SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 49 Issue: 5

New properties of the generalized Dini function

Ebrahim Analouei Adegani(Shahrood University of Technology)0000-0001-9176-3932
Teodor Bulboaca(Babes-Bolyai University)0000-0001-8026-218X
Pages
—
Publication Date
2020-10-06
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Furthermore, we investigate sufficient conditions which these functions are uniformly $k$-starlike functions of complex order $b$ in the open unit disk, and some consequences of the main results are also presented. ****************************************************************************************************************************

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this work we study some properties of the normalized form of generalized Dini function like close-to-convexity of some order and close-to-convex with respect to another convex function.
📊
Key Findings & Data:In this work we study some properties of the normalized form of generalized Dini function like close-to-convexity of some order and close-to-convex with respect to another convex function.
💡
Conclusion & Impact:Furthermore, we investigate sufficient conditions which these functions are uniformly $k$-starlike functions of complex order $b$ in the open unit disk, and some consequences of the main results are also presented. ****************************************************************************************************************************
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Analytic functions · univalent function · Bessel functions of first kind of order $\nu$

Abstract

In this work we study some properties of the normalized form of generalized Dini function like close-to-convexity of some order and close-to-convex with respect to another convex function. Furthermore, we investigate sufficient conditions which these functions are uniformly $k$-starlike functions of complex order $b$ in the open unit disk, and some consequences of the main results are also presented. ****************************************************************************************************************************

🔖

Cite This Article

Adegani, E. A., Bulboaca, T. (2020). New properties of the generalized Dini function. Hacettepe Journal of Mathematics and Statistics, Volume: 49 Issue: 5. https://doi.org/10.15672/hujms.552260

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (17)

  1. D. Bansal, M.K. Soni and A. Soni, Certain geometric properties of the modified Dini function, Anal. Math. Phys. 9, 1383–1392, 2019.
  2. Á. Baricz, E. Deniz and N. Yagmur, Close-to-convexity of normalized Dini functions, Math. Nachr. 289, 1721–1726, 2016.
  3. Á. Baricz, P.A. Kupán and R. Szász, The radius of starlikeness of normalized Bessel functions of the first kind, Proc. Amer. Math. Soc. 142 (6), 2019–2025, 2014.
  4. Á. Baricz, S. Ponnusamy and S. Singh, Modified Dini functions: monotonicity pat- terns and functional inequalities, Acta Math. Hungar. 149 (1), 120–142, 2016.
  5. Á. Baricz, E. Toklu and E. Kadioğlu, Radii of starlikeness and convexity of Wright functions, Math. Commun. 23 (1), 97–117, 2018.
  6. S.Z.H. Bukhari, J. Sokól and S. Zafar, Unified approach to starlike and convex func- tions involving convolution between analytic functions, Results Math. 73, Article num- ber: 30, 2018.
  7. M.U. Din, M. Raza, S. Hussain and M. Darus, Certain geometric properties of gen- eralized Dini functions, J. Funct. Spaces, 2018, Art. ID 2684023, 1–9, 2018.
  8. A.W. Goodman, On uniformly convex functions, Ann. Polon. Math. 56, 87–92, 1991.
  9. A.W. Goodman, On uniformly starlike functions, Ann. Polon. Math. 155, 364–370, 1991.
  10. S. Kanas and A. Wiśniowska, Conic regions and k-uniform convexity, J. Comput. Appl. Math. 105, 327–336, 1999.
  11. S. Kanas and A. Wiśniowska, Conic regions and k-starlike functions, Rev. Roumaine Math. Pures Appl. 45 (4), 647–657, 2000.
  12. J.K. Prajapat, Certain geometric properties of the Wright functions, Integral Trans- forms Spec. Funct. 26 (3), 203–212, 2015.
  13. D. Răducanu, Geometric properties of Mittag-Leffler functions, in: Models and The- ories in Social Systems, Studies in Systems, Decision and Control 79, 403–415, Springer, Cham, 2018.
  14. F. Rönning, On starlike functions associated with parabolic regions, Ann. Univ. Mariae Curie-Sklodowska Sect. A, 45, 117–122, 1991.
  15. F. Rönning, Uniformly convex functions and a corresponding class of starlike func- tions. Proc. Amer. Math. Soc. 1 (18), 189–196, 1993.
  16. S. Owa, M. Nunokawa, H. Saitoh and H.M. Srivastava, Close-to-convexity, starlike- ness and convexity of certain analytic functions, Appl. Math. Lett. 15, 63–69, 2002.
  17. S.K. Sahoo and N.L. Sharma, On a generalization of close-to-convex functions, Ann. Polon. Math. 113 (1), 93–108, 2015.