Research Article
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Year 2020, Volume: 69 Issue: 1, 394 - 412, 30.06.2020
https://doi.org/10.31801/cfsuasmas.596546

Abstract

References

  • Airault, H. and Bouali, A. Differential calculus on the Faber polynomials, Bull. Sci. Math., 130 (2006), 179-222.
  • Airault, H. and Ren, J. An algebra of differential operators and generating functions on the set of univalent functions, Bull. Sci. Math., 126 (2002), 343-367.
  • Alamoush, A. G. and Darus, M. On coefficient estimates for bi-univalent functions of Fox-Wright functions, Far East J. Math. Sci. (FJMS), 89 (2014), 249-262.
  • Algahtani, O. Estimates of initial coefficients for certain subclasses of bi-univalent functions involving quasi-subordination, J. Nonlinear Sci. Appl., 10 (2017), 1004-1011.
  • Aouf, M. K. and Bulboacă, T. Subordination and superordination properties of multivalent functions defined by certain integral operator, J. Franklin Institute, 347 (3) (2010), 641-653.
  • Aouf, M. K. and Dziok, J., Distortion and convolution theorems for operators of generalized fractional calculus involving Wright function, J. Appl. Anal., 14 (2008), 183-192.
  • Bukhari, S. Z. H., Bulboacă, T., Shabbir, M. S., Subordination and superordination results for analytic functions with respect to symmetrical points, Quaest. Math., 41 (1) (2018) 65-79.
  • Bulboacă, T. On some classes of differential subordinations, Studia Univ. Babeş-Bolyai Math., 31 (1986), 45-50.
  • Bulboacă, T. On some classes of differential subordinations (II), Studia Univ. Babeş-Bolyai Math., 31 (1986), 13-21.
  • Bulut, S. Coefficient estimates for initial Taylor-Maclaurin coefficients for a subclass of analytic and bi-univalent functions defined by Al-Oboudi differential operator, Sci. World J., (2013), Art. ID 171039, 6 pages.
  • Duren, P. L. Univalent Functions, Grundlehren der Mathematischen Wissenschaften, 259, Springer, New York, (1983).
  • El-Ashwah, R. M., Aouf, M. K., Bulboacă, T. Differential subordinations for classes of meromorphic p-valent functions defined by multiplier transformations, Bull. Aust. Math. Soc., 83 (2011), 353-368.
  • Kanas, S., Tudor, A. E. Differential subordinations and harmonic means, Bull. Malays. Math. Sci. Soc. (2), 38 (2015), 1243-1253.
  • Keogh, F. R., Merkes, E. P. A coeffcient inequality for certain classes of analytic functions, Proc. Amer. Math. Soc., 20 (1969), 8-12.
  • Kumar, S., Ravichandran, V. Subordinations for functions with positive real part, Complex Anal. Oper. Theory, (2017), 1-15. DOI:10.1007/s11785-017-0690-4
  • Hamidi, S. G., Jahangiri, J. M. Faber polynomial coefficient estimates for analytic bi-close-toconvex functions, C. R. Math. Acad. Sci. Paris, 352 (2014), 17-20.
  • Hamidi, S. G., Jahangiri, J. M. Faber polynomial coefficients of bi-subordinate functions, C. R. Math. Acad. Sci. Paris, 354 (2016), 365-370.
  • Miller, S. S., Mocanu, P. T. Second-order differential inequalities in the complex plane, J. Math. Anal. Appl., 65 (1978), 298-305.
  • Nunokawa, M., Sokół, J. On multivalent starlike functions and Ozaki condition, Complex Var. Elliptic Equ., (2018), 1-15, DOI:10.1080/17476933.2017.1419209
  • Nunokawa, M., Sokół, J. On some differential subordinations, Studia Sci. Math. Hungar., 54 (2017), 436-445.
  • Murugusundaramoorthy, G. Coefficient estimates of bi-Bazilević functions defined by Srivastava-Attiya operator, Matematiche (Catania), 69 (2014), 43-56.
  • Murugusundaramoorthy, G., Janani, T., Purohit, S. D. Coefficient estimate of bi-Bazilević functions associated with fractional q-calculus operators, Fund. Inform., 151 (2017), 49-62.
  • Orhan, H., Magesh, N., Balaji, V. K. Initial coeffcient Bounds for a general class of bi-univalent functions, Filomat, 29 (2015), 1259-1267.
  • Owa, S., Srivastava, H. M. Univalent and starlike generalized hypergeometric functions, Canad. J. Math., 39 (1987), 1057-1077.
  • Purohit, S. D., Raina, R. K. Certain subclasses of analytic functions associated with fractional q-calculus operators, Math. Scand., 10 (2011), 55-70.
  • Srivatava, H. M., Aouf, M. K. Some applications of fractional calculus operators to certain subclasses of prestarlike functions with negative coefficients, Comput. Math. Appl., 30 (1) (1995), 53-61.
  • Srivastava, H. M., Gaboury, S., Ghanim, F. Coefficient estimates for a general subclass of analytic and bi-univalent functions of the Ma-Minda type, RACSAM Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat., (2017), DOI:10.1007/s13398-017-0416-5
  • Srivastava, H. M., Murugusundaramoorthy, G., Vijaya, K. Coefficient estimates for some families of bi-Bazilević functions of the Ma-Minda type involvig the Hohlov operator, J. Classical Anal., 2 (2013), 167-181.
  • Todorov, P. G., On the Faber polynomials of the univalent functions of class Σ, J. Math. Anal. Appl., 162 (1991), 268-276.
  • Zireh, A., Adegani, E. A., Bulut, S. Faber polynomial coefficient estimates for a comprehensive subclass of analytic bi-univalent functions defined by subordination, Bull. Belg. Math. Soc. Simon Stevin, 23 (2016), 487-504.

Simple criteria for univalence and coefficient bounds for a certain subclass of analytic functions

Year 2020, Volume: 69 Issue: 1, 394 - 412, 30.06.2020
https://doi.org/10.31801/cfsuasmas.596546

Abstract

In the first part of this work we present several new geometric properties of analytic functions by applying the differential subordination. In addition, several results in the geometric functions theory pointed out. In the second part we find upper bounds for coefficients of functions in class $\mathcal{B}_\Sigma^{q,\mu}(\beta,\lambda,h)$ which is defined by fractional $q$-calculus operators.

References

  • Airault, H. and Bouali, A. Differential calculus on the Faber polynomials, Bull. Sci. Math., 130 (2006), 179-222.
  • Airault, H. and Ren, J. An algebra of differential operators and generating functions on the set of univalent functions, Bull. Sci. Math., 126 (2002), 343-367.
  • Alamoush, A. G. and Darus, M. On coefficient estimates for bi-univalent functions of Fox-Wright functions, Far East J. Math. Sci. (FJMS), 89 (2014), 249-262.
  • Algahtani, O. Estimates of initial coefficients for certain subclasses of bi-univalent functions involving quasi-subordination, J. Nonlinear Sci. Appl., 10 (2017), 1004-1011.
  • Aouf, M. K. and Bulboacă, T. Subordination and superordination properties of multivalent functions defined by certain integral operator, J. Franklin Institute, 347 (3) (2010), 641-653.
  • Aouf, M. K. and Dziok, J., Distortion and convolution theorems for operators of generalized fractional calculus involving Wright function, J. Appl. Anal., 14 (2008), 183-192.
  • Bukhari, S. Z. H., Bulboacă, T., Shabbir, M. S., Subordination and superordination results for analytic functions with respect to symmetrical points, Quaest. Math., 41 (1) (2018) 65-79.
  • Bulboacă, T. On some classes of differential subordinations, Studia Univ. Babeş-Bolyai Math., 31 (1986), 45-50.
  • Bulboacă, T. On some classes of differential subordinations (II), Studia Univ. Babeş-Bolyai Math., 31 (1986), 13-21.
  • Bulut, S. Coefficient estimates for initial Taylor-Maclaurin coefficients for a subclass of analytic and bi-univalent functions defined by Al-Oboudi differential operator, Sci. World J., (2013), Art. ID 171039, 6 pages.
  • Duren, P. L. Univalent Functions, Grundlehren der Mathematischen Wissenschaften, 259, Springer, New York, (1983).
  • El-Ashwah, R. M., Aouf, M. K., Bulboacă, T. Differential subordinations for classes of meromorphic p-valent functions defined by multiplier transformations, Bull. Aust. Math. Soc., 83 (2011), 353-368.
  • Kanas, S., Tudor, A. E. Differential subordinations and harmonic means, Bull. Malays. Math. Sci. Soc. (2), 38 (2015), 1243-1253.
  • Keogh, F. R., Merkes, E. P. A coeffcient inequality for certain classes of analytic functions, Proc. Amer. Math. Soc., 20 (1969), 8-12.
  • Kumar, S., Ravichandran, V. Subordinations for functions with positive real part, Complex Anal. Oper. Theory, (2017), 1-15. DOI:10.1007/s11785-017-0690-4
  • Hamidi, S. G., Jahangiri, J. M. Faber polynomial coefficient estimates for analytic bi-close-toconvex functions, C. R. Math. Acad. Sci. Paris, 352 (2014), 17-20.
  • Hamidi, S. G., Jahangiri, J. M. Faber polynomial coefficients of bi-subordinate functions, C. R. Math. Acad. Sci. Paris, 354 (2016), 365-370.
  • Miller, S. S., Mocanu, P. T. Second-order differential inequalities in the complex plane, J. Math. Anal. Appl., 65 (1978), 298-305.
  • Nunokawa, M., Sokół, J. On multivalent starlike functions and Ozaki condition, Complex Var. Elliptic Equ., (2018), 1-15, DOI:10.1080/17476933.2017.1419209
  • Nunokawa, M., Sokół, J. On some differential subordinations, Studia Sci. Math. Hungar., 54 (2017), 436-445.
  • Murugusundaramoorthy, G. Coefficient estimates of bi-Bazilević functions defined by Srivastava-Attiya operator, Matematiche (Catania), 69 (2014), 43-56.
  • Murugusundaramoorthy, G., Janani, T., Purohit, S. D. Coefficient estimate of bi-Bazilević functions associated with fractional q-calculus operators, Fund. Inform., 151 (2017), 49-62.
  • Orhan, H., Magesh, N., Balaji, V. K. Initial coeffcient Bounds for a general class of bi-univalent functions, Filomat, 29 (2015), 1259-1267.
  • Owa, S., Srivastava, H. M. Univalent and starlike generalized hypergeometric functions, Canad. J. Math., 39 (1987), 1057-1077.
  • Purohit, S. D., Raina, R. K. Certain subclasses of analytic functions associated with fractional q-calculus operators, Math. Scand., 10 (2011), 55-70.
  • Srivatava, H. M., Aouf, M. K. Some applications of fractional calculus operators to certain subclasses of prestarlike functions with negative coefficients, Comput. Math. Appl., 30 (1) (1995), 53-61.
  • Srivastava, H. M., Gaboury, S., Ghanim, F. Coefficient estimates for a general subclass of analytic and bi-univalent functions of the Ma-Minda type, RACSAM Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat., (2017), DOI:10.1007/s13398-017-0416-5
  • Srivastava, H. M., Murugusundaramoorthy, G., Vijaya, K. Coefficient estimates for some families of bi-Bazilević functions of the Ma-Minda type involvig the Hohlov operator, J. Classical Anal., 2 (2013), 167-181.
  • Todorov, P. G., On the Faber polynomials of the univalent functions of class Σ, J. Math. Anal. Appl., 162 (1991), 268-276.
  • Zireh, A., Adegani, E. A., Bulut, S. Faber polynomial coefficient estimates for a comprehensive subclass of analytic bi-univalent functions defined by subordination, Bull. Belg. Math. Soc. Simon Stevin, 23 (2016), 487-504.
There are 30 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Mostafa Jafari This is me 0000-0002-2144-1097

Teodor Bulboaca 0000-0001-8026-218X

Ahmad Zireh 0000-0002-3405-853X

Ebrahim Analouei Adegani 0000-0001-9176-3932

Publication Date June 30, 2020
Submission Date July 25, 2019
Acceptance Date November 1, 2019
Published in Issue Year 2020 Volume: 69 Issue: 1

Cite

APA Jafari, M., Bulboaca, T., Zireh, A., Analouei Adegani, E. (2020). Simple criteria for univalence and coefficient bounds for a certain subclass of analytic functions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(1), 394-412. https://doi.org/10.31801/cfsuasmas.596546
AMA Jafari M, Bulboaca T, Zireh A, Analouei Adegani E. Simple criteria for univalence and coefficient bounds for a certain subclass of analytic functions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. June 2020;69(1):394-412. doi:10.31801/cfsuasmas.596546
Chicago Jafari, Mostafa, Teodor Bulboaca, Ahmad Zireh, and Ebrahim Analouei Adegani. “Simple Criteria for Univalence and Coefficient Bounds for a Certain Subclass of Analytic Functions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, no. 1 (June 2020): 394-412. https://doi.org/10.31801/cfsuasmas.596546.
EndNote Jafari M, Bulboaca T, Zireh A, Analouei Adegani E (June 1, 2020) Simple criteria for univalence and coefficient bounds for a certain subclass of analytic functions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 1 394–412.
IEEE M. Jafari, T. Bulboaca, A. Zireh, and E. Analouei Adegani, “Simple criteria for univalence and coefficient bounds for a certain subclass of analytic functions”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 69, no. 1, pp. 394–412, 2020, doi: 10.31801/cfsuasmas.596546.
ISNAD Jafari, Mostafa et al. “Simple Criteria for Univalence and Coefficient Bounds for a Certain Subclass of Analytic Functions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/1 (June 2020), 394-412. https://doi.org/10.31801/cfsuasmas.596546.
JAMA Jafari M, Bulboaca T, Zireh A, Analouei Adegani E. Simple criteria for univalence and coefficient bounds for a certain subclass of analytic functions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:394–412.
MLA Jafari, Mostafa et al. “Simple Criteria for Univalence and Coefficient Bounds for a Certain Subclass of Analytic Functions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 69, no. 1, 2020, pp. 394-12, doi:10.31801/cfsuasmas.596546.
Vancouver Jafari M, Bulboaca T, Zireh A, Analouei Adegani E. Simple criteria for univalence and coefficient bounds for a certain subclass of analytic functions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(1):394-412.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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