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Univalence of certain integral operators involving normalized wright functions

Year 2017, Volume: 66 Issue: 1, 19 - 28, 01.02.2017
https://doi.org/10.1501/Commua1_0000000771

Abstract

In this paper our main aim is to give some su¢ cient conditions
for functions represented with normalized Wright functions to be univalent
in the open unit disk. The key tools in our proofs are the Beckerís and the
generalized version of the well-known Ahlforís and Beckerís univalence criteria.

References

  • Altinta¸s, O., Irmak, H., Owa, S., Srivastava, H. M., Coe¢ cient bounds for some families of starlike and convex functions of complex order, Applied Mathematics Letters 20 (2007), 1222.
  • Baricz, A., Frasin, B. A., Univalence of integral operators involving Bessel functions, Applied Mathematics Letters, 23 (2010), 371-376.
  • Becker, J., Löwnersche Diğerentialgleichung und quasikonform fortsetzbare schlichte Funk- tionen, J. Reine Angew Math. 255 (1972), 23-43 (in German).
  • Blezu, D., On Univalence Criteria, General Mathematics, 14 2006, 87-93.
  • Breaz, D., Breaz, N., Srivastava, H. M., An extension of the univalent condition for a family of integral oprator, Applied Mathematics Letters, 22 (2009), 41-44.
  • Breaz, D., Günay, H. Ö., On the univalence criterion of a general integral operator, J. Inequal. Appl. 8 (2008), Art. ID 702715.
  • Gao, C.-Y., Yuan, S.-M., Srivastava,H. M., Some functional inequalities and inclusion re- lationships associated with certain families of integral operators, Comput. Math. Appl. 49 (2015), 1787-1795.
  • Owa, S., Nunokawa, M., Saitoh, H., Srivastava, H. M., Close-to-convexity, starlikeness and convexity of certain analytic functions, Appl. Math. Lett. 15 (2002), 63-69.
  • Pescar, V., A new generalization of Ahlfor’s and Becker’s criterion of univalence, Bull. Math. Soc. (Second Series), 9 (1996), 53-54.
  • Pescar, V., Univalence of certain integral operators, Acta Univ. Apulensis Math. Infom., 12 (2006), 43-48.
  • Prajapat, J. K., Certain geometric properties of the Wright function. Integral Transform and Special Functions, 26 (2015), 203-212.
  • Wright, E. M., On the coe¢ cients of power series having exponential singularities, J. London Math. Soc. 8 (1933), 71-79.
  • Current address : N. Mustafa: Department of Mathematics, Faculty of Science and Letters, Kafkas University, Kars, 36100, Turkey.
Year 2017, Volume: 66 Issue: 1, 19 - 28, 01.02.2017
https://doi.org/10.1501/Commua1_0000000771

Abstract

References

  • Altinta¸s, O., Irmak, H., Owa, S., Srivastava, H. M., Coe¢ cient bounds for some families of starlike and convex functions of complex order, Applied Mathematics Letters 20 (2007), 1222.
  • Baricz, A., Frasin, B. A., Univalence of integral operators involving Bessel functions, Applied Mathematics Letters, 23 (2010), 371-376.
  • Becker, J., Löwnersche Diğerentialgleichung und quasikonform fortsetzbare schlichte Funk- tionen, J. Reine Angew Math. 255 (1972), 23-43 (in German).
  • Blezu, D., On Univalence Criteria, General Mathematics, 14 2006, 87-93.
  • Breaz, D., Breaz, N., Srivastava, H. M., An extension of the univalent condition for a family of integral oprator, Applied Mathematics Letters, 22 (2009), 41-44.
  • Breaz, D., Günay, H. Ö., On the univalence criterion of a general integral operator, J. Inequal. Appl. 8 (2008), Art. ID 702715.
  • Gao, C.-Y., Yuan, S.-M., Srivastava,H. M., Some functional inequalities and inclusion re- lationships associated with certain families of integral operators, Comput. Math. Appl. 49 (2015), 1787-1795.
  • Owa, S., Nunokawa, M., Saitoh, H., Srivastava, H. M., Close-to-convexity, starlikeness and convexity of certain analytic functions, Appl. Math. Lett. 15 (2002), 63-69.
  • Pescar, V., A new generalization of Ahlfor’s and Becker’s criterion of univalence, Bull. Math. Soc. (Second Series), 9 (1996), 53-54.
  • Pescar, V., Univalence of certain integral operators, Acta Univ. Apulensis Math. Infom., 12 (2006), 43-48.
  • Prajapat, J. K., Certain geometric properties of the Wright function. Integral Transform and Special Functions, 26 (2015), 203-212.
  • Wright, E. M., On the coe¢ cients of power series having exponential singularities, J. London Math. Soc. 8 (1933), 71-79.
  • Current address : N. Mustafa: Department of Mathematics, Faculty of Science and Letters, Kafkas University, Kars, 36100, Turkey.
There are 13 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Nizami Mustafa This is me

Publication Date February 1, 2017
Published in Issue Year 2017 Volume: 66 Issue: 1

Cite

APA Mustafa, N. (2017). Univalence of certain integral operators involving normalized wright functions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 66(1), 19-28. https://doi.org/10.1501/Commua1_0000000771
AMA Mustafa N. Univalence of certain integral operators involving normalized wright functions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2017;66(1):19-28. doi:10.1501/Commua1_0000000771
Chicago Mustafa, Nizami. “Univalence of Certain Integral Operators Involving Normalized Wright Functions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66, no. 1 (February 2017): 19-28. https://doi.org/10.1501/Commua1_0000000771.
EndNote Mustafa N (February 1, 2017) Univalence of certain integral operators involving normalized wright functions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66 1 19–28.
IEEE N. Mustafa, “Univalence of certain integral operators involving normalized wright functions”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 66, no. 1, pp. 19–28, 2017, doi: 10.1501/Commua1_0000000771.
ISNAD Mustafa, Nizami. “Univalence of Certain Integral Operators Involving Normalized Wright Functions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66/1 (February 2017), 19-28. https://doi.org/10.1501/Commua1_0000000771.
JAMA Mustafa N. Univalence of certain integral operators involving normalized wright functions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66:19–28.
MLA Mustafa, Nizami. “Univalence of Certain Integral Operators Involving Normalized Wright Functions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 66, no. 1, 2017, pp. 19-28, doi:10.1501/Commua1_0000000771.
Vancouver Mustafa N. Univalence of certain integral operators involving normalized wright functions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66(1):19-28.

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