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Some subordination and superordination results associated with generalized Srivastava-Attiya operator. (English) Zbl 1488.30163

Summary: By using the generalized Srivastava-Attiya operator we give some results of differential subordination and superordination of analytic functions. Some applications and examples are also obtained.

MSC:

30C80 Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination
30C10 Polynomials and rational functions of one complex variable
11M35 Hurwitz and Lerch zeta functions
Full Text: DOI

References:

[1] J.W. Alexander, Functions which map the interior of the unit circle upon simple region, Annals of Math. 17(1915), 12-22. · JFM 45.0672.02
[2] A.A. Attiya and A. Hakami, Some subordination results associated with generalized Srivastava-Attiya operator, Adv. Difference Equ. 2013, 2013:105, 14 pp. · Zbl 1380.30018
[3] A.Attiya, Oh Sang Kwon, Park Ji Hyang and Nak Eun Cho, An integrodifferential operator for meromorphic functions associated with the Hurwitz-Lerch Zeta Function, Filomat, in Press · Zbl 1458.30007
[4] S.D. Bernardi, Convex and starlike univalent functions, Trans. Amer. Math. Soc. 135(1969), 429-449.N. E. Cho and T. H. Kim, Multiplier transformations and strongly close-to-convex functions, Bull. Korean Math. Soc. 40 (2003), no. 3, 399- 410. · Zbl 1032.30007
[5] T. Bulboaca, Differential Subordinations and Superordinaions, Casa Cartii de Stiinta, Cluj-Napoca, 2005.
[6] J. Choi, D.S. Jang and H.M. Srivastava, A generalization of the Hurwitz-Lerch Zeta function, Integral Transforms Spec. Funct. 19(2008), no. 1-2, 65-79. · Zbl 1145.11068
[7] N. E. Cho and T. H. Kim, Multiplier transformations and strongly close-to-convex functions, Bull. Korean Math. Soc. 40 (2003), no. 3, 399- 410. · Zbl 1032.30007
[8] N.E. Cho, I.H. Kim and H.M. Srivastava, Sandwich-type theorems for multivalent functions associated with the Srivastava-Attiya operator, Appl. Math. Comput. 217 (2010), no. 2, 918-928. · Zbl 1202.30017
[9] N. E. Cho and H. M. Srivastava, Argument estimates of certain analytic functions defined by a class of multiplier transformations, Math. Comput. Modelling 37 (2003), no. 1-2, 39-49. · Zbl 1050.30007
[10] E.A. Elrifai and H.E and A.R. Ahmed, Some applications of Srivastava-Attiya operator to p-valent starlike functions. J. Inequal. Appl. 2010(2010), 1-11. · Zbl 1201.30012
[11] C. Ferreira and J.L. L ´opez, Asymptotic expansions of the Hurwitz-Lerch zeta function, J. Math. Anal. Appl. 298(2004), 210-224. · Zbl 1106.11034
[12] P.L. Gupta, R.C. Gupta, S. Ong and H.M. Srivastava, A class of Hurwitz-Lerch zeta distributions and their applications in reliability, Appl. Math. Comput. 196 (2008), no. 2, 521-531. · Zbl 1131.62093
[13] J.B. Jung, Y.C. Kim and H.M. Srivastava, The Hardy space of analytic functions associated with certain one-parameter families of integral operator, J. Math. Anal. Appl. 176(1993), 138-147. · Zbl 0774.30008
[14] M.A. Kutbi and A.A. Attiya, Differential subordination result with the Srivastava-Attiya integral operator, J. Inequal. Appl. 2010(2010), 1-10. · Zbl 1203.30020
[15] M.A. Kutbi and A.A. Attiya, Differential subordination results for certain integrodifferential operator and it’s applications, Abs. Appl. Anal., 2012(2012), 13 pp. · Zbl 1256.30008
[16] R.J. Libera, Some classes of regular univalent functions, Proc. Amer. Math. Soc. 16(1965), 755-758. · Zbl 0158.07702
[17] Jin-Lin Liu, Subordinations for certain multivalent analytic functions associated with the generalized Srivastava-Attiya operator, Integral Transforms Spec. Funct.19 (2008), no. 11-12, 893-901. · Zbl 1151.30004
[18] Q.M. Luo and H.M. Srivastava, Some generalizations of the Apostol-Bernoulli and Apostol-Euler polynomials, J. Math. Anal. Appl. 308(2005), 290-302. · Zbl 1076.33006
[19] S.S. Miller and P.T. Mocanu, Differential Subordinations: Theory and Applications, Series in Pure and Applied Mathematics, No. 225, Marcel Dekker, Inc., New York, 2000. · Zbl 0954.34003
[20] K.I. Noor and S.Z. Bukhari, Some subclasses of analytic and spiral-like functions of complex order involving the Srivastava-Attiya integral operator, Integral Transforms Spec. Funct. 21 (2010), no. 12, 907-916. · Zbl 1206.30028
[21] S. Owa and A.A. Attiya, An application of differential subordinations to the class of certain analytic functions, Taiwanese J. Math., 13(2009), no. 2A, 369-375. · Zbl 1176.30053
[22] G.S. Salagean, Subclasses of univalent functions, Complex analysis, fifth Romanian-Finnish seminar, Part 1 (Bucharest, 1981), 362-372, Lecture Notes in Math., 1013, Springer, Berlin, 1983. · Zbl 0531.30009
[23] H.M. Srivastava and A.A. Attiya, An integral operator associated with the Hurwitz-Lerch zeta function and differential subordination, Integral Transforms Spec. Funct. 18 (2007), no. 3-4, 207-216. · Zbl 1112.30007
[24] H.M. Srivastava and J. Choi, Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, 2001. · Zbl 1014.33001
[25] H. M. Srivastava and S. Gaboury, A new class of analytic functions defined by means of a generalization of the Srivastava-Attiya operator, J. Inequal. Appl. 2015 (2015), Article ID 39, 1-15. · Zbl 1308.30024
[26] H.M. Srivastava, D. R˘aducanu and G. S˘al˘agean, A new class of generalized close-to-starlike functions defined by the SrivastavaAttiya operator, Acta Math. Sin. (Engl. Ser.) 29 (2013), no. 5, 833-840. · Zbl 1293.30038
[27] H. M. Srivastava, S. Gaboury and F. Ghanim, A unified class of analytic functions involving a generalization of the SrivastavaAttiya operator, Appl. Math. Comput. 251 (2015), 35-45. · Zbl 1328.30012
[28] B. A. Uralegaddi and C. Somanatha, Certain classes of univalent functions, Current topics in analytic function theory, 371-374, World Sci. Publ., River Edge, NJ, 1992 · Zbl 0987.30508
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