Applications of the q-Sălăgean Differential Operator Involving Multivalent Functions
Abstract
1. Introduction
2. Preliminaries
3. Main Results
4. Conclusions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
- Jackson, F.H. q-Difference equations. Am.J. Math. 1910, 32, 305–314. [Google Scholar] [CrossRef]
- Jackson, F.H. On q-definite integrals. Quart. J. Pure Appl. Math. 1910, 41, 193–203. [Google Scholar]
- Srivastava, H.M. Univalent functions, fractional calculus and associated generalized hypergeometric functions. In Univalent Functions, Fractional Calculus, and Their Applications; Srivastava, H.M., Owa, S., Eds.; Halsted Press (Ellis Horwood Limited): Chichester, UK; John Wiley and Sons: New York, NY, USA, 1989; pp. 329–354. [Google Scholar]
- Ismail, M.E.-H.; Merkes, E.; Styer, D. A generalization of starlike functions. Complex Var. Theory Appl. 1990, 14, 77–84. [Google Scholar] [CrossRef]
- Agrawal, S.; Sahoo, S.K. A generalization of starlike functions of order α. Hokkaido Math. J. 2017, 46, 15–27. [Google Scholar] [CrossRef]
- Tang, H.; Khan, S.; Hussain, S.; Khan, N. Hankel and Toeplitz determinant for a subclass of multivalent q-starlike functions of order α. AIMS Math. 2021, 6, 5421–5439. [Google Scholar] [CrossRef]
- Mahmood, S.; Jabeen, M.; Malik, S.N.; Srivastava, H.M.; Manzoor, R.; Riaz, S.M.J. Some coefficient inequalities of q-starlike functions associated with conic domain defined by q-derivative. J. Funct. Spaces 2018, 2018, 8492072. [Google Scholar] [CrossRef]
- Mahmood, S.; Ahmad, Q.Z.; Srivastava, H.M.; Khan, N.; Khan, B.; Tahir, M. A certain subclass of meromorphically q-starlike functions associated with the Janowski functions. J. Inequal. Appl. 2019, 2019, 88. [Google Scholar] [CrossRef]
- Shi, L.; Khan, Q.; Srivastava, G.; Liu, J.-L.; Arif, M. A study of multivalent q-starlike functions connected with circular domain. Mathematics 2019, 7, 670. [Google Scholar] [CrossRef]
- Khan, B.; Liu, Z.-G.; Srivastava, H.M.; Khan, N.; Darus, M.; Tahir, M. A Study of Some Families of Multivalent q-Starlike Functions Involving Higher-Order q-Derivatives. Mathematics 2020, 8, 1470. [Google Scholar] [CrossRef]
- Rehman, M.S.; Ahmad, Q.Z.; Srivastava, H.M.; Khan, B.; Khan, N. Partial sums of generalized q-Mittag-Leffler functions. AIMS Math. 2019, 5, 408–420. [Google Scholar] [CrossRef]
- Hadi, S.H.; Darus, M.; Park, C.; Lee, J.R. Some geometric properties of multivalent functions associated with a new generalized q-Mittag-Leffler function. AIMS Math. 2022, 7, 11772–11783. [Google Scholar] [CrossRef]
- Aouf, M.K.; Madian, S.M. Fekete–Szegö properties for classes of complex order and defined by new generalization of q-Mittag Leffler function. Afr. Mat. 2022, 33, 15. [Google Scholar] [CrossRef]
- Srivastava, H.M. Operators of basic (or q-) calculus and fractional q-calculus and their applications in geometric function theory of complex analysis. Iran. J. Sci. Technol. Trans. ASci. 2020, 44, 327–344. [Google Scholar] [CrossRef]
- Kanas, S.; Răducanu, D. Some class of analytic functions related to conic domains. Math. Slovaca 2014, 64, 1183–1196. [Google Scholar] [CrossRef]
- Selvakurmaran, K.A.; Purohit, S.D.; Secer, A.; Bayram, M. Convexity of certain q-integral operators of p-valent functions. Abstr. Appl. Anal. 2014, 2014, 925902. [Google Scholar] [CrossRef]
- Arif, M.; Srivastava, H.M.; Umar, S. Some application of a q-analogue of the Ruscheweyh type operator for multivalent functions. Rev. Real Acad. Cienc. Exactas Fis. Natur. Ser. A Mat. 2019, 113, 1121–1221. [Google Scholar] [CrossRef]
- Govindaraj, M.; Sivasubramanian, S. On a class of analytic functions related to conic domains involving q-calculus. Anal. Math. 2017, 43, 475–487. [Google Scholar] [CrossRef]
- Hussain, S.; Khan, S.; Zaighum, M.A.; Darus, M. Applications of a q-Salagean type operator on multivalent functions. J. Inequal. Appl. 2018, 2018, 301. [Google Scholar] [CrossRef]
- Khan, S.; Hussain, S.; Zaighum, M.A.; Darus, M. A Subclass of uniformly convex functions and a corresponding subclass of starlike function with fixed coefficient associated with q-analogue of Ruscheweyh operator. Math. Slovaca 2019, 69, 825–832. [Google Scholar] [CrossRef]
- Zainab, S.; Raza, M.; Xin, Q.; Jabeen, M.; Malik, S.N.; Riaz, S. On q-Starlike Functions Defined by q-Ruscheweyh Differential Operator in Symmetric Conic Domain. Symmetry 2021, 13, 1947. [Google Scholar] [CrossRef]
- Naeem, M.; Hussain, S.; Mahmood, T.; Khan, S.; Darus, M. A New Subclass of Analytic Functions Defined by Using Sălăgean q-Differential Operator. Mathematics 2019, 7, 458. [Google Scholar] [CrossRef]
- Wongsaijai, B.; Sukantamala, N. Applications of fractional q-calculus to certain subclass of analytic p-valent functions with negative coefficients. Abstr. Appl. Anal. 2015, 2015, 273236. [Google Scholar] [CrossRef]
- Srivastava, H.M.; Mostafa, A.O.; Aouf, M.K.; Zayed, H.M. Basic and fractional q-calculus and associated Fekete-Szego problem for p-valently q-starlike functions and p-valently q-convex functions of complex order. Miskolc Math.Notes 2019, 20, 489–509. [Google Scholar] [CrossRef]
- Khan, B.; Srivastava, H.M.; Arjika, S.; Khan, S.; Khan, N.; Ahmad, Q.Z. A certain q-Ruscheweyh type derivative operator and its applications involiving multivalent functions. Adv. Differ. Equ. 2021, 2021, 279. [Google Scholar] [CrossRef]
- Miller, S.S.; Mocanu, P.T. Second order-differential inequalities in the complex plane. J. Math. Anal.Appl. 1978, 65, 298–305. [Google Scholar] [CrossRef]
- Miller, S.S.; Mocanu, P.T. Differential subordinations and univalent functions. Mich. Math. J. 1981, 28, 157–171. [Google Scholar] [CrossRef]
- Sălăgean, G.Ş. Subclasses of univalent functions. Lect. Notes Math. 1983, 1013, 362–372. [Google Scholar]
- Alb Lupaş, A. Subordination Results on the q-Analogue of the Sălăgean Differential Operator. Symmetry 2022, 14, 1744. [Google Scholar] [CrossRef]
- Miller, S.S.; Mocanu, P.T. On some classes of first-order differential subordinations. Mich. Math. J. 1985, 32, 185–195. [Google Scholar] [CrossRef]
- Robertson, M.S. Certain classes of starlike functions. Mich. Math. J. 1985, 32, 135–140. [Google Scholar] [CrossRef]
- Rao, G.S.; Saravanan, R. Some results concerning best uniform co-approximation. J. Inequal. Pure Appl. Math. 2002, 3, 24. [Google Scholar]
- Rao, G.S.; Chandrasekaran, K.R. Characterization of elements of best co-approximation in normed linear spaces. Pure Appl. Math. Sci. 1987, 26, 139–147. [Google Scholar]
- El-Deeb, S.M.; Bulboacă, T. Differential Sandwich-Type Results for Symmetric Functions Connected with a q-Analog Integral Operator. Mathematics 2019, 7, 1185. [Google Scholar] [CrossRef]
- Hadi, S.A.; Darus, M. Differential subordination and superordination for a q-derivative operator connected with the q-exponential function. Int. J. Nonlinear Anal. Appl. 2022, 13, 2795–2806. [Google Scholar]
- Owa, S.; Guney, H.O. New Applications of the Bernardi Integral Operator. Mathematics 2020, 8, 1180. [Google Scholar] [CrossRef]
- Oros, G.I.; Oros, G.; Owa, S. Applications of Certain p-Valently Analytic Functions. Mathematics 2022, 10, 910. [Google Scholar] [CrossRef]
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Alb Lupaş, A. Applications of the q-Sălăgean Differential Operator Involving Multivalent Functions. Axioms 2022, 11, 512. https://doi.org/10.3390/axioms11100512
Alb Lupaş A. Applications of the q-Sălăgean Differential Operator Involving Multivalent Functions. Axioms. 2022; 11(10):512. https://doi.org/10.3390/axioms11100512
Chicago/Turabian StyleAlb Lupaş, Alina. 2022. "Applications of the q-Sălăgean Differential Operator Involving Multivalent Functions" Axioms 11, no. 10: 512. https://doi.org/10.3390/axioms11100512
APA StyleAlb Lupaş, A. (2022). Applications of the q-Sălăgean Differential Operator Involving Multivalent Functions. Axioms, 11(10), 512. https://doi.org/10.3390/axioms11100512