Document Type : Research Paper
Authors
1 Department of Applied Mathematics and Science, National University of Science & Technology, Muscat, PC 130, Oman.
2 Mathematics Section, Department of Information Technology, University of Technology and Applied Sciences - Al Mussanah, Oman.
Abstract
Using subordination, we introduce a new class of symmetric functions associated with a vertical strip domain. We have provided some interesting deviations or adaptation which are helpful in unification and extension of various studies of analytic functions. Inclusion relations, geometrical interpretation, coefficient estimates, inverse function coefficient estimates and solution to the Fekete-Szeg\H{o} problem of the defined class are our main results. Applications of our main results are given as corollaries.
Keywords
Main Subjects
[1] M. Ahmad, B.A. Frasin, G. Murugusundaramoorthy and A. Alkhazaleh, An application of Mittag–Leffler-type Poisson distribution on certain subclasses of analytic functions associated with conic domains, Heliyon, 7 (10) (2021), Art. ID e08109, pp. 1-5.
[2] S. Altınkaya and S. Yalçın, Upper bound of second Hankel determinant for bi-Bazilevič functions, Mediterr. J. Math., 13 (6) (2016), pp. 4081-4090.
[3] S. Altınkaya and S. Yalçın, Faber polynomial coefficient bounds for a subclass of bi-univalent functions, C. R. Math. Acad. Sci. Paris, 353 (12) (2015), pp. 1075-1080.
[4] S.Altınkaya and S. Yalçın, Coefficient estimates for two new subclasses of biunivalent functions with respect to symmetric points, J. Funct. Spaces, 2015 (2015), Art. ID 145242, pp. 1-5.
[5] S. Altınkaya and S. Yalçın,Coefficient bounds for certain subclasses of m-fold symmetric biunivalent functions, J. Math., 2015 (2015), Art. ID 241683, pp. 1-5.
[6] S. Altınkaya and S. Yalçın, Fekete-Szegő inequalities for certain classes of biunivalent functions, International Scholarly Research Notices, 2014 (2014), Art. ID 327962, pp. 1-6.
[7] E. Amini, S. Al-Omari, K. Nonlaopon and D. Baleanu, Estimates for coefficients of bi-univalent functions associated with a fractional q-difference operator, Symmetry, 14 (5) (2022), 879.
[8] A. Amourah, B.A. Frasin, M. Ahmad and F. Yousef, Exploiting the Pascal distribution series and Gegenbauer Polynomials to construct and study a new subclass of analytic bi-univalent functions, Symmetry, 14 (1) (2022), 147.
[9] D. Breaz, K.R. Karthikeyan, E. Umadevi and A. Senguttuvan, Some properties of Bazilevič functions involving Srivastava–Tomovski operator, Axioms, 11 (12) (2022), 687.
[10] D. Breaz, L.-I. Cotîrlă, E. Umadevi and K.R. Karthikeyan, Properties of meromorphic spiral-like functions associated with symmetric functions, J. Funct. Spaces, 2022 (2022), Art. ID 3444854, pp. 1-10.
[11] S. Bulut, Coefficient estimates for functions associated with vertical strip domain, Commun. Korean Math. Soc., 37 (2) (2022), pp. 537-549.
[12] N.E. Cho, A. Ebadian, S. Bulut and A.E. Adegani, Subordination implications and coefficient estimates for subclasses of starlike functions, Mathematics, 8 (2020), 1150.
[13] N.E. Cho, O.S. Kwon and V. Ravichandran, Coefficient, distortion and growth inequalities for certain close-to-convex functions, J. Inequal. Appl., 2011 (2011), Article No. 2011:100, pp. 1-7.
[14] P.L. Duren, Univalent functions, Grundlehren der mathematischen Wissenschaften, 259, Springer-Verlag, New York, 1983.
[15] B.A. Frasin and M.K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett., 24 (9) (2011), pp. 1569-1573.
[16] C. Gao and S. Zhou, On a class of analytic functions related to the starlike functions, Kyungpook Math. J., 45 (1) (2005), pp. 123-130.
[17] I. Graham and G. Kohr, Geometric function theory in one and higher dimensions, Monographs and Textbooks in Pure and Applied Mathematics, 255, Marcel Dekker, Inc., New York, 2003.
[18] R. Kargar, A. Ebadian and J. Sokół, Radius problems for some subclasses of analytic functions, Complex Anal. Oper. Theory, 11 (7) (2017), pp. 1639-1649.
[19] K.R. Karthikeyan, N.E. Cho and G. Murugusundaramoorthy, On classes of non-Carathéodory functions associated with a family of functions starlike in the direction of the real axis, Axioms., 12 (1) (2023), 24.
[20] K.R. Karthikeyan, K.A. Reddy and G. Murugusundaramoorthy, On classes of Janowski functions associated with a conic domain, Italian J. Pure Appl. Math., 47 (2022), pp. 684-698.
[21] K.R. Karthikeyan, G. Murugusundaramoorthy, A. Nistor-Şerban and D. Răducanu, Coefficient estimates for certain subclasses of starlike functions of complex order associated with a hyperbolic domain, Bull. Transilv. Univ. Braşov Ser. III, 13 (62) (2020), pp. 595-609.
[22] K.R. Karthikeyan, K. Srinivasan and K. Ramachandran, On a class of multivalent starlike functions with a bounded positive real part, Palest. J. Math., 5 (1) (2015), pp. 59-64.
[23] F.R. Keogh and E.P. Merkes, A coefficient inequality for certain classes of analytic functions, Proc. Amer. Math. Soc., 20 (1969), pp. 8-12.
[24] D. Khurana, R. Kumar, S. Verma and G. Murugusundaramoorthy, A generalized class of univalent harmonic functions associated with a multiplier transformation, Sahand Commun. Math. Anal., 18 (3) (2021), pp. 27-39.
[25] W. Koepf, On the Fekete-Szegő problem for close-to-convex functions, Proc. Amer. Math. Soc., 101 (1) (1987), pp. 89-95.
[26] W. Koepf, Convex functions and the Nehari univalence criterion, in Complex analysis, Joensuu 1987, 214-218, Lecture Notes in Math., 1351, Springer, Berlin.
[27] K. Kuroki and S. Owa, Notes on New Class for Certain Analytic Functions, RIMS Kokyuroku, 1772 (2011), pp. 21-25
[28] O.S. Kwon, Y.J. Sim, N.E. Cho and H.M. Srivastava, Some radius problems related to a certain subclass of analytic functions, Acta Math. Sin. (Engl. Ser.), 30 (7) (2014), pp. 1133-1144.
[29] M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc., 18 (1967), pp. 63-68.
[30] S. Li, H. Tang, L.-I. Ma and X. Niu, A new subclass of analytic functions associated with the strip domains, Acta Math. Sci. Ser. A (Chinese Ed.), 35 (5) (2015), pp. 970-986.
[31] S. Mahmood, M. Jabeen, S.N. Malik, H.M. Srivastava, R. Manzoor and S.M. Jawwad Riaz, Some coefficient inequalities of q-starlike functions associated with [32] H. Mahzoon and J. Sokół, On coefficients of a certain subclass of starlike and bi-starlike functions, Kyungpook Math. J., 61 (3) (2021), pp. 513-522.
[33] Z. Nehari, A property of convex conformal maps, J. Analyse Math., 30 (1976), pp. 390-393.
[34] K.I. Noor and S.A. Shah, On certain generalized Bazilevic type functions associated with conic regions, Sahand Commun. Math. Anal., 17 (4) (2020), pp. 13-23.
[35] J.K. Prajapat, A new subclass of close-to-convex functions, Surv. Math. Appl., 11 (2016), pp. 11-19.
[36] K.A. Reddy, K.R. Karthikeyan and G. Murugusundaramoorthy, Inequalities for the Taylor coefficients of spiralike functions involving q-differential operator, Eur. J. Pure Appl. Math., 12 (3) (2019), pp. 846-856.
[37] W. Rogosinski, On the coefficients of subordinate functions, Proc. London Math. Soc., (2) 48 (1943), pp. 48-82.
[38] B. Şeker and S.S. Eker, On subclasses of bi-close-to-convex functions related to the odd-starlike functions, Palest. J. Math., 6 (2017), Special Issue II, pp. 215-221.
[39] B. Şeker, S.S. Eker and B. Cekic, On subclasses of analytic functions associated with Miller-Ross-type Poisson distribution series, Sahand Commun. Math. Anal., 19 (4) (2022), pp. 69-79.
[40] Y.J. Sim and O.S. Kwon, Some results on analytic functions associated with vertical strip domain, Proc. Jangjeon Math. Soc., 19 (4) (2016), pp. 653-661.
[41] Y.J. Sim and O.S. Kwon, On certain classes of convex functions, Int. J. Math. Math. Sci., 2013 (2013), Art. ID 294378, pp. 1-6.
[42] A. Soni and S. Kant, A new subclass of close-to-convex functions with Fekete-Szego problem, J. Rajasthan Acad. Phys. Sci., 12 (2) (2013), pp. 125-138.
[43] Y. Sun, Y.-P. Jiang and A. Rasila, Coefficient estimates for certain subclasses of analytic and bi-univalent functions, Filomat, 29 (2) (2015), pp. 351-360.
[44] Y. Sun, Y.-P. Jiang, A. Rasila and H. M. Srivastava, Integral representations and coefficient estimates for a subclass of meromorphic starlike functions, Complex Anal. Oper. Theory, 11 (1) (2017), pp. 1-19.
[45] Y. Sun, Z.-G. Wang, A. Rasila and J. Sokół, On a subclass of starlike functions associated with a vertical strip domain, J. Inequal. Appl., 2019 (2019), pp. 1-14.
[46] A. K. Wanas and L.-I. Cotîrlǎ, Applications of (M,N)-Lucas polynomials on a certain family of bi-univalent functions, Mathematics, 10 (4) (2022), 595.
[47] A.K. Wanas and H. Güney, Coefficient bounds and Fekete-Szegő inequality for a new family of bi-univalent functions defined by Horadam polynomials, Afr. Mat., 33 (3) (2022), pp. 1-9.
[48] Z.-G. Wang and D.-Z. Chen, On a subclass of close-to-convex functions, Hacet. J. Math. Stat., 38 (2) (2009), pp. 95-101.
[49] Ì. Yıldız, O. Mert and A. Akyar, Convex and starlike functions defined on the subclass of the class of the univalent functions S with order 2−r, Sahand Commun. Math. Anal., 19 (4) (2022), pp. 109-116.
[50] F. Yousef, A. Amourah, B.A. Frasin and T. Bulboacă, An Avant-Garde construction for subclasses of analytic bi-univalent functions, Axioms, 11 (6) (2022), 267.
[2] S. Altınkaya and S. Yalçın, Upper bound of second Hankel determinant for bi-Bazilevič functions, Mediterr. J. Math., 13 (6) (2016), pp. 4081-4090.
[3] S. Altınkaya and S. Yalçın, Faber polynomial coefficient bounds for a subclass of bi-univalent functions, C. R. Math. Acad. Sci. Paris, 353 (12) (2015), pp. 1075-1080.
[4] S.Altınkaya and S. Yalçın, Coefficient estimates for two new subclasses of biunivalent functions with respect to symmetric points, J. Funct. Spaces, 2015 (2015), Art. ID 145242, pp. 1-5.
[5] S. Altınkaya and S. Yalçın,Coefficient bounds for certain subclasses of m-fold symmetric biunivalent functions, J. Math., 2015 (2015), Art. ID 241683, pp. 1-5.
[6] S. Altınkaya and S. Yalçın, Fekete-Szegő inequalities for certain classes of biunivalent functions, International Scholarly Research Notices, 2014 (2014), Art. ID 327962, pp. 1-6.
[7] E. Amini, S. Al-Omari, K. Nonlaopon and D. Baleanu, Estimates for coefficients of bi-univalent functions associated with a fractional q-difference operator, Symmetry, 14 (5) (2022), 879.
[8] A. Amourah, B.A. Frasin, M. Ahmad and F. Yousef, Exploiting the Pascal distribution series and Gegenbauer Polynomials to construct and study a new subclass of analytic bi-univalent functions, Symmetry, 14 (1) (2022), 147.
[9] D. Breaz, K.R. Karthikeyan, E. Umadevi and A. Senguttuvan, Some properties of Bazilevič functions involving Srivastava–Tomovski operator, Axioms, 11 (12) (2022), 687.
[10] D. Breaz, L.-I. Cotîrlă, E. Umadevi and K.R. Karthikeyan, Properties of meromorphic spiral-like functions associated with symmetric functions, J. Funct. Spaces, 2022 (2022), Art. ID 3444854, pp. 1-10.
[11] S. Bulut, Coefficient estimates for functions associated with vertical strip domain, Commun. Korean Math. Soc., 37 (2) (2022), pp. 537-549.
[12] N.E. Cho, A. Ebadian, S. Bulut and A.E. Adegani, Subordination implications and coefficient estimates for subclasses of starlike functions, Mathematics, 8 (2020), 1150.
[13] N.E. Cho, O.S. Kwon and V. Ravichandran, Coefficient, distortion and growth inequalities for certain close-to-convex functions, J. Inequal. Appl., 2011 (2011), Article No. 2011:100, pp. 1-7.
[14] P.L. Duren, Univalent functions, Grundlehren der mathematischen Wissenschaften, 259, Springer-Verlag, New York, 1983.
[15] B.A. Frasin and M.K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett., 24 (9) (2011), pp. 1569-1573.
[16] C. Gao and S. Zhou, On a class of analytic functions related to the starlike functions, Kyungpook Math. J., 45 (1) (2005), pp. 123-130.
[17] I. Graham and G. Kohr, Geometric function theory in one and higher dimensions, Monographs and Textbooks in Pure and Applied Mathematics, 255, Marcel Dekker, Inc., New York, 2003.
[18] R. Kargar, A. Ebadian and J. Sokół, Radius problems for some subclasses of analytic functions, Complex Anal. Oper. Theory, 11 (7) (2017), pp. 1639-1649.
[19] K.R. Karthikeyan, N.E. Cho and G. Murugusundaramoorthy, On classes of non-Carathéodory functions associated with a family of functions starlike in the direction of the real axis, Axioms., 12 (1) (2023), 24.
[20] K.R. Karthikeyan, K.A. Reddy and G. Murugusundaramoorthy, On classes of Janowski functions associated with a conic domain, Italian J. Pure Appl. Math., 47 (2022), pp. 684-698.
[21] K.R. Karthikeyan, G. Murugusundaramoorthy, A. Nistor-Şerban and D. Răducanu, Coefficient estimates for certain subclasses of starlike functions of complex order associated with a hyperbolic domain, Bull. Transilv. Univ. Braşov Ser. III, 13 (62) (2020), pp. 595-609.
[22] K.R. Karthikeyan, K. Srinivasan and K. Ramachandran, On a class of multivalent starlike functions with a bounded positive real part, Palest. J. Math., 5 (1) (2015), pp. 59-64.
[23] F.R. Keogh and E.P. Merkes, A coefficient inequality for certain classes of analytic functions, Proc. Amer. Math. Soc., 20 (1969), pp. 8-12.
[24] D. Khurana, R. Kumar, S. Verma and G. Murugusundaramoorthy, A generalized class of univalent harmonic functions associated with a multiplier transformation, Sahand Commun. Math. Anal., 18 (3) (2021), pp. 27-39.
[25] W. Koepf, On the Fekete-Szegő problem for close-to-convex functions, Proc. Amer. Math. Soc., 101 (1) (1987), pp. 89-95.
[26] W. Koepf, Convex functions and the Nehari univalence criterion, in Complex analysis, Joensuu 1987, 214-218, Lecture Notes in Math., 1351, Springer, Berlin.
[27] K. Kuroki and S. Owa, Notes on New Class for Certain Analytic Functions, RIMS Kokyuroku, 1772 (2011), pp. 21-25
[28] O.S. Kwon, Y.J. Sim, N.E. Cho and H.M. Srivastava, Some radius problems related to a certain subclass of analytic functions, Acta Math. Sin. (Engl. Ser.), 30 (7) (2014), pp. 1133-1144.
[29] M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc., 18 (1967), pp. 63-68.
[30] S. Li, H. Tang, L.-I. Ma and X. Niu, A new subclass of analytic functions associated with the strip domains, Acta Math. Sci. Ser. A (Chinese Ed.), 35 (5) (2015), pp. 970-986.
[31] S. Mahmood, M. Jabeen, S.N. Malik, H.M. Srivastava, R. Manzoor and S.M. Jawwad Riaz, Some coefficient inequalities of q-starlike functions associated with [32] H. Mahzoon and J. Sokół, On coefficients of a certain subclass of starlike and bi-starlike functions, Kyungpook Math. J., 61 (3) (2021), pp. 513-522.
[33] Z. Nehari, A property of convex conformal maps, J. Analyse Math., 30 (1976), pp. 390-393.
[34] K.I. Noor and S.A. Shah, On certain generalized Bazilevic type functions associated with conic regions, Sahand Commun. Math. Anal., 17 (4) (2020), pp. 13-23.
[35] J.K. Prajapat, A new subclass of close-to-convex functions, Surv. Math. Appl., 11 (2016), pp. 11-19.
[36] K.A. Reddy, K.R. Karthikeyan and G. Murugusundaramoorthy, Inequalities for the Taylor coefficients of spiralike functions involving q-differential operator, Eur. J. Pure Appl. Math., 12 (3) (2019), pp. 846-856.
[37] W. Rogosinski, On the coefficients of subordinate functions, Proc. London Math. Soc., (2) 48 (1943), pp. 48-82.
[38] B. Şeker and S.S. Eker, On subclasses of bi-close-to-convex functions related to the odd-starlike functions, Palest. J. Math., 6 (2017), Special Issue II, pp. 215-221.
[39] B. Şeker, S.S. Eker and B. Cekic, On subclasses of analytic functions associated with Miller-Ross-type Poisson distribution series, Sahand Commun. Math. Anal., 19 (4) (2022), pp. 69-79.
[40] Y.J. Sim and O.S. Kwon, Some results on analytic functions associated with vertical strip domain, Proc. Jangjeon Math. Soc., 19 (4) (2016), pp. 653-661.
[41] Y.J. Sim and O.S. Kwon, On certain classes of convex functions, Int. J. Math. Math. Sci., 2013 (2013), Art. ID 294378, pp. 1-6.
[42] A. Soni and S. Kant, A new subclass of close-to-convex functions with Fekete-Szego problem, J. Rajasthan Acad. Phys. Sci., 12 (2) (2013), pp. 125-138.
[43] Y. Sun, Y.-P. Jiang and A. Rasila, Coefficient estimates for certain subclasses of analytic and bi-univalent functions, Filomat, 29 (2) (2015), pp. 351-360.
[44] Y. Sun, Y.-P. Jiang, A. Rasila and H. M. Srivastava, Integral representations and coefficient estimates for a subclass of meromorphic starlike functions, Complex Anal. Oper. Theory, 11 (1) (2017), pp. 1-19.
[45] Y. Sun, Z.-G. Wang, A. Rasila and J. Sokół, On a subclass of starlike functions associated with a vertical strip domain, J. Inequal. Appl., 2019 (2019), pp. 1-14.
[46] A. K. Wanas and L.-I. Cotîrlǎ, Applications of (M,N)-Lucas polynomials on a certain family of bi-univalent functions, Mathematics, 10 (4) (2022), 595.
[47] A.K. Wanas and H. Güney, Coefficient bounds and Fekete-Szegő inequality for a new family of bi-univalent functions defined by Horadam polynomials, Afr. Mat., 33 (3) (2022), pp. 1-9.
[48] Z.-G. Wang and D.-Z. Chen, On a subclass of close-to-convex functions, Hacet. J. Math. Stat., 38 (2) (2009), pp. 95-101.
[49] Ì. Yıldız, O. Mert and A. Akyar, Convex and starlike functions defined on the subclass of the class of the univalent functions S with order 2−r, Sahand Commun. Math. Anal., 19 (4) (2022), pp. 109-116.
[50] F. Yousef, A. Amourah, B.A. Frasin and T. Bulboacă, An Avant-Garde construction for subclasses of analytic bi-univalent functions, Axioms, 11 (6) (2022), 267.
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