization of Mittag-Leffler function and its properties. Journal of Mathematical Analysis and Applications, 336, 797-811. https://doi.org/10.1016/j.jmaa.2007.03.018
Srivastava, H. M., & Owa, S. (Eds.). (1992). Current topics in analytic function theory. World Scientific Publishing Company. https://doi.org/10.1142/1628
Srivastava, H. M., & Tomovski, Z. (2009). Fractional calculus with an integral operator containing a generalized Mittag-Leffler function in the kernel. Applied Mathematics and Computation, 211, 198-210. https://doi.org/10.1016/j.amc.2009.01.055
Tang, H., & Deniz, E. (2014). Third-order differential subordination results for analytic functions involving the generalized Bessel functions. Acta Mathematica Scientia. Series B, 34, 1707-1719. https://doi.org/10.1016/S0252-9602(14)60116-8
Wanas, A. K., & Alina, A. L. (2020). Some subordination and superordination results for normalized analytic functions defined by convolution structure associated with Wanas differential operator. Earthline Journal of Mathematical Sciences, 4(1), 115-127. https://doi.org/10.34198/ejms.4120.115127
Wanas, A. K., & Khudher, F. C. (2023). Differential subordination and superordination for fractional integral involving Wanas operator defined by convolution structure. Earthline Journal of Mathematical Sciences, 12(1), 121-139. https://doi.org/10.34198/ejms.12123.121139
Xu, Q.-H., Xiao, H.-G., & Srivastava, H. M. (2014). Some applications of differential subordination and the Dziok-Srivastava convolution operator. Applied Mathematics and Computation, 230, 496-508. https://doi.org/10.1016/j.amc.2013.12.065
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