Certain Geometric Properties of an Integral Operator Involving Bessel Functions

  • Selvakumaran, Kuppathai Appasamy (Department of Mathematics, R. M. K College of Engineering and Technology) ;
  • Szasz, Robert (Sapientia Hungarian University of Transylvania)
  • Received : 2017.04.17
  • Accepted : 2018.08.27
  • Published : 2018.09.23


In this article, we introduce a new integral operator involving normalized Bessel functions of the first kind and we obtain a set of sufficient conditions for univalence. Our results contain some interesting corollaries as special cases. Further, as particular cases, we improve some of the univalence conditions proved in [2].


analytic functions;Bessel functions;integral operator;univalent functions


  1. A. Baricz, Geometric properties of generalized Bessel functions, Publ. Math. Debrecen, 73(1-2)(2008), 155-178.
  2. A. Baricz and B. A. Frasin, Univalence of integral operators involving Bessel functions, Appl. Math. Lett., 23(4)(2010), 371-376.
  3. A. Baricz and S. Ponnusamy, Starlikeness and convexity of generalized Bessel functions, Integral Transforms Spec. Func., 21(9)(2010), 641-653.
  4. D. Breaz, N. Breaz and H. M. Srivastava, An extension of the univalent condition for a family of integral operators, Appl. Math. Lett., 22(2009), no. 1, 41-44.
  5. E. Deniz, H. Orhan and H. M. Srivastava, Some sufficient conditions for univalence of certain families of integral operators involving generalized Bessel functions, Taiwanese J. Math., 15(2)(2011), 883-917.
  6. B. A. Frasin, Sufficient conditions for integral operator defined by Bessel functions, J. Math. Inequal., 4(2)(2010), 301-306.
  7. S. S. Miller and P. T. Mocanu, Differential subordinations, Monographs and Textbooks in Pure and Applied Mathematics 225, Marcel Dekker, Inc., New York, 2000.
  8. N. N. Pascu, An improvement of Becker's univalence criterion, Proceedings of the Commemorative Session: Simion Stoilow (Brasov, 1987), 43-48, Univ. Brasov, Brasov, 1987.
  9. V. Pescar, A new generalization of Ahlfors's and Becker's criterion of univalence, Bull. Malaysian Math. Soc. (2), 19(2)(1996), 53-54.
  10. H. M. Srivastava, E. Deniz and H. Orhan, Some general univalence criteria for a family of integral operators, Appl. Math. Comput., 215(10)(2010), 3696-3701.
  11. H. M. Srivastava, B. A. Frasin and V. Pescar, Univalence of integral operators involving Mittag-Leffler functions, Appl. Math. Inf. Sci., 11(3)(2017), 635-641.
  12. H. M. Srivastava, J. K. Prajapat, G. I. Oros and R. Sendrutiu, Geometric properties of a certain general family of integral operators, Filomat, 28(4)(2014), 745-754.
  13. H. M. Srivastava, K. A. Selvakumaran and S. D. Purohit, Inclusion properties for certain subclasses of analytic functions defined by using the generalized Bessel functions, Malaya J. Mat., 3(3)(2015), 360-367.
  14. L. F. Stanciu, D. Breaz and H. M. Srivastava, Some criteria for univalence of a certain integral operator, Novi Sad J. Math., 43(2)(2013), 51-57.
  15. R. Szasz, About the starlikeness of Bessel functions, Integral Transforms Spec. Funct., 25(9)(2014), 750-755.
  16. R. Szasz and P. A. Kupan, About the univalence of the Bessel functions, Stud. Univ. Babes-Bolyai Math., 54(1) (2009), 127-132.
  17. N. Ularu, Two integral operators defined with Bessel functions on the class N(${\beta}$), J. Basic Apll. Sci., 9(2013), 57-59.