Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
권호 표지
DOI QR코드

DOI QR Code

Differential Subordination and Superordination Results associated with Srivastava-Attiya Integral Operator

  • Received : 2016.02.29
  • Accepted : 2016.12.06
  • Published : 2017.06.23
Download PDF
⟨ Previous Next ⟩

Abstract

Differential subordination and superordination results associated with a generalized Hurwitz-Lerch Zeta function in the open unit disk are obtained by investigating appropriate classes of admissible functions. In particular some inequalities for generalized Hurwitz-Lerch Zeta function are obtained.

Keywords

References

  1. R. Aghalary, S. B. Joshi, R. N. Mohapatra and V. Ravichandran, Subordinations for analytic functions defined by the Dziok-Srivastava linear operator, Appl. Math. Comput., 187(1)(2007), 13-19. https://doi.org/10.1016/j.amc.2006.08.097
  2. R. M. Ali, V. Ravichandran and N. Seenivasagan, Subordination and superordination of the Liu-Srivastava linear operator on meromorphic functions, Bull. Malays. Math. Sci. Soc., 31(2008), 192-207.
  3. R. M. Ali, V. Ravichandran and N. Seenivasagan, Differential subordination and superordination of analytic functions defined by the Dziok-Srivastava linear operator, J. Franklin Inst., 347(2010), 1762-1781. https://doi.org/10.1016/j.jfranklin.2010.08.009
  4. A. Baricz, E. Deniz, M. Caglar and H. Orhan, Differential subordinations involving generalized Bessel functions, Bull. Malays. Math. Sci. Soc., 38(3)(2015), 1255-1280. https://doi.org/10.1007/s40840-014-0079-8
  5. S. D. Bernardi, Convex and starlike univalent functions, Trans. Amer. Math. Soc., 135(1969), 429-446. https://doi.org/10.1090/S0002-9947-1969-0232920-2
  6. B. C. Carlson and D. B. Shaffer, Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal., 15(1984), 737-745. https://doi.org/10.1137/0515057
  7. N. E. Cho and H. M. Srivastava, Argument estimates of certain analytic functions defined by a class of multiplier transformation, Math. Comput. Modeling, 37(2003), 39-49. https://doi.org/10.1016/S0895-7177(03)80004-3
  8. J. H. Choi, M. Saigo and H. M. Srivastava, Some inclusion properties of a certain family of integral operators, J. Math. Anal. Appl., 276(2002), 432-445. https://doi.org/10.1016/S0022-247X(02)00500-0
  9. J. Dziok and H. M. Srivastava, Classes of analytic functions associated with the generalized hypergeometric function, Appl. Math. Comput., 103(1999), 1-13. https://doi.org/10.1016/S0377-0427(98)00235-0
  10. J. Dziok and H. M. Srivastava, Certain subclasses of analytic functions associated with the generalized hypergeometric function, Integral Transforms Spec. Funct., 14(2003), 7-18. https://doi.org/10.1080/10652460304543
  11. M. Garg, K. Jain and S. L. Kalla, On generalized Hurwitz-Lerch Zeta distributions, Appl. Appl. Math., 4(2009), 26-39.
  12. S. P. Goyal and R. K. Laddha, On the generalized Riemann zeta functions and the generalized Lambert transform, Ganita Sandesh, 11(1997), 99-108.
  13. S. P. Goyal and J. K. Prajapat, Certain formulas for Unified Riemann Zeta and related functions, J. Rajasthan Acad. Phys. Sci., 3(4)(2004), 267-274.
  14. I. B. Jung, Y. C. Kim and H. M. Srivastava, The Hardy space of analytic functions associated with certain one-parameter families of integral operators, J. Math. Anal. Appl., 176(1993), 138-147. https://doi.org/10.1006/jmaa.1993.1204
  15. Y. C. Kim and H. M. Srivastava, Inequalities involving certain families of integral and convolution operators, Math. Inequal. Appl., 7(2)(2004), 227-234.
  16. S.-D. Lin and H. M. Srivastava, Some families of the Hurwitz-Lerch Zeta functions and associated fractional derivative and other integral representations, Appl. Math. Comput., 154(2004), 725-733.
  17. S. S. Miller and P. T. Mocanu, Differential Subordinations. Theory and Applications, New York and Basel, Marcel Dekker, (2000).
  18. S. S. Miller and P. T. Mocanu, Subordinants of differential superordinations, Complex Var. Theory Appl., 48(2003), 815-826.
  19. K. I. Noor and S. Z. H. Bukhari, Some subclasses of analytic and spiral-like functions of complex order involving the Srivastava-Attiya integral operator, Integral Transforms Spec. Funct., 21(12)(2010), 907-916. https://doi.org/10.1080/10652469.2010.487305
  20. J. K. Prajapat and T. Bulboaca, Double subordination preserving properties for a new generalized Srivastava-Attiya integral operator, Chin. Ann. Math. Ser. B, 33(4)(2012), 569-582. https://doi.org/10.1007/s11401-012-0722-3
  21. A. Soni, S. Kant and J. K. Prajapat, Strong differential subordination and superordination for multivalently meromorphic functions involving the Hurwitz-Lerch Zeta functions, Proc. Nat. Acad. Sci. India Sec. A, 85(3)(2015), 385-393. https://doi.org/10.1007/s40010-015-0211-7
  22. H. M. Srivastava and J. Choi, Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, Boston and London, 2001.
  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(3-4)(2007), 207-216. https://doi.org/10.1080/10652460701208577
  24. H. M. Srivastava, Some Fox-Wright generalized hypergeometric functions and associated families of convolution operators, Appl. Anal. Discrete Math. 1(2007), 56-71. https://doi.org/10.2298/AADM0701056S
  25. H. M. Srivastava and J. Choi, Zeta and q-zeta functions and associated series and integrals, Elsevier, Inc., Amsterdam, 2012.
  26. H. M. Srivastava, A new family of the $\lambda$-Generalized Hurwitz-Lerch Zeta functions with applications, Appl. Math. Inf. Sci., 8(2014), 1485-1500. https://doi.org/10.12785/amis/080402
  27. Z.-G. Wang, Q.-G. Li and Y.-P. Jiang, Certain subclasses of multivalent analytic functions involving the generalized Srivastava-Attiya operator, Integral Transforms Spec. Funct., 21(2010), 221-234. https://doi.org/10.1080/10652460903098248
  28. R.G. Xiang, Z.G. Wang and M. Darus, A family of integral operators preserving subordination and superordination, Bull. Malays. Math. Sci. Soc., 33(1)(2010), 121-131.