Research Article
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Year 2023, , 2093 - 2104, 01.09.2023
https://doi.org/10.21597/jist.1273661

Abstract

References

  • Abdel-Gawad, H. R. and Thomas, D. K. (1992). The Fekete-Szegö problem for strongly close-to-convex functions. Proc. Am. Math. Soc., 114, 345-349.
  • Al-Oboudi, F. M. (2004). On univalent functions defined by a generalized Sălăgean operator. Int. J. Math. Math. Sci., 27, 1429–1436.
  • Chonweerayoot, A., Thomas, D. K. and Upakarnitikaset, W. (1992). On the Fekete-Szegö theorem for close-to-convex functions. Publ. Inst. Math. (Beograd) (N.S.), 66, 18-26.
  • Çağlar, M. and Orhan, H. (2021). Fekete-Szegö problem for certain subclasses of analytic functions defined by the combination of differential operators. Bol. Soc. Mat. Mex., 27, 41.
  • Darus, M. and Thomas, D. K. (1996). On the Fekete-Szegö theorem for close-to-convex functions. Math. Jpn., 44, 507–511.
  • Darus, M. and Thomas, D. K. (1998). On the Fekete-Szegö theorem for close-to-convex functions. Math. Jpn., 47, 125–132.
  • Deniz, E. and Orhan, H. (2010). The Fekete-Szegö problem for a generalized subclass of analytic functions. Kyungpook Math. J., 50, 37–47.
  • Deniz, E., Çağlar, M. and Orhan, H. (2012). The Fekete-Szegö problem for a class of analytic functions defined by Dziok-Srivastava operator. Kodai Math. J., 35, 439–462.
  • Fekete, M. and Szegö, G. (1933). Eine Bemerkung u¨ber ungerade schlichte Funktionen. J. Lond. Math. Soc., 8, 85–89.
  • Kanas, S. and Darwish, H. E. (2010). Fekete-Szegö problem for starlike and convex functions of complex order. Appl. Math. Lett., 23(7), 777–782.
  • Kazımoğlu, S. and Deniz, E., (2020). Fekete-Szegö problem for generalized bi-subordinate functions of complex order. Hacettepe Journal of Mathematics and Statistics, 49(5), 1695-1705.
  • Kazımoğlu, S. and Mustafa, N., (2020). Bounds for the initial coefficients of a certain subclass of bi-univalent functions of complex order. Palestine Journal of Mathematics, 9(2), 1020-1031.
  • Keogh, F. R. and Merkes, E. P. (1969). A coefficient inequality for certain classes of analytic functions. Proc. Am. Math. Soc., 20, 8–12.
  • Koepf, W. (1987). On the Fekete-Szegö problem for close-to-convex functions. Proc. Am. Math. Soc., 101, 89–95.
  • London, R. R. (1993). Fekete-Szegö inequalities for close-to-convex functions. Proc. Am. Math. Soc., 117, 947–950.
  • Ma, W. and Minda, D. (1994). A unified treatment of some special classes of univalent functions. In: Li, Z., Ren, F., Yang, L. and Zhang, S. (eds.) Proceeding of the International Conference on Complex Analysis, 157–169. Int. Press, Boston.
  • Nasr, M. A. and Aouf, M. K. (1985). Starlike function of complex order. J. Nat. Sci. Math., 25, 1–12.
  • Nasr, M. A. and Aouf, M. K. (1982). On convex functions of complex order. Mansoura Sci. Bull., 8, 565–582.
  • Noor, K. I. (1999). On new classes of integral operators. J. Nat. Geometry, 16, 71-80.
  • Orhan, H., Deniz, E. and Çağlar, M. (2012). Fekete-Szegö problem for certain subclasses of analytic functions. Demonstr. Math., 45(4), 835–846.
  • Orhan, H., Deniz, E. and Răducanu, D. (2010). The Fekete-Szegö problem for subclasses of analytic functions defined by a differential operator related to conic domains. Comput. Math. Appl., 59, 283–295.
  • Orhan, H. and Răducanu, D. (2009). Fekete-Szegö problem for strongly starlike functions associated with generalized hypergeometric functions. Math. Comput. Model., 50, 430–438.
  • Pfluger, A. (1984). The Fekete-Szegö inequality by a variational method. Ann. Acad. Sci. Fenn. Ser. AI, 10, 447–454.
  • Pommerenke, C. (1975). Univalent functions. In: Studia Mathematica Mathematische Lehrbucher, Vandenhoeck and Ruprecht, Göttingen.
  • Răducanu, D. and Orhan, H. (2010). Subclasses of analytic functions defined by a generalized differential operator. Int. J. Math. Anal., 4(1), 1–15.
  • Ruscheweyh, S. (1975). New criteria for univalent functions. Proc. Am. Math. Soc., 49, 109–115.
  • Sălăgean, G. S. (1983). Subclasses of univalent functions. In: Complex analysis–Proc. 5th Rom.-Finn. Semin., Bucharest 1981, Part 1, Lect. Notes Math. 1013, 362-372.
  • Sokol, J. and Bansal, D. (2012). Coefficients bounds in some subclass of analytic functions. Tamkang Journal of Mathematics, 43(4), 621–630.
  • Wiatrowski, P. (1971). The coefficients of a certain family of holomorphic functions. Zeszyty Nauk. Uniw. Lodz., Nauki. Mat. Przyrod. Ser. II, 39, 75–85.

Fekete-Szegö Inequality for Certain Subclasses of Analytic Functions Defined by The Combination of Differential and Integral Operators

Year 2023, , 2093 - 2104, 01.09.2023
https://doi.org/10.21597/jist.1273661

Abstract

In this paper, we introduced certain general new subclasses of analytic functions defined by the combination of two special operator which one of them derivative (Deniz-Orhan derivative operator) and other integral (Noor integral operators). For these classes coefficient estimates and the Fekete–Szegö inequality is completely solved.

References

  • Abdel-Gawad, H. R. and Thomas, D. K. (1992). The Fekete-Szegö problem for strongly close-to-convex functions. Proc. Am. Math. Soc., 114, 345-349.
  • Al-Oboudi, F. M. (2004). On univalent functions defined by a generalized Sălăgean operator. Int. J. Math. Math. Sci., 27, 1429–1436.
  • Chonweerayoot, A., Thomas, D. K. and Upakarnitikaset, W. (1992). On the Fekete-Szegö theorem for close-to-convex functions. Publ. Inst. Math. (Beograd) (N.S.), 66, 18-26.
  • Çağlar, M. and Orhan, H. (2021). Fekete-Szegö problem for certain subclasses of analytic functions defined by the combination of differential operators. Bol. Soc. Mat. Mex., 27, 41.
  • Darus, M. and Thomas, D. K. (1996). On the Fekete-Szegö theorem for close-to-convex functions. Math. Jpn., 44, 507–511.
  • Darus, M. and Thomas, D. K. (1998). On the Fekete-Szegö theorem for close-to-convex functions. Math. Jpn., 47, 125–132.
  • Deniz, E. and Orhan, H. (2010). The Fekete-Szegö problem for a generalized subclass of analytic functions. Kyungpook Math. J., 50, 37–47.
  • Deniz, E., Çağlar, M. and Orhan, H. (2012). The Fekete-Szegö problem for a class of analytic functions defined by Dziok-Srivastava operator. Kodai Math. J., 35, 439–462.
  • Fekete, M. and Szegö, G. (1933). Eine Bemerkung u¨ber ungerade schlichte Funktionen. J. Lond. Math. Soc., 8, 85–89.
  • Kanas, S. and Darwish, H. E. (2010). Fekete-Szegö problem for starlike and convex functions of complex order. Appl. Math. Lett., 23(7), 777–782.
  • Kazımoğlu, S. and Deniz, E., (2020). Fekete-Szegö problem for generalized bi-subordinate functions of complex order. Hacettepe Journal of Mathematics and Statistics, 49(5), 1695-1705.
  • Kazımoğlu, S. and Mustafa, N., (2020). Bounds for the initial coefficients of a certain subclass of bi-univalent functions of complex order. Palestine Journal of Mathematics, 9(2), 1020-1031.
  • Keogh, F. R. and Merkes, E. P. (1969). A coefficient inequality for certain classes of analytic functions. Proc. Am. Math. Soc., 20, 8–12.
  • Koepf, W. (1987). On the Fekete-Szegö problem for close-to-convex functions. Proc. Am. Math. Soc., 101, 89–95.
  • London, R. R. (1993). Fekete-Szegö inequalities for close-to-convex functions. Proc. Am. Math. Soc., 117, 947–950.
  • Ma, W. and Minda, D. (1994). A unified treatment of some special classes of univalent functions. In: Li, Z., Ren, F., Yang, L. and Zhang, S. (eds.) Proceeding of the International Conference on Complex Analysis, 157–169. Int. Press, Boston.
  • Nasr, M. A. and Aouf, M. K. (1985). Starlike function of complex order. J. Nat. Sci. Math., 25, 1–12.
  • Nasr, M. A. and Aouf, M. K. (1982). On convex functions of complex order. Mansoura Sci. Bull., 8, 565–582.
  • Noor, K. I. (1999). On new classes of integral operators. J. Nat. Geometry, 16, 71-80.
  • Orhan, H., Deniz, E. and Çağlar, M. (2012). Fekete-Szegö problem for certain subclasses of analytic functions. Demonstr. Math., 45(4), 835–846.
  • Orhan, H., Deniz, E. and Răducanu, D. (2010). The Fekete-Szegö problem for subclasses of analytic functions defined by a differential operator related to conic domains. Comput. Math. Appl., 59, 283–295.
  • Orhan, H. and Răducanu, D. (2009). Fekete-Szegö problem for strongly starlike functions associated with generalized hypergeometric functions. Math. Comput. Model., 50, 430–438.
  • Pfluger, A. (1984). The Fekete-Szegö inequality by a variational method. Ann. Acad. Sci. Fenn. Ser. AI, 10, 447–454.
  • Pommerenke, C. (1975). Univalent functions. In: Studia Mathematica Mathematische Lehrbucher, Vandenhoeck and Ruprecht, Göttingen.
  • Răducanu, D. and Orhan, H. (2010). Subclasses of analytic functions defined by a generalized differential operator. Int. J. Math. Anal., 4(1), 1–15.
  • Ruscheweyh, S. (1975). New criteria for univalent functions. Proc. Am. Math. Soc., 49, 109–115.
  • Sălăgean, G. S. (1983). Subclasses of univalent functions. In: Complex analysis–Proc. 5th Rom.-Finn. Semin., Bucharest 1981, Part 1, Lect. Notes Math. 1013, 362-372.
  • Sokol, J. and Bansal, D. (2012). Coefficients bounds in some subclass of analytic functions. Tamkang Journal of Mathematics, 43(4), 621–630.
  • Wiatrowski, P. (1971). The coefficients of a certain family of holomorphic functions. Zeszyty Nauk. Uniw. Lodz., Nauki. Mat. Przyrod. Ser. II, 39, 75–85.
There are 29 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Matematik / Mathematics
Authors

Sercan Kazımoğlu 0000-0002-1023-4500

Early Pub Date August 29, 2023
Publication Date September 1, 2023
Submission Date March 30, 2023
Acceptance Date May 2, 2023
Published in Issue Year 2023

Cite

APA Kazımoğlu, S. (2023). Fekete-Szegö Inequality for Certain Subclasses of Analytic Functions Defined by The Combination of Differential and Integral Operators. Journal of the Institute of Science and Technology, 13(3), 2093-2104. https://doi.org/10.21597/jist.1273661
AMA Kazımoğlu S. Fekete-Szegö Inequality for Certain Subclasses of Analytic Functions Defined by The Combination of Differential and Integral Operators. J. Inst. Sci. and Tech. September 2023;13(3):2093-2104. doi:10.21597/jist.1273661
Chicago Kazımoğlu, Sercan. “Fekete-Szegö Inequality for Certain Subclasses of Analytic Functions Defined by The Combination of Differential and Integral Operators”. Journal of the Institute of Science and Technology 13, no. 3 (September 2023): 2093-2104. https://doi.org/10.21597/jist.1273661.
EndNote Kazımoğlu S (September 1, 2023) Fekete-Szegö Inequality for Certain Subclasses of Analytic Functions Defined by The Combination of Differential and Integral Operators. Journal of the Institute of Science and Technology 13 3 2093–2104.
IEEE S. Kazımoğlu, “Fekete-Szegö Inequality for Certain Subclasses of Analytic Functions Defined by The Combination of Differential and Integral Operators”, J. Inst. Sci. and Tech., vol. 13, no. 3, pp. 2093–2104, 2023, doi: 10.21597/jist.1273661.
ISNAD Kazımoğlu, Sercan. “Fekete-Szegö Inequality for Certain Subclasses of Analytic Functions Defined by The Combination of Differential and Integral Operators”. Journal of the Institute of Science and Technology 13/3 (September 2023), 2093-2104. https://doi.org/10.21597/jist.1273661.
JAMA Kazımoğlu S. Fekete-Szegö Inequality for Certain Subclasses of Analytic Functions Defined by The Combination of Differential and Integral Operators. J. Inst. Sci. and Tech. 2023;13:2093–2104.
MLA Kazımoğlu, Sercan. “Fekete-Szegö Inequality for Certain Subclasses of Analytic Functions Defined by The Combination of Differential and Integral Operators”. Journal of the Institute of Science and Technology, vol. 13, no. 3, 2023, pp. 2093-04, doi:10.21597/jist.1273661.
Vancouver Kazımoğlu S. Fekete-Szegö Inequality for Certain Subclasses of Analytic Functions Defined by The Combination of Differential and Integral Operators. J. Inst. Sci. and Tech. 2023;13(3):2093-104.