Coefficient inequalities of a comprehensive subclass of analytic functions with respect to symmetric points. (English) Zbl 1535.30043
Summary: We have introduced a comprehensive subclass of analytic functions with respect to \((j, k)\) - symmetric points. We have obtained the interesting coefficient bounds for the newly defined classes of functions. Further, we have extended the study using quantum calculus. Our main results have several applications, here we have presented only a few of them.
MSC:
| 30C45 | Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) |
| 30C50 | Coefficient problems for univalent and multivalent functions of one complex variable |
Keywords:
classes of analytic functions; star-like functions; convex functions; coefficient estimatesReferences:
| [1] | P. Agarwal, R. P. Agarwal & M. Ruzhansky (2020). Special functions and analysis of differential equations (1st ed.). Chapman and Hall/CRC, London, United Kingdom. |
| [2] | P. Agarwal, S. S. Dragomir, M. Jleli & B. Samet (2018). Advances in mathematical inequalities and applications. Birkhäuser/Springer, Singapore. · Zbl 1410.26009 |
| [3] | P. Agarwal, M. Vivas-Cortez, Y. Rangel-Oliveros & M. A. Ali (2022). New Ostrowski type inequalities for generalized s-convex functions with applications to some special means of real numbers and to midpoint formula. AIMS Mathematics, 7(1), 1429-1444. https://doi.org/ 10.3934/math.2022084. · doi:10.3934/math.2022084 |
| [4] | O. Ahuja, N. Bohra, A. Çetinkaya & S. Kumar (2021). Univalent functions associated with the symmetric points and cardioid-shaped domain involving (p, q)-calculus. Kyungpook Mathe-matical Journal, 61(1), 75-98. · Zbl 1476.30036 |
| [5] | F. S. M. Al Sarari, B. A. Frasin, T. Al-Hawary & S. Latha (2016). A few results on general-ized Janowski type functions associated with (j, k)-symmetrical functions. Acta Universitatis Sapientiae Mathematica, 8(2), 195-205. https://doi.org/10.1515/ausm-2016-0012. · Zbl 1359.30018 · doi:10.1515/ausm-2016-0012 |
| [6] | F. S. M. Al Sarari, S. Latha & T. Bulboacă (2019). On Janowski functions associated with (n, m)-symmetrical functions. Journal of Taibah University for Science, 13(1), 972-978. https: //doi.org/10.1080/16583655.2019.1665487. · doi:10.1080/16583655.2019.1665487 |
| [7] | M. A. Ali, M. Abbas, H. Budak, P. Agarwal, G. Murtaza & Y.-M. Chu (2021). New quan-tum boundaries for quantum Simpson’s and quantum Newton’s type inequalities for prein-vex functions. Advances in Difference Equations, 2021(1), 1-21. https://doi.org/10.1186/ s13662-021-03226-x. · Zbl 1487.26060 · doi:10.1186/s13662-021-03226-x |
| [8] | M. H. Annaby & Z. S. Mansour (2012). q-fractional calculus and equations. Springer, Heidel-berg, Berlin. · Zbl 1267.26001 |
| [9] | M. K. Aouf, J. Dziok & J. Sokół(2011). On a subclass of strongly starlike functions. Applied Mathematics Letters, 24(1), 27-32. https://doi.org/10.1016/j.aml.2010.08.004. · Zbl 1202.30014 · doi:10.1016/j.aml.2010.08.004 |
| [10] | A. Aral, V. Gupta & R. P. Agarwal (2013). Applications of q-calculus in operator theory. Springer, New York, NY. · Zbl 1273.41001 |
| [11] | H. Bayram & S. Yalçin (2020). On a new subclass of harmonic univalent functions. Malaysian Journal of Mathematical Sciences, 14(1), 63-75. · Zbl 1456.31001 |
| [12] | S. Bulut (2020). Comprehensive subclasses of analytic functions and coefficient bounds. AIMS Mathematics, 5(5), 4260-4268. https://doi.org/10.3934/math.2020271. · Zbl 1485.30005 · doi:10.3934/math.2020271 |
| [13] | B. C. Carlson & D. B. Shaffer (1984). Starlike and prestarlike hypergeometric functions. SIAM Journal on Mathematical Analysis, 15(4), 737-745. https://doi.org/10.1137/0515057. · Zbl 0567.30009 · doi:10.1137/0515057 |
| [14] | J. Dziok, R. K. Raina & J. Sokół(2011). Certain results for a class of convex functions re-lated to a shell-like curve connected with Fibonacci numbers. Computers & Mathematics with Applications, 61(9), 2605-2613. https://doi.org/10.1016/j.camwa.2011.03.006. · Zbl 1222.30009 · doi:10.1016/j.camwa.2011.03.006 |
| [15] | J. Dziok, R. K. Raina & J. Sokół(2011). On α-convex functions related to shell-like functions connected with Fibonacci numbers. Applied Mathematics and Computation, 218(3), 996-1002. https://doi.org/10.1016/j.amc.2011.01.059. · Zbl 1225.30009 · doi:10.1016/j.amc.2011.01.059 |
| [16] | J. Dziok, R. K. Raina & J. Sokół(2013). On a class of starlike functions related to a shell-like curve connected with Fibonacci numbers. Mathematical and Computer Modelling, 57(5-6), 1203-1211. https://doi.org/10.1016/j.mcm.2012.10.023. · doi:10.1016/j.mcm.2012.10.023 |
| [17] | S. Gandhi & V. Ravichandran (2017). Starlike functions associated with a lune. · Zbl 1386.30015 |
| [18] | Asian-European Journal of Mathematics, 10(4), 1750064, 12. https://doi.org/10.1142/ S1793557117500644. · Zbl 1386.30015 · doi:10.1142/S1793557117500644 |
| [19] | A. W. Goodman (1983). Univalent functions. Vol. II. Mariner Publishing Company Inc, Tampa, FL. · Zbl 1041.30500 |
| [20] | M. Ibrahim, A. Senguttuvan, D. Mohankumar & R. G. Raman (2020). On classes of Janowski functions of complex order involving a q-derivative operator. International Journal of Mathe-matics and Computer Science, 15(4), 1161-1172. · Zbl 1444.30010 |
| [21] | W. Janowski (1973). Some extremal problems for certain families of analytic functions I. Annales Polonici Mathematici, 28(3), 297-326. https://doi.org/10.4064/ap-28-3-297-326. · Zbl 0275.30009 · doi:10.4064/ap-28-3-297-326 |
| [22] | M. Kadakal, I. İşcan, P. Agarwal & M. Jleli (2021). Exponential trigonometric convex func-tions and Hermite-Hadamard type inequalities. Mathematica Slovaca, 71(1), 43-56. https: //doi.org/10.1515/ms-2017-0410. · Zbl 1479.26011 · doi:10.1515/ms-2017-0410 |
| [23] | S. Kanas & D. Răducanu (2014). Some class of analytic functions related to conic domains. Mathematica Slovaca, 64(5), 1183-1196. https://doi.org/10.2478/s12175-014-0268-9. · Zbl 1349.30054 · doi:10.2478/s12175-014-0268-9 |
| [24] | K. R. Karthikeyan, G. Murugusundaramoorthy, S. D. Purohit & D. L. Suthar (2021). Certain class of analytic functions with respect to symmetric points defined by Q-calculus. Journal of Mathematics, 2021, Article ID: 8298848, 9 pages. https://doi.org/10.1155/2021/8298848. · Zbl 1477.30011 · doi:10.1155/2021/8298848 |
| [25] | K. R. Karthikeyan, S. Lakshmi, S. Varadharajan, D. Mohankumar & E. Umadevi (2022). Star-like functions of complex order with respect to symmetric points defined using higher order derivatives. Fractal and Fractional, 6(2), 116. https://doi.org/10.3390/fractalfract6020116. · doi:10.3390/fractalfract6020116 |
| [26] | K. R. Karthikeyan, G. Murugusundaramoorthy & T. Bulboacă (2021). Properties of λ-pseudo-starlike functions of complex order defined by subordination. Axioms, 10(2), 86. https://doi.org/10.3390/axioms10020086. · doi:10.3390/axioms10020086 |
| [27] | K. Khatter, V. Ravichandran & S. Sivaprasad Kumar (2019). Starlike functions associated with exponential function and the lemniscate of Bernoulli. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matematicas, 113(1), 233-253. https://doi.org/10. 1007/s13398-017-0466-8. · Zbl 1412.30048 · doi:10.1007/s13398-017-0466-8 |
| [28] | O. Kwon & Y. Sim (2013). A certain subclass of Janowski type functions associated with k-symmetric points. Communications of the Korean Mathematical Society, 28(1), 143-154. https: //doi.org/10.4134/CKMS.2013.28.1.143. · Zbl 1281.30013 · doi:10.4134/CKMS.2013.28.1.143 |
| [29] | P. Liczberski & J. Poł ubiński (1995). On (j, k)-symmetrical functions. Mathematica Bohemica, 120(1), 13-28. https://doi.org/10.21136/MB.1995.125897. · Zbl 0838.30004 · doi:10.21136/MB.1995.125897 |
| [30] | W. C. Ma & D. Minda (1992). A unified treatment of some special classes of univalent func-tions. In Proceedings of the International Conference on Complex Analysis, pp. 157-169. Interna-tional Press Inc., Tianjin, China. · Zbl 0823.30007 |
| [31] | R. Mendiratta, S. Nagpal & V. Ravichandran (2014). A subclass of starlike functions associ-ated with left-half of the lemniscate of Bernoulli. International journal of Mathematics, 25(9), 1450090, 17. https://doi.org/10.1142/S0129167X14500906. · Zbl 1301.30015 · doi:10.1142/S0129167X14500906 |
| [32] | P. Neang, K. Nonlaopon, J. Tariboon, S. K. Ntouyas & P. Agarwal (2021). Some trapezoid and midpoint type inequalities via fractional (p, q)-calculus. Advances in Difference Equations, 2021, Article ID: 333, 22 pages. https://doi.org/10.1186/s13662-021-03487-6. · Zbl 1494.26028 · doi:10.1186/s13662-021-03487-6 |
| [33] | S. O. Olatunji & H. Dutta (2019). Sigmoid function in the space of univalent λ-pseudo-(p, q)-derivative operators related to shell-like curves connected with Fibonacci numbers of Sakaguchi type functions. Malaysian Journal of Mathematical Sciences, 13(1), 95-106. · Zbl 1429.30019 |
| [34] | R. K. Raina & J. Sokół(2015). Some properties related to a certain class of starlike functions. Comptes Rendus Mathématique, 353(11), 973-978. https://doi.org/10.1016/j.crma.2015.09.011. · Zbl 1333.30025 · doi:10.1016/j.crma.2015.09.011 |
| [35] | R. K. Raina & J. Sokół(2016). Fekete-Szegö problem for some starlike functions re-lated to shell-like curves. Mathematica Slovaca, 66(1), 135-140. https://doi.org/10.1515/ ms-2015-0123. · Zbl 1389.30082 · doi:10.1515/ms-2015-0123 |
| [36] | M. Ruzhansky, Y. J. Cho, P. Agarwal & I. Area (2017). Advances in real and complex analysis with applications. Birkhäuser/Springer, Singapore. |
| [37] | K. Sakaguchi (1959). On a certain univalent mapping. Journal of the Mathematical Society of Japan, 11, 72-75. https://doi.org/10.2969/jmsj/01110072. · Zbl 0085.29602 · doi:10.2969/jmsj/01110072 |
| [38] | F. M. Sakar & H. O. Güney (2017). Faber polynomial coefficient estimates for subclasses of m-fold symmetric bi-univalent functions defined by fractional derivative. Malaysian Journal of Mathematical Sciences, 11(2), 275-287. · Zbl 1527.30013 |
| [39] | C. Selvaraj, K. R. Karthikeyan & G. Thirupathi (2014). Multivalent functions with respect to symmetric conjugate points. Punjab University Journal of Mathematics, 46(1), 1-8. · Zbl 1316.30017 |
| [40] | A. Senguttuvan & K. R. Karthikeyan (2015). Certain classes of meromorphic functions with respect to (j, k) symmetric points. Aryabhatta journal Of Mathematics and Informatics, 7(2), 401-406. |
| [41] | T. M. Seoudy & A. E. Shammaky (2021). Certain subclasses of spiral-like functions associated with q-analogue of Carlson-Shaffer operator. AIMS Mathematics, 6(3), 2525-2538. https: //doi.org/10.3934/math.2021153. · Zbl 1525.30016 · doi:10.3934/math.2021153 |
| [42] | J. Sokól (2009). Coefficient estimates in a class of strongly starlike functions. Kyungpook Mathematical Journal, 49(2), 349-353. https://doi.org/10.5666/KMJ.2009.49.2.349. · Zbl 1176.30068 · doi:10.5666/KMJ.2009.49.2.349 |
| [43] | H. M. Srivastava (1989). Univalent functions, fractional calculus, and associated generalized hypergeometric functions. In H. M. Srivastava & S. Owa (Eds.), Univalent Functions, Fractional Calculus, and Their Applications, pp. 329-354. Ellis Horwood Ltd, Horwood, Chichester. · Zbl 0693.30013 |
| [44] | H. M. Srivastava (2020). Operators of basic (or q-) calculus and fractional q-calculus and their applications in geometric function theory of complex analysis. Iranian Journal of Science and Technology, Transactions A: Science, 44(1), 327-344. https://doi.org/10.1007/ s40995-019-00815-0. · doi:10.1007/s40995-019-00815-0 |
| [45] | H. M. Srivastava, S. Z. H. Bukhari & M. Nazir (2018). A subclass of α-convex functions with respect to (2j, k)-symmetric conjugate points. Bulletin of the Iranian Mathematical Society, 44(5), 1227-1242. https://doi.org/10.1007/s41980-018-0086-x. · Zbl 1409.30019 · doi:10.1007/s41980-018-0086-x |
| [46] | K. Ullah, S. Zainab, M. Arif, M. Darus & M. Shutaywi (2021). Radius problems for starlike functions associated with the tan hyperbolic function. Journal of Function Spaces, 2021, Article ID: 9967640, 15 pages. https://doi.org/10.1155/2021/9967640. · Zbl 1476.30076 · doi:10.1155/2021/9967640 |
| [47] | M. Vivas-Cortez, M. A. Ali, H. Budak, H. Kalsoom & P. Agarwal (2021). Some new Hermite-Hadamard and related inequalities for convex functions via (p, q)-integral. Entropy, 23(7), 828. https://doi.org/10.3390/e23070828. · doi:10.3390/e23070828 |
| [48] | X.-X. You, M. A. Ali, H. Budak, P. Agarwal & Y.-M. Chu (2021). Extensions of Hermite-Hadamard inequalities for harmonically convex functions via generalized fractional inte-grals. Journal of Inequalities and Applications, 2021, Article ID: 102, 22 pages. https://doi. org/10.1186/s13660-021-02638-3. · Zbl 1504.26078 · doi:10.1186/s13660-021-02638-3 |
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