Differential subordination and superordination results associated with the Wright function

Document Type : Research Paper

Authors

1 Department of Economics‎, ‎Babes-Bolyai University‎, ‎400591 Cluj-Napoca‎, ‎Romania and ‎Institute of Applied Mathematics‎, ‎'Obuda University‎, ‎1034 Budapest‎, ‎Hungary.

2 Department of Mathematics‎, ‎Government Dungar College‎, ‎334001 Bikaner‎, ‎India.

3 Department of Mathematics‎, ‎Central University of Rajasthan‎, ‎305817 Kishangarh‎, ‎Rajasthan‎, ‎India.

Abstract

An operator associated with the Wright function is introduced in the open unit disk. Differential subordination and superordination results associated with this operator are obtained by investigating appropriate classes of admissible functions. In particular, some inequalities for modified Bessel functions are also obtained.

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References

R. Aghalary, S. B. Joshi, R. N. Mohapatra and V. Ravichandran, Subordination for analytic functions defined by the Dziok-Srivastava linear operator, Appl. Math. Comput. 187 (2007), no. 1, 13--19.
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. (2) 31 (2008), no. 2, 192--207.
R. M. Ali, V. Ravichandran and N. Seenivasagan, Differential subordination and superordination of analytic functions defined by the Dziok-Srivastava operator, J. Franklin Inst. 347 (2010), no. 9, 1762--1781.
A. Baricz, Geometric properties of generalized Bessel functions, Publ. Math. Debrecen 73 (2008) 155--178.
A. Baricz, Generalized Bessel Functions of the First Kind, Lecture Notes in Math. Springer, New York, 2010.
A. Baricz, E. Deniz, M. Caglar and H. Orhan, Differential subordinations involving generalized Bessel functions, Bull. Malays. Math. Sci. Soc. 38 (2015), no. 3, 1255--1280.
A. Baricz, P. A. Kupan and R. Szasz, The radius of starlikeness of normalized Bessel functions of the first kind, Proc. Amer. Math. Soc. 142 (2014), no. 6, 2019--2025.
A. Baricz and S. Ponnusamy, Starlikeness and convexity of generalized Bessel functions, Integral Transforms Spec. Funct. 21 (2010), no. 9, 641--653.
R. Goreno, Y. Luchko and F. Mainardi, Analytic properties and applications of Wright functions, Fract. Calc. Appl. Anal. 2 (1999), no. 4, 383--414.
Y. C. Kim and H. M. Srivastava, Inequalities involving certain families of integral and convolution operators, Math. Inequal. Appl. 7 (2004), no. 2, 227--234.
V. Kiryakova, Generalized Fractional Calculus and Applications, Pitman Research Notes in Mathematics Series, 301, Longman Scientific & Technical, Harlow, UK, 1994.
F. Mainardi, A. Mura and G. Pagnini, The M-Wright function in time-fractional diffusion processes: a tutorial survey, Int. J. Differ. Equ. (2010), Article 104505, 29 pages.
S. S. Miller and P. T. Mocanu, Differential Subordinations, Theory and Applications, New York and Basel, Marcel Dekker, 2000.
S. S. Miller and P. T. Mocanu, Subordinants of differential superordinations, Complex Var. Theory Appl. 48 (2003), no. 10, 815--826.
S. R. Mondal and A. Swaminathan, Geometric properties of generalized Bessel functions, Bull. Malays. Math. Soc. (2) 35 (2012), no. 1, 179--194.
I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
J. K. Prajapat, Certain geometric properties of normalized Bessel functions, Appl. Math. Lett. 24 (2011), no. 12, 2133--2139.
J. K. Prajapat, Certain geometric properties of the Wright functions, Integral Transforms Spec. Funct. 26 (2015), no. 3, 203--212.
S. G. Samko, A. A. Kilbas and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, New York, 1993.
A. Soni, S. Kant and J. K. Prajapat, Differential subordinations and superordinations for multivalently meromorphic functions involving the Hurwitz-Lerch Zeta functions, Proc. Nat. Acad. Sci. India Sect. A 85 (2015), no. 3, 385--393.
R. Szasz and P. A. Kup_an, About the univalence of the Bessel functions, Stud. Univ. Babes-Bolyai Math. 54 (2009), no. 1, 127--132.
E. M. Wright, On the coefficients of power series having exponential singularities, J. London Math. Soc. 8 (1933) 71--79.
R. G. Xiang, Z. G. Wang and M. Darus, A family of integral operators preserving subordination and superordination, Bull. Malays. Math. Sci. Soc. (2) 33 (2010), no. 1, 121--131.
Bulletin of the Iranian Mathematical Society
Volume 42, Issue 6
December 2016
Pages 1459-1477

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History

  • Receive Date: 11 August 2015
  • Revise Date: 18 September 2015
  • Accept Date: 18 September 2015

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