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Journals / Konuralp Journal of Mathematics / 2018 / Cilt: 6 - Sayı: 2

Certain class of analytic functions involving Salagean type q-difference operator

Sibel Yalçın
Kaliappan Vijaya
Gangadharan Murugusundaramoorthy
Pages
264–271
Publication Date
2018-10-15
DOI
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AI Summary & Key Takeaways

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

The usefulness of the main result not only provide the unification of the results discussed in the literature but also generate certain new results.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we define a new subclass of analytic functions with negative coefficients involving Salagean type q-difference operator and discuss certain characteristic properties and inclusion relations involving Nδ(e) of this generalized function class.
📊
Key Findings & Data:Further, we determine partial sums results for the function class.
💡
Conclusion & Impact:The usefulness of the main result not only provide the unification of the results discussed in the literature but also generate certain new results.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Analytic · Univalent · q-difference operator

Abstract

In this paper, we define a new subclass of analytic functions with negative coefficients involving Salagean type q-difference operator and discuss certain characteristic properties and inclusion relations involving Nδ(e) of this generalized function class. Further, we determine partial sums results for the function class. The usefulness of the main result not only provide the unification of the results discussed in the literature but also generate certain new results.

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Cite This Article

Yalçın, S., Vijaya, K., Murugusundaramoorthy, G. (2018). Certain class of analytic functions involving Salagean type q-difference operator. Konuralp Journal of Mathematics, Cilt: 6 - Sayı: 2, 264–271. https://ajindex.com/articles/786558

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References (16)

  1. S¸. Altınkaya, and S. Yalc¸ın, Faber polynomial coefficient estimates for a class of bi-univalent functions based on the symmetric q-derivative operator, Journal of Fractional Calculus and Applications, Vol:8, No:2 (2017), 79-87
  2. S¸. Altınkaya, and S. Yalc¸ın, On the Fekete-Szeg¨o problem for analytic functions defined by using symmetric q-derivative operator, Konuralp Journal of Mathematics, Vol:5, No:1 (2017), 176-186
  3. S. Araci, U. Duran, M. Acikgoz and H. M. Srivastava, A certain (p, q)-derivative operator and associated divided differences, J. Inequal. Appl., (2016) 2016:301
  4. Aral, A., Gupta, V. and Agarwal, R. P., Applications of q-calculus in operator theory, Springer, New York, 2013
  5. B.A. Frasin, Partial sums of certain analytic and univalent functions, Acta Math. Acad. Paed. Nyir. Vol:21 (2005), 135-145
  6. B.A. Frasin and G.Murugusundaramoorthy Partial sums of certain analytic functions, Mathematica,Tome 53, Vol:76, No:2,(2011), 131-142
  7. A.W.Goodman, Univalent functions and nonanalytic curves, Proc. Amer. Math. Soc., Vol:8 (1957), 598-601
  8. F. H. Jackson, On q-functions and a certain difference operator, Transactions of the Royal Society of Edinburgh, Vol:46 (1908), 253-281
  9. S. Kanas and D. R˘aducanu, Some subclass of analytic functions related to conic domains, Math. Slovaca, Vol:64, No:5 (2014), 1183-1196
  10. Z. Karahuseyin, S¸. Altınkaya and S. Yalc¸ın, On H3(1) Hankel determinant for univalent functions defined by using q􀀀derivative operator, Transylv. J. Math. Mech., Vol:9, No:1 (2017), 25-33
  11. M.Govindaraj, and S. Sivasubramanian, On a class of analytic function related to conic domains involving q􀀀calculus, Analysis Math., Vol:43, No:5 (2017), 475-487
  12. G.Murugusundaramoorthy and H. M. Srivastava, Neighborhoods of certain classes of analytic functions of complex order, Journal of Ineql. In Pure and Appl. Maths., Vol:5, No:2, Art.24 (2004) 1-8
  13. S. D. Purohit, and R. K. Raina, Fractional q-calculus and certain subclasses of univalent analytic functions, Mathematica Vol:55(78), No:1 (2013), 62-74
  14. T. Rosy, K.G. Subramanian and G. Murugusundaramoorthy, Neighborhoods and partial sums of starlike based on Ruscheweyeh derivatives, J. Ineq. Pure Appl. Math., Vol:4, No:4, Art. 64 (2003), 1-8
  15. S. Ruscheweyh, Neighborhoods of univalent functions, Proc. Amer. Math. Soc., Vol:81 (1981), 521-527
  16. Salagean, G. S., Subclasses of univalent functions, Lecture Notes in Math., Springer-Verlag, 10