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Certain Geometric Properties of an Integral Operator Involving Bessel Functions

Kuppathai Appasamy Selvakumaran|Robert Szasz
경북대학교 자연과학대학 수학과|2018.09|Kyungpook Mathematical Journal|제58권 제3호|pp. 507-517

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키워드

analytic functionsunivalent functionsintegral operatorBessel functions
주제분류수학

초록

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].

Abstract

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].

참고문헌 (17)

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  2. A. Baricz, "Univalence of integral operators involving Bessel functions", Appl. Math. Lett, 23(4), pp.371~376 (2010)
  3. A. Baricz, "Starlikeness and convexity of generalized Bessel functions", Integral Transforms Spec. Func, 21(9), pp.641~653 (2010)
  4. D. Breaz, "An extension of the univalent condition for a family of integral operators", Appl. Math. Lett, 22(1), pp.41~44 (2009)
  5. E. Deniz, "Some sufficient conditions for univalence of certain families of integral operators involving generalized Bessel functions", Taiwanese J. Math, 15(2), pp.883~917 (2011)
  6. B. A. Frasin, "Sufficient conditions for integral operator defined by Bessel functions", J. Math. Inequal, 4(2), pp.301~306 (2010)
  7. S. S. Miller, "Differential subordinations" (2000), Marcel Dekker, Inc
  8. N. N. Pascu, "An improvement of Becker’s univalence criterion", Proceedings of the Commemorative Session: Simion Stoılow, pp.43~48 (1987), Univ. Bra¸sov
  9. V. Pescar, "A new generalization of Ahlfors’s and Becker’s criterion of univalence", Bull. Malaysian Math. Soc, 19(2), pp.53~54 (1996)
  10. H. M. Srivastava, "Some general univalence criteria for a family of integral operators", Appl. Math. Comput, 215(10), pp.3696~3701 (2010)
  11. H. M. Srivastava, "Univalence of integral operators involving Mittag-Leffler functions", Appl. Math. Inf. Sci, 11(3), pp.635~641 (2017)
  12. H. M. Srivastava, "Geometric properties of a certain general family of integral operators", Filomat, 28(4), pp.745~754 (2014)
  13. H. M. Srivastava, "Inclusion properties for certain subclasses of analytic functions defined by using the generalized Bessel functions", Malaya J. Mat, 3(3), pp.360~367 (2015)
  14. L. F. Stanciu, "Some criteria for univalence of a certain integral operator", Novi Sad J. Math, 43(2), pp.51~57 (2013)
  15. R. SzAsz, "About the starlikeness of Bessel functions", Integral Transforms Spec. Funct, 25(9), pp.750~755 (2014)
  16. R. SzAsz, "About the univalence of the Bessel functions", Stud. Univ. Babes-Bolyai Math, 54(1), pp.127~132 (2009)
  17. N. Ularu, "Two integral operators defined with Bessel functions on the class N(β)", J. Basic Apll. Sci, 9, pp.57~59 (2013)

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