SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2018 / Cilt: 47 - Sayı: 4

q− Harmonic mappings for which analytic part is q− convex functions of complex order

Yaşar POLATOĞLU
Asena ÇETİNKAYA
Pages
813–820
Publication Date
2022-10-18
DOI
—
🏛️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)

In this paper, we investigate properties of the class SHCq(b) by using subordination techniques.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We introduce a new class of harmonic function f, that is subclass of planar harmonic mapping associated with q− difference operator.
📊
Key Findings & Data:Let h and g are analytic functions in the open unit disc D = {z : |z| < 1}.
💡
Conclusion & Impact:In this paper, we investigate properties of the class SHCq(b) by using subordination techniques.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

We introduce a new class of harmonic function f, that is subclass of planar harmonic mapping associated with q− difference operator. Let h and g are analytic functions in the open unit disc D = {z : |z| < 1}. If f = h + g is the solution of the non-linear partial dierential equation wq(z) = Dqg(z) Dqh(z) = fz fz with |wq(z)| < 1, wq(z) ≺ b1 1+z 1−qz and h is q− convex function of complex order, then the class of such functions are called q− harmonic functions for which analytic part is q− convex functions of complex order denoted by SHCq(b). Obviously that the class SHCq(b) is the subclass of SH. In this paper, we investigate properties of the class SHCq(b) by using subordination techniques.

🔖

Cite This Article

POLATOĞLU, Y., ÇETİNKAYA, A. (2022). q− Harmonic mappings for which analytic part is q− convex functions of complex order. Hacettepe Journal of Mathematics and Statistics, Cilt: 47 - Sayı: 4, 813–820. https://ajindex.com/articles/529861

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (11)

  1. Andrews, G.E. Applications of basic hypergeometric functions, SIAM Rev. 16 (1974), 441- 484. Çetinkaya, A. and Mert, O. A certain class of harmonic mappings related to functions of bounded boundary rotation, Proc. of 12th Symposium on Geometric Function Theory and Applications (2016), 67-76.
  2. Duren, P. Harmonic mappings in the plane, Cambridge Tracts in Math. 2004.
  3. Fine, N.J. Basic hypergeometric series and applications, Math. Surveys Monogr. 1988.
  4. Gasper, G. and Rahman, M. Basic hypergeometric series, Cambridge University Press, 2004.
  5. Goodman, A.W. Univalent functions Volume I and II, Polygonal Pub. House, 1983.
  6. Jack, I.S. Functions starlike and convex of order α, J. Lond. Math. Soc. (2), 3 (1971), 469-474.
  7. Jackson, F.H. On q− functions and a certain di erence operator, Trans. Roy. Soc. Edin. 46 (1908), 253-281.
  8. Jackson, F.H. On q− di erence integrals, Quart. J. Pure Appl. Math. 41 (1910), 193-203.
  9. Kac, V. and Cheung, P. Quantum calculus, Springer, 2001.
  10. Lewy, H. On the non-vanishing of the Jacobian in certain one-to-one mappings, Bull. Amer. Math. Soc. 42 (1936), 689-692.
  11. Polatoglu, Y., Aydogan, M. and Mert, O. Some properties of q− convex functions of complex order, Sarajevo J. Math. Submitted, 2016