A Subclass of Janowski Starlike Functions Involving Mathieu-Type Series
Abstract
:1. Introduction and Motivation
- The functions class with was presented and studied by Cho et al. [3].
- The functions class with maps the open unit disc onto the interior of the nephroid, a 2-cusped kidney-shaped region was familiarized and investigated by Wani and Swaminathan [4].
- The functions class with was presented by Sharma et al. [5].
- The functions class with was introduced and deliberated by Mendiratta et al. [6].
- The functions class with which maps open unit disk to crescent shaped region, was given in [7].
2. Main Results
3. Results Related to Partial Sum
4. Concluding Remarks and Observation
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
- Miller, S.S.; Mocanu, P.T. Differential subordination and univalent functions. Mich. Math. J. 1981, 28, 157–171. [Google Scholar] [CrossRef]
- Miller, S.S.; Mocanu, P.T. Differential Subordinations Theory and Applications; CRC Press: Boca Raton, FL, USA, 2000. [Google Scholar]
- Cho, N.E.; Kumar, S.; Kumar, V.; Ravichandran, V. Radius problems for starlike functions associated with the sine function. Bull. Iran. Math. Soc. 2019, 45, 213–232. [Google Scholar] [CrossRef]
- Wani, L.A.; Swaminathan, A. Starlike and convex functions associated with a Nephroid domain. Bull. Malays. Math. Sci. Soc. 2021, 44, 79–104. [Google Scholar] [CrossRef]
- Sharma, K.; Jain, N.K.; Ravichandran, V. Starlike functions associated with cardioid. Afr. Math. 2016, 27, 923–939. [Google Scholar] [CrossRef]
- Mendiratta, R.; Nagpal, S.; Ravichandran, V. On a subclass of strongly starlike functions associated exponential function. Bull. Malays. Math. Sci. Soc. 2015, 38, 365–386. [Google Scholar] [CrossRef]
- Raina, R.K.; Sokól, J. On coefficient estimates for a certain class of starlike functions. Hacet. J. Math. Stat. 2015, 44, 1427–1433. [Google Scholar] [CrossRef]
- Kanas, S.; Răducanu, D. Some classes of analytic functions related to conic domains. Math. Slovaca 2014, 64, 1183–1196. [Google Scholar] [CrossRef]
- Dzoik, J.; Raina, R.K.; Sokół, J. On certain subclasses of starlike functions related to a shell-like curve connected with Fibonacci numbers. Math. Comput. Model. 2013, 57, 1203–1211. [Google Scholar] [CrossRef]
- Cho, N.E.; Kumar, S.; Kumar, V.; Ravichandran, V.; Srivastava, H.M. Starlike functions related to the Bell numbers. Symmetry 2019, 11, 219. [Google Scholar] [CrossRef] [Green Version]
- Janowski, W. Some extremal problem for certain families of analytic functions I. Ann. Pol. Math. 1973, 28, 298–326. [Google Scholar] [CrossRef] [Green Version]
- Hu, Q.; Srivastava, H.M.; Ahmad, B.; Khan, N.; Khan, M.G.; Mashwani, W.K.; Khan, B. A subclass of multivalent Janowski type q-starlike functions and its consequences. Symmetry 2021, 13, 1275. [Google Scholar] [CrossRef]
- Islam, S.; Khan, M.G.; Ahmad, B.; Arif, M.; Chinram, R. q-Extension of Starlike Functions Subordinated with a Trigonometric Sine Function. Mathematics 2020, 8, 1676. [Google Scholar] [CrossRef]
- Shi, L.; Srivastava, H.M.; Khan, M.G.; Khan, N.; Ahmad, B.; Khan, B.; Mashwani, W.K. Certain Subclasses of Analytic Multivalent Functions Associated with Petal-Shape Domain. Axioms 2021, 10, 291. [Google Scholar] [CrossRef]
- Ebadian, A.; Cho, N.E.; Adegani, E.A.; Yalçın, S. New Criteria for Meromorphic Starlikeness and Close-to-Convexity. Mathematics 2020, 8, 847. [Google Scholar] [CrossRef]
- Naeem, M.; Hussain, S.; Mahmood, T.; Khan, S.; Darus, M. A New Subclass of Analytic Functions Defined by Using Salagean q-Differential Operator. Mathematics 2019, 7, 458. [Google Scholar] [CrossRef] [Green Version]
- Liu, L.; Liu, J.-L. Properties of Certain Multivalent Analytic Functions Associated with the Lemniscate of Bernoulli. Axioms 2021, 10, 160. [Google Scholar] [CrossRef]
- Soybaş, D.; Joshi, S.B.; Pawar, H. On a Certain Subclass of Analytic Functions Involving Integral Operator Defined by Polylogarithm Function. Mathematics 2019, 7, 66. [Google Scholar] [CrossRef] [Green Version]
- Mathieu, E.L. Traité de Physique Mathematique. VI-VII: Theory del Elasticité des Corps Solides (Part 2); Gauthier-Villars: Paris, France, 1890. [Google Scholar]
- Emersleben, O. Über die Reihe . Math. Ann. 1952, 125, 165–171. [Google Scholar] [CrossRef]
- Tomovski, Z. New integral and series representations of the generalized Mathieu series. Appl. Anal. Discret. Math. 2008, 2, 205–212. [Google Scholar] [CrossRef] [Green Version]
- Bansal, D.; Sokól, J. Geometric properties of Mathieu–type power series inside unit disk. J. Math. Ineq. 2019, 13, 911–918. [Google Scholar] [CrossRef] [Green Version]
- Nunokawa, M.; Sokól, J. On an extension of Sakaguchi’s result. J. Math. Ineq. 2015, 9, 683–697. [Google Scholar] [CrossRef]
- Bansal, D.; Sokól, J. Univalency of starlikeness of Harwitz-Lerch Zeta function inside unit disk. J. Math. Ineq. 2017, 11, 863–871. [Google Scholar] [CrossRef] [Green Version]
- Sokól, J.; Witowicz, P. On an application of Vietoris’s inequality. J. Math. Ineq. 2016, 10, 829–836. [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 involving multivalent functions. Adv. Differ. Equ. 2021, 2021, 279. [Google Scholar] [CrossRef]
- Srivastava, H.M.; Ahmad, Q.Z.; Khan, N.; Khan, B. Hankel and Toeplitz determinants for a subclass of q-starlike functions associated with a general conic domain. Mathematics 2019, 7, 181. [Google Scholar] [CrossRef] [Green Version]
- 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. A Sci. 2021, 44, 327–344. [Google Scholar] [CrossRef]
- Srivastava, H.M.; Wanas, A.K.; Srivastava, R. Applications of the q-Srivastava-Attiya operator involving a certain family of bi-univalent functions associated with the Horadam polynomials. Symmetry 2021, 13, 1230. [Google Scholar] [CrossRef]
- Shi, L.; Khan, M.G.; Ahmad, B.; Mashwani, W.K.; Agarwal, P.; Momani, S. Certain coefficient estimates problems for three-leaf-type starlike functions. Fractal Fract. 2021, 5, 137. [Google Scholar] [CrossRef]
- Attiya, A.A.; Lashin, A.M.; Ali, E.E.; Agarwal, P. Coefficient bounds for certain classes of analytic functions associated with Faber polynomial. Symmetry 2021, 13, 302. [Google Scholar] [CrossRef]
- Shi, L.; Ahmad, B.; Khan, N.; Khan, M.G.; Araci, S.; Mashwani, W.K.; Khan, B. Coefficient Estimates for a subclass of meromorphic multivalent q-Close-to-convex functions. Symmetry 2021, 13, 1840. [Google Scholar] [CrossRef]
- Srivastava, H.M. Some parametric and argument variations of the operators of fractional calculus and related special functions and integral transformatioons. J. Nonlinear Convex Anal. 2021, 22, 1501–1520. [Google Scholar]
- Khan, M.G.; Ahmad, B.; Mostafa, S.; Mashwani, W.K.; Arjika, S.; Khan, B. Pascu-type analytic functions by Using Mittag-Leffler functions in Janowski domain. Math. Probl. Eng. 2021, 2021, 1209871. [Google Scholar]
- Khan, M.G.; Ahmad, B.; Khan, N.; Mashwani, W.K.; Arjika, S.; Khan, B.; Chinram, R. Applications of Mittag-Leffer type poisson distribution to a subclass of analytic functions involving conic-type regions. J. Funct. Spaces 2021, 2021, 4343163. [Google Scholar] [CrossRef]
- Keogh, F.R.; Merkes, E.P. A coefficient inequality for certain classes of analytic functions. Proc. Am. Math. Soc. 1969, 20, 8–12. [Google Scholar] [CrossRef]
- Ma, W.; Minda, D. A unified treatment of some special classes of univalent functions. In Proceedings of the Conference on Complex Analysis, Tianjin, China, 19–23 June 1992; Li, Z., Ren, F., Yang, L., Zhang, S., Eds.; International Press: Cambridge, MA, USA, 1994; pp. 157–169. [Google Scholar]
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Liu, D.; Araci, S.; Khan, B. A Subclass of Janowski Starlike Functions Involving Mathieu-Type Series. Symmetry 2022, 14, 2. https://doi.org/10.3390/sym14010002
Liu D, Araci S, Khan B. A Subclass of Janowski Starlike Functions Involving Mathieu-Type Series. Symmetry. 2022; 14(1):2. https://doi.org/10.3390/sym14010002
Chicago/Turabian StyleLiu, Dong, Serkan Araci, and Bilal Khan. 2022. "A Subclass of Janowski Starlike Functions Involving Mathieu-Type Series" Symmetry 14, no. 1: 2. https://doi.org/10.3390/sym14010002
APA StyleLiu, D., Araci, S., & Khan, B. (2022). A Subclass of Janowski Starlike Functions Involving Mathieu-Type Series. Symmetry, 14(1), 2. https://doi.org/10.3390/sym14010002