Subclasses of Analytic Functions with Negative Coefficients Involving q-Derivative Operator
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Abstract
Let A denote the class of functions f which are analytic in the open unit disk U. The subclass of A consisting of univalent functions is denoted by M. In this paper, we also consider a subclass of M which is denoted by V, consisting of functions with negative coefficients. In addition, this paper also studies the q-derivative operator. By combining the ideas, this paper introduced three subclasses of A with negative coefficients involving q-derivative. Furthermore, the coefficient estimates, growth results and extreme points were obtained for all of these classes.
References
Al-Abbadi, M. H. and M. Darus (2010). On Subclass of Analytic Univalent Functions Associated with Negative Coefficients. International Journal of Mathematics and Mathematical Sciences, 2010; 1–11
Al Shaqsi, K. and M. Darus (2007). On Certain Subclass of Analytic Univalent Functions with Negative Coefficients. Applied Mathematical Sciences, 1(21-24); 1121–1128
Aral, A., V. Gupta, and R. P. Agarwal (2013). Applications of q-Calculus in Operator Theory. Springer
Atshan, W. G. and H. Y. Ghawi (2012). On a New Class of Univalent Functions with Negative Coefficients. European Journal of Scientific Research, 74(4); 601–608
Breaz, D. and L. I. Cotîrlă (2021). The Study of The New Classes of m-Fold Symmetric Bi-Univalent Functions. Mathematics, 10(1); 75
Bucur, R. and D. Breaz (2020). Properties of a New Subclass of Analytic Functions with Negative Coefficients Defined by Using The q-Derivative. Applied Mathematics and Nonlinear Sciences, 5(1); 303–308
Choo, C. P. and A. Janteng (2013). Estimate on The Second Hankel Functional for a Subclass of Close-to-Convex Functions with Respect to Symmetric Points. International Journal of Mathematics Analysis, 7; 781–788
Clunie, J. and F. Keogh (1960). On Starlike and Convex Schlicht Functions. Journal of The London Mathematical Society, 1(2); 229–233
Halim, S., A. Janteng, and M. Darus (2005). Coefficient Properties for Classes with Negative Coefficients and Starlike with Respect to Other Points. In Proceeding of The 13th Mathematical Sciences National Symposium, 2; 658–663
Halim, S. A., A. Janteng, and M. Darus (2006). Classes with Negative Coefficients and Starlike with Respect to Other Points II. Tamkang Journal of Mathematics, 37(4); 345–354
Ibrahim, R. W. (2020). Geometric Process Solving a Class of Analytic Functions Using q-Convolution Differential Operator. Journal of Taibah University for Science, 14(1); 670–677
Jabeen, M., S. Nawaz Malik, S. Mahmood, S. Riaz, and M. Ali (2022). On q-Convex Functions Defined by The q-Ruscheweyh Derivative Operator in Conic Regions. Journal of Mathematics, 2022; 1–13
Jackson, F. H. (1909). On q-Functions and a Certain Difference Operator. Earth and Environmental Science Transactions of the Royal Society of Edinburgh, 46(2); 253–281
Janteng, A. and S. A. Halim (2009). A Subclass Quasi-Convex Functions with Respect to Symmetric Points. Applied Mathematical Sciences, 3(12); 551–556
Janteng, A., A. L. P. Hern, and R. Omar (2020). Fekete-Szegö Functional of Classes of Analytic Functions Involving The q-Derivative Operator. Applied Mathematical Sciences, 14(10); 481–488
Karahuseyin, Z., S. Altinkaya, and S. Yalçin (2017). On H3(1) Hankel Determinant for Univalent Functions Defned by Using q-Derivative Operator. Transylvanian Journal of Mathematics and Mechanics, 9; 25–33
Khan, B., Z. G. Liu, T. G. Shaba, S. Araci, N. Khan, and M. G. Khan (2022). Applications of-Derivative Operator to The Subclass of Bi-Univalent Functions Involving-Chebyshev Polynomials. Journal of Mathematics, 2022
Murugusundaramoorthy, G., T. Janani, and M. Darus (2015). Coefficient Estimate of Biunivalent Functions Based on q-Hypergeometric Functions. Applied Sciences, 17; 75–85
Najafzadeh, S. (2021). (p, q)-Derivative on Univalent Functions Associated with Subordination Structure. General Mathematics, 29(2); 99–106
Najafzadeh, S. and Z. Salleh (2022). Univalent Functions by Means of Chebyshev Polynomials. Journal of Function Spaces, 2022
Oluwayemi, M. O., K. Vijaya, and A. Cătaş (2022). Certain Properties of a Class of Functions Defined by Means of a Generalized Differential Operator. Mathematics, 10(2); 174
Oshah, A. and M. Darus (2015). New Subclass of Analytic Functions Defined by q-Differentiation. International Information Institute (Tokyo). Information, 18(7); 2897
Porwal, S., B. M. Indu, and M. Nanjundan (2022). On Certain Subclasses of Univalent Functions Associated with Wright Function. Theory and Applications of Mathematics & Computer Science, 12(1); 13–20
Rashid, A. M. and A. R. S. Juma (2022). A Class of Harmonic Univalent Functions Defined by The q-Derivative Operator. International Journal of Nonlinear Analysis and Applications, 13(1); 2713–2722
Shilpa, N. (2022). Fekete-Szegö Inequalities for Certain Analytic Functions Associated with q-Derivative Operator. Advances and Applications in Mathematical Sciences, 21(4); 2125–2135
Silverman, H. (1975). Univalent Functions with Negative Coefficients. Proceedings of The American Mathematical Society, 51(1); 109–116
Al Shaqsi, K. and M. Darus (2007). On Certain Subclass of Analytic Univalent Functions with Negative Coefficients. Applied Mathematical Sciences, 1(21-24); 1121–1128
Aral, A., V. Gupta, and R. P. Agarwal (2013). Applications of q-Calculus in Operator Theory. Springer
Atshan, W. G. and H. Y. Ghawi (2012). On a New Class of Univalent Functions with Negative Coefficients. European Journal of Scientific Research, 74(4); 601–608
Breaz, D. and L. I. Cotîrlă (2021). The Study of The New Classes of m-Fold Symmetric Bi-Univalent Functions. Mathematics, 10(1); 75
Bucur, R. and D. Breaz (2020). Properties of a New Subclass of Analytic Functions with Negative Coefficients Defined by Using The q-Derivative. Applied Mathematics and Nonlinear Sciences, 5(1); 303–308
Choo, C. P. and A. Janteng (2013). Estimate on The Second Hankel Functional for a Subclass of Close-to-Convex Functions with Respect to Symmetric Points. International Journal of Mathematics Analysis, 7; 781–788
Clunie, J. and F. Keogh (1960). On Starlike and Convex Schlicht Functions. Journal of The London Mathematical Society, 1(2); 229–233
Halim, S., A. Janteng, and M. Darus (2005). Coefficient Properties for Classes with Negative Coefficients and Starlike with Respect to Other Points. In Proceeding of The 13th Mathematical Sciences National Symposium, 2; 658–663
Halim, S. A., A. Janteng, and M. Darus (2006). Classes with Negative Coefficients and Starlike with Respect to Other Points II. Tamkang Journal of Mathematics, 37(4); 345–354
Ibrahim, R. W. (2020). Geometric Process Solving a Class of Analytic Functions Using q-Convolution Differential Operator. Journal of Taibah University for Science, 14(1); 670–677
Jabeen, M., S. Nawaz Malik, S. Mahmood, S. Riaz, and M. Ali (2022). On q-Convex Functions Defined by The q-Ruscheweyh Derivative Operator in Conic Regions. Journal of Mathematics, 2022; 1–13
Jackson, F. H. (1909). On q-Functions and a Certain Difference Operator. Earth and Environmental Science Transactions of the Royal Society of Edinburgh, 46(2); 253–281
Janteng, A. and S. A. Halim (2009). A Subclass Quasi-Convex Functions with Respect to Symmetric Points. Applied Mathematical Sciences, 3(12); 551–556
Janteng, A., A. L. P. Hern, and R. Omar (2020). Fekete-Szegö Functional of Classes of Analytic Functions Involving The q-Derivative Operator. Applied Mathematical Sciences, 14(10); 481–488
Karahuseyin, Z., S. Altinkaya, and S. Yalçin (2017). On H3(1) Hankel Determinant for Univalent Functions Defned by Using q-Derivative Operator. Transylvanian Journal of Mathematics and Mechanics, 9; 25–33
Khan, B., Z. G. Liu, T. G. Shaba, S. Araci, N. Khan, and M. G. Khan (2022). Applications of-Derivative Operator to The Subclass of Bi-Univalent Functions Involving-Chebyshev Polynomials. Journal of Mathematics, 2022
Murugusundaramoorthy, G., T. Janani, and M. Darus (2015). Coefficient Estimate of Biunivalent Functions Based on q-Hypergeometric Functions. Applied Sciences, 17; 75–85
Najafzadeh, S. (2021). (p, q)-Derivative on Univalent Functions Associated with Subordination Structure. General Mathematics, 29(2); 99–106
Najafzadeh, S. and Z. Salleh (2022). Univalent Functions by Means of Chebyshev Polynomials. Journal of Function Spaces, 2022
Oluwayemi, M. O., K. Vijaya, and A. Cătaş (2022). Certain Properties of a Class of Functions Defined by Means of a Generalized Differential Operator. Mathematics, 10(2); 174
Oshah, A. and M. Darus (2015). New Subclass of Analytic Functions Defined by q-Differentiation. International Information Institute (Tokyo). Information, 18(7); 2897
Porwal, S., B. M. Indu, and M. Nanjundan (2022). On Certain Subclasses of Univalent Functions Associated with Wright Function. Theory and Applications of Mathematics & Computer Science, 12(1); 13–20
Rashid, A. M. and A. R. S. Juma (2022). A Class of Harmonic Univalent Functions Defined by The q-Derivative Operator. International Journal of Nonlinear Analysis and Applications, 13(1); 2713–2722
Shilpa, N. (2022). Fekete-Szegö Inequalities for Certain Analytic Functions Associated with q-Derivative Operator. Advances and Applications in Mathematical Sciences, 21(4); 2125–2135
Silverman, H. (1975). Univalent Functions with Negative Coefficients. Proceedings of The American Mathematical Society, 51(1); 109–116
Authors
Hern, A. L. P., Janteng, A. ., & Omar, R. (2022). Subclasses of Analytic Functions with Negative Coefficients Involving q-Derivative Operator. Science and Technology Indonesia, 7(3), 327–332. https://doi.org/10.26554/sti.2022.7.3.327-332
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