Study on the q-analogue of a certain family of linear operators
Study on the q-analogue of a certain family of linear operators
In this paper, we introduce the q-analogue of a certain family of linear operators in geometric function theory.Our main purpose is to define some subclasses of analytic functions by means of the q-analogue of linear operators andinvestigate various inclusion relationships with integral preserving properties.
___
- [1] Adams CR. On the linear ordinary q-difference equation. Annals of Mathematics 1929; 30: 195-205.
- [2] Altıntaş O, Mustafa N. Coefficient bounds and distortion theorems for the certain analytic functions. Turkish
Journal of Mathematics 2019; 43: 985-997.
- [3] Arif M, Ul-Haq M, Liu JL. A subfamily of univalent functions associated with q-analogue of Noor integral operator.
Journal of Function Spaces 2018; 2018; 3818915.
- [4] Carmichael RD. The general theory of linear q-difference equations. American Journal of Mathematics 1912; 34:
147-168.
- [5] Exton H. q-Hypergeometric Functions and Applications. Chichester, UK: Ellis Horwood Limited, 1983.
- [6] Gasper G, Rahman M. Basic Hypergeometric Series. Cambridge, UK: Cambridge University Press, 1990.
- [7] Ghany HA. q-derivative of basic hypergeomtric series with respect to parameters. International Journal of Mathematical
Analysis 2009; 3: 1617-1632.
- [8] Govindaraj M, Sivasubramanian S. On a class of analytic functions related to conic domains involving q-calculus.
Analysis Mathematica 2017; 43: 475-487.
- [9] Husain S, Khan S, Zaighum MA, Darus M. Certain subclass of analytic functions related with conic domains and
associated with Salagean q-differential operator. AIMS Mathematics 2017; 2(4): 622-634.
- [10] Husain S, Khan S, Zaighum MA, Darus M. Applications of a q-Salagean type operator on multivalent functions.
Journal of Inequalities and Applications 2018; 2018: 301.
- [11] Ismail MEH, Merkes E, Styer D. A generalization of starlike functions. Complex Variables 1990; 14: 77-84.
- [12] Jackson FH. On q-functions and a certain difference operator. Transactions of the Royal Society of Edinburgh 1908;
46: 253-281.
- [13] Jackson FH. On q-definite integrals. Quarterly Journal of Pure and Applied Mathematics 1910; 41: 193-203.
- [14] Janowski W. Some extremal problems for certain families of analytic functions. Annales Polonici Mathematici 1973;
28: 297-326.
- [15] Kanas S, Raducanu D. Some classes of analytic functions related to conic domains. Mathematica Slovaca 2014; 64,
1183-1196.
- [16] Koc V, Cheung P. Quantum Calculus. Berlin, Germany: Springer, 2001.
- [17] Mason TE. On properties of the solution of linear q-difference equations with entire function coefficients. American
Journal of Mathematics 1915; 37: 439-444.
- [18] Miller SS, Mocanu PT. Differential Subordinations Theory and Applications. New York, NY, USA: Marcel Dekker,
2000.
- [19] Noor KI. On generalized q-close-to-convexity. Applied Mathematics and Information Sciences 2017; 11 (5): 1383-
1388.
- [20] Noor KI. Some classes of analytic functions associated with q-Rischeweyh differential operator. Facta Universitatis
Series Mathematics and Informatics 2018; 33: 531-538.
- [21] Noor KI, Riaz S. Generalized q-starlike functions. Studia Scientiarum Mathematicarum Hungarica 2017; 54: 509-
522.
- [22] Noor KI, Riaz S, Noor MA. On q-Bernardi integral operator. TWMS Journal of Pure and Applied Mathematics
2017; 8: 3-11.
- [23] Shamsan H, Latha S. On generalized bounded Mocanu variation related to q-derivative and conic regions. Annals
of Pure and Applied mathematics 2018; 17 (1): 67-83.
- [24] Srivastava HM, Attiya AA. An integral operator associated with the Hurwitz-Lerch Zeta function and differential
subordination. Integral Transform and Special Functions 2007; 18: 207-216.
- [25] Srivastava HM, Choi J. Series associated with zeta and related function. Dordrecht, the Netherlands: Kluwer
Academic Publisher, 2001.
- [26] Trijitzinsky WJ. Analytic theory of linear q-difference equations. Acta Mathematica 1933; 61 (1): 1-38.
- [27] Uçar HEÖ. Coefficient inequality for q-starlike functions. Applied Mathematics and Computation 2016; 276: 122-
126.
- [28] Uçar HEÖ, Mert O, Polatoğlu Y. Some properties of q-close-to-convex functions. Hacettepe Journal of Mathematics
and Statistics 2017; 46 (6): 1105-1112.