The Subclasses of Analytic Functions of Complex Order with Application of q-Derivative Operators
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Keywords:
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Analytic, q-Derivative Operator, Fekete-Szegö Inequality
Abstract
In this article, we represent A as the of analytic functions in the open unit disk. Further, new subclasses of analytic functions of complex order utilising q-derivative operator are generated. The subclasses are symbolised by Hq,b(ϕ) and Iq,b(ϕ). Additionally, we discover that these function classes are implicated with the Fekete-Szegö inequalities.
References
Aldweby and Darus (2016). Coefficient Estimates of Classes of Q-starlike and Q-convex Functions. Advanced Studies in Contemporary Mathematics, 26(1); 21–26
Aldweby, H. and M. Darus (2017). On Fekete-Szegö Problems for Certain Subclasses Defined by Derivative. Journal of Function Spaces, 2017; 1–5
Ali, E. and R. El Ashwah (2021). Convolution Properties of Bounded Analytic Function Classes with Higher and Complex Order Defined by q-derivatives Operator. Journal of Physics: Conference Series, 1943; 012115
Alsoboh, A. and M. Darus (2019). On Fekete-Szegö Problem Associated with q-derivative Operator. Journal of Physics: Conference Series, 1212; 012003
Altinkaya, Ş. and S. Yalçin (2017). On The Fekete-Szegö Problem For Analytic Functions Defined by Using Symmetric q-derivative Operator. Konuralp Journal of Mathematics, 5(1); 176–186
Aral, A., V. Gupta, and R. P. Agarwal (2013). Applications of q-calculus in Operator Theory. Springer
Bulut, S. (2017). Certain Subclasses of Analytic and Biunivalent Functions Involving the q derivative Operator. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 66(1); 108–114
Hern, A. L. P., A. Janteng, and R. Omar (2020). Hankel Determinant H2(3) for Certain Subclasses of Univalent Functions. Mathematics and Statistics, 8(5); 566–569
Hern, A. L. P., A. Janteng, and R. Omar (2022). Subclasses of Analytic Functions with Negative Coefficients Involving q-Derivative Operator. Sciences and Technology Indonesia, 7(3); 327–332
Ibrahim, M., A. Senguttuvan, D. Mohankumar, and R. G. Raman (2020). On Classes of Janowski Functions of Complex Order Involving a q-Derivative Operator. International Journal of Mathematics and Computer Science, 15(4); 1161–1172
Jackson, F. H. (1908). On q-Functions and a Certain Difference Operator. Transactions of the Royal Society of Edinburgh, 46; 253–281
Jackson, F. H. (1910). On q-definite Integrals. Quarterly Journal of Pure and Applied Mathematics, 41; 193–203
Janteng and Halim (2020). Fekete-Szegö Functional of Classes of Analytic Functions Involving the q-Derivative Operator. Applied Mathematical Sciences, 14(10); 481–488
Janteng, A. and S. A. Halim (2009a). Coefficient Estimate for a Subclass of Close-to-convex Functions with Respect to Symmetric Points. International Journal of Mathematical Analysis, 3(7); 309–313
Janteng, A. and S. A. Halim (2009b). A Subclass Quasi-convex Functions with Respect to Symmetric Points. Applied Mathematical Sciences, 3(12); 551–556
Jeyaraman, M. and T. Suresh (2014). Subordination Properties of Multivalent Functions Defined by Generalized Multiplier Transformation. Journal of Complex Analysis, 2014; 1–12
Karahuseyin, A. S. Y. S., Z. (2017). On H2(1) Hankel Determinant for Univalent Functions Defined by Using q-DerivOn H2(1) Hankel Determinant for Univalent Functions Defined by Using q-Deriv. Turkish Journal of Mathematics and Mathematics Education, 9(1); 25–33
Lashin, A. M. Y., B. M. Algethami, and A. O. Badghaish (2021). Convolution Properties of Certain Classes of Analytic Functions Defined by Jackson q-Derivative. Mathematics, 10(1); 105
Ma, W. and M. Minda (1992). A Unified Treatment of Some Special Classes of Univalent Functions. International Conference on Complex Analysis at the Nankai Institute of Mathematics; 157–169
Olatunji, S. and H. Dutta (2018). Fekete-Szegö Problem for Certain Analytic Functions Defined By q-Derivative Operator with Respect to Symmetric and Conjugate Points. Proyecciones (Antofagasta), 37(4); 627–635
Piejko, K. and J. Sokół (2020). On Convolution and q-calculus. Boletín de la Sociedad Matemática Mexicana, 26(2); 349–359
Purohit, S. and R. Raina (2014). Some Classes of Analytic and Multivalent Functions Associated with q-derivative Operators. Acta Universitatis Sapientiae, Mathematica, 6(1); 5–23
Ramachandran, C., T. Soupramanien, and B. Frasin (2017). New Subclasses of Analytic Function Associated with Q-difference Operator. European Journal of Pure and Applied Mathematics, 10(2); 348–362
Selvaraj, C., K. Karthikeyan, and S. Lakshmi (2017). Coefficient Estimates of New Classes of q- Starlike and q- Convex Functions of Complex Order with Respect to (j, k)- Symmetric Points. Omanian Journal of Mathematics and Computer Science, 7; 29–40
Seoudy, T. and M. Aouf (2016). Coefficient Estimates of New Classes of q-starlike and q-convex Functions of Complex Order. Journal of Mathematical Inequalities, 10(1); 135–145
Shamsan, H., R. S. Qahtan, and S. Latha (2021). Coeffıcient Estimates for Bi-univalent Ma-minda Type Functions Associated With q-derivative. TWMS J. App. and Eng. Math, 11(4); 1100–1109
Shilpa, N. (2022). Fekete-Szegö Inequalities for Certain Analytic FunctionsAssociated with q Derivative Operator. Advances and Applications in Mathematical Sciences, 21(4); 2125–2135
Srivastava, H. M. and S. M. El Deeb (2020). A Certain Class of Analytic Functions of Complex Order Connected with a q-analogue of Integral Operators. Miskolc Mathematical Notes, 21(1); 417–433
Srivastava, R. and H. M. Zayed (2019). Subclasses of Analytic Functions of Complex Order Defined By q-derivative Operator. Stud. University Babes-Bolyai Math, 64(1); 71–80
Aldweby, H. and M. Darus (2017). On Fekete-Szegö Problems for Certain Subclasses Defined by Derivative. Journal of Function Spaces, 2017; 1–5
Ali, E. and R. El Ashwah (2021). Convolution Properties of Bounded Analytic Function Classes with Higher and Complex Order Defined by q-derivatives Operator. Journal of Physics: Conference Series, 1943; 012115
Alsoboh, A. and M. Darus (2019). On Fekete-Szegö Problem Associated with q-derivative Operator. Journal of Physics: Conference Series, 1212; 012003
Altinkaya, Ş. and S. Yalçin (2017). On The Fekete-Szegö Problem For Analytic Functions Defined by Using Symmetric q-derivative Operator. Konuralp Journal of Mathematics, 5(1); 176–186
Aral, A., V. Gupta, and R. P. Agarwal (2013). Applications of q-calculus in Operator Theory. Springer
Bulut, S. (2017). Certain Subclasses of Analytic and Biunivalent Functions Involving the q derivative Operator. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 66(1); 108–114
Hern, A. L. P., A. Janteng, and R. Omar (2020). Hankel Determinant H2(3) for Certain Subclasses of Univalent Functions. Mathematics and Statistics, 8(5); 566–569
Hern, A. L. P., A. Janteng, and R. Omar (2022). Subclasses of Analytic Functions with Negative Coefficients Involving q-Derivative Operator. Sciences and Technology Indonesia, 7(3); 327–332
Ibrahim, M., A. Senguttuvan, D. Mohankumar, and R. G. Raman (2020). On Classes of Janowski Functions of Complex Order Involving a q-Derivative Operator. International Journal of Mathematics and Computer Science, 15(4); 1161–1172
Jackson, F. H. (1908). On q-Functions and a Certain Difference Operator. Transactions of the Royal Society of Edinburgh, 46; 253–281
Jackson, F. H. (1910). On q-definite Integrals. Quarterly Journal of Pure and Applied Mathematics, 41; 193–203
Janteng and Halim (2020). Fekete-Szegö Functional of Classes of Analytic Functions Involving the q-Derivative Operator. Applied Mathematical Sciences, 14(10); 481–488
Janteng, A. and S. A. Halim (2009a). Coefficient Estimate for a Subclass of Close-to-convex Functions with Respect to Symmetric Points. International Journal of Mathematical Analysis, 3(7); 309–313
Janteng, A. and S. A. Halim (2009b). A Subclass Quasi-convex Functions with Respect to Symmetric Points. Applied Mathematical Sciences, 3(12); 551–556
Jeyaraman, M. and T. Suresh (2014). Subordination Properties of Multivalent Functions Defined by Generalized Multiplier Transformation. Journal of Complex Analysis, 2014; 1–12
Karahuseyin, A. S. Y. S., Z. (2017). On H2(1) Hankel Determinant for Univalent Functions Defined by Using q-DerivOn H2(1) Hankel Determinant for Univalent Functions Defined by Using q-Deriv. Turkish Journal of Mathematics and Mathematics Education, 9(1); 25–33
Lashin, A. M. Y., B. M. Algethami, and A. O. Badghaish (2021). Convolution Properties of Certain Classes of Analytic Functions Defined by Jackson q-Derivative. Mathematics, 10(1); 105
Ma, W. and M. Minda (1992). A Unified Treatment of Some Special Classes of Univalent Functions. International Conference on Complex Analysis at the Nankai Institute of Mathematics; 157–169
Olatunji, S. and H. Dutta (2018). Fekete-Szegö Problem for Certain Analytic Functions Defined By q-Derivative Operator with Respect to Symmetric and Conjugate Points. Proyecciones (Antofagasta), 37(4); 627–635
Piejko, K. and J. Sokół (2020). On Convolution and q-calculus. Boletín de la Sociedad Matemática Mexicana, 26(2); 349–359
Purohit, S. and R. Raina (2014). Some Classes of Analytic and Multivalent Functions Associated with q-derivative Operators. Acta Universitatis Sapientiae, Mathematica, 6(1); 5–23
Ramachandran, C., T. Soupramanien, and B. Frasin (2017). New Subclasses of Analytic Function Associated with Q-difference Operator. European Journal of Pure and Applied Mathematics, 10(2); 348–362
Selvaraj, C., K. Karthikeyan, and S. Lakshmi (2017). Coefficient Estimates of New Classes of q- Starlike and q- Convex Functions of Complex Order with Respect to (j, k)- Symmetric Points. Omanian Journal of Mathematics and Computer Science, 7; 29–40
Seoudy, T. and M. Aouf (2016). Coefficient Estimates of New Classes of q-starlike and q-convex Functions of Complex Order. Journal of Mathematical Inequalities, 10(1); 135–145
Shamsan, H., R. S. Qahtan, and S. Latha (2021). Coeffıcient Estimates for Bi-univalent Ma-minda Type Functions Associated With q-derivative. TWMS J. App. and Eng. Math, 11(4); 1100–1109
Shilpa, N. (2022). Fekete-Szegö Inequalities for Certain Analytic FunctionsAssociated with q Derivative Operator. Advances and Applications in Mathematical Sciences, 21(4); 2125–2135
Srivastava, H. M. and S. M. El Deeb (2020). A Certain Class of Analytic Functions of Complex Order Connected with a q-analogue of Integral Operators. Miskolc Mathematical Notes, 21(1); 417–433
Srivastava, R. and H. M. Zayed (2019). Subclasses of Analytic Functions of Complex Order Defined By q-derivative Operator. Stud. University Babes-Bolyai Math, 64(1); 71–80
Authors
Janteng, A., Yiing, D. L. C. ., Lun, Y. E. ., Janteng, J., Keong, L. S. ., Omar, R. ., & Hern, A. L. P. . (2023). The Subclasses of Analytic Functions of Complex Order with Application of q-Derivative Operators. Science and Technology Indonesia, 8(3), 436–442. https://doi.org/10.26554/sti.2023.8.3.436-442
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