International Journal of Nonlinear Analysis and Applications

A new subclass of univalent holomorphic functions based on $q$-analogue of Noor operator

Document Type : Research Paper

Authors

Department of Mathematics, Payame Noor University, Tehran, Iran

Abstract

In this article, we introduce another new subclass by using $q$-analogue of the Noor operator and based on it we investigate a subclass with fixed finitely many coefficients for the univalent holomorphic functions. We obtain a number of useful properties such as coefficient estimates, extreme points, convexity and convolution-preserving properties.

Keywords

[1] B. Ahmad, M.G. Khan, B.A. Fasin, M.K. Aouf, T. Abdeljawad, W.K. Mashwani and M. Arif, On q-analogue of meromorphic multivalent functions in lemniscate of Bernoulli domain, AIMS Math. 6 (2021), 3037—3052.
[2] A. Akgul and B. Alcin, Based on a family of bi-univalent functions introduced through the q-analogue of Noor integral operator, Int. J. Open Prob. Compt. Math. 15 (2022), 20—33.
[3] A. Akgul and F.M. Sakar, A certain subclass of bi-univalent analytic functions introduced by means of the q-analogue of Noor integral operator and Horadam polynomials, Turk. J. Math. 43 (2019), 2275—2286.
[4] H. Aldweby and M. Darus, q-analogue of Ruscheweyh operator and its applications to certain subclass of uniformly starlike functions, AIP Conf. Proc. 1602 (2014), no. 1, 767–771.
[5] S.G. Ali Shah, S. Khan, S. Hussain and M. Darus, q-Noor integral operator associated with starlike functions and q-conic domains, AIMS Math. 7 (2022), 10842–10859.
[6] S. Altinkaya, Inclusion properties of Lucas polynomials for bi-univalent functions introduced through the q-analogue of Noor integral operator, Turk. J. Math. 43 (2019), 620—629.
[7] A. Aral, E. Deniz and H. Erbay, The Picard and Gauss–Weierstrass Singular Integrals in (p, q)-Calculus, Bull. Malays. Math. Sci. Soc. 43 (2020), 1569-–1583.
[8] M. Arif, M.U. Haq and J.L. Liu, A subfamily of univalent functions associated with-analogue of Noor integral operator, J. Funct. Biomater. 2018 (2018), 1—5.
[9] M. Arif, H.M. Srivastava, and S. Umar, Some applications of a q-analogue of the Ruscheweyh type operator for multivalent functions, RACSAM. 113 (2019), 1211—1221.
[10] P.L. Duren, Univalent functions, Grundlehren der mathematischen Wissenschaften, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1993.
[11] B. Khan, H.M. Srivastava, M. Tahir, M. Darus, Q.Z. Ahmed and N. Khan, Applications of a certain q-integral operator to the subclasses of analytic and bi-univalent functions, AIMS Math. 6 (2020), 1024—1039.
[12] P. Long, J. Liu, M. Gangadharan and W. Wang, Certain subclass of analytic functions based on q-derivative operator associated with the generalized Pascal snail and its applications, AIMS Math. 7 (2022), 13423–13441.
[13] S. Mahmood and J. Sokol, New subclass of analytic functions in conical domain associated with Ruscheweyh q-differential operator, Results Math. 71 (2017), 1–13.
[14] F. Muge Sakar and A. Akgul, Based on a family of bi-univalent functions introduced through the Faber polynomial expansions and Noor integral operator, AIMS Math. 7 (2022), 5146–5155.
[15] S. Najafzadeh, Some results on univalent holomorphic functions based on q-analogue of Noor operator, Int. J. Appl. Math. 32 (2019), 775–784.
[16] S. Najafzadeh and D.O. Makinde, Certain subfamily of harmonic functions related to Salagean q-differential operator, Int. J. Anal. Appl. 18 (2020), 254–261.
[17] K.I. Noor, S. Altinkaya and S. Yalcin, Coefficient inequalities of analytic functions equipped with conic domains involving q-analogue of Noor integral operator, Tbilisi Math. J. 14 (2021), 1–14.
[18] K.I. Noor and M.A. Noor, On integral operators, J. Math. Anal. Appl. 238 (1999), 341–352.
[19] S.H. Sayedain Boroujeni, S. Najafzadeh, Error function and certain subclasses of analytic univalent functions, Sahand Commun. Math. Anal. 20 (2023), no. 1, 107–117.
[20] T.M. Seoudy and M.K. Aouf, Coefficient estimates of new classes of q-starlike and q-convex functions of complex order, J. Math. Ineq. 10 (2016), 135–145.
[21] M. Tamer and E. Amnah, Certain subclasses of spiral-like functions associated with q-analogue of Carlson-Shaffer operator, AIMS Math. 6 (2021), 2525–2538.
[22] B. Wang and R. Srivastava and L.L. Jin, Certain properties of multivalent analytic functions defined by q-difference operator involving the Janowski function, AIMS Math. 6 (2021), 8497–8508.
International Journal of Nonlinear Analysis and Applications
Volume 14, Issue 11
November 2023
Pages 181-189
  • Receive Date: 17 November 2022
  • Accept Date: 28 January 2023