Coefficient Bound of a New Generalized Class of Tilted Analytic Univalent Functions
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Keywords:
-
Analytic Functions, Univalent Functions, Representation Theorem, Coefficient Bound
Abstract
This paper is concerned with the new generalized class of tilted analytic univalent functions,
S*(q,a,s,t)
which denoted as.
Re{ei????f′(z) z }>????,
m(z)
for cos ???? > ????, |????| < ????, 0 ≤ ???? <1, m(z)= z , s ≠ 1, -1 ≤ t < 1, s ≠ t and s, t ∈ C which is analytic in the unit disk Δ={w:|w|<1}. The
(1−sz) (1−tz)
coefficient bound as well as representation theorem of extremal properties is obtained S∗(????,????,s,t).
References
Adegani, E. A., N. E. Cho, D. Alimohammadi, A. Motamednezhad, and I. Shahrood (2021). Coefficient Bounds for Certain Two Subclasses of Bi-Univalent Functions. AIMS Mathematics, 6(9); 9126–9137
Akbarally, A., D. Mohamad, S. C. Soh, and N. Kaharudin (2011). On The Properties of a New Class of ????-Close-to-Convex Functions. International Journal of Mathematical Analysis, 5(8); 387–396
Brickman, L., D. Hallenbeck, T. MacGregor, and D. Wilken (1973). Convex Hulls and Extreme Points of Families of Starlike and Con- vex Mappings. Transactions of The American Mathematical Society, 185; 413–428
Çağlar, M., H. Orhan, and N. Yağmur (2013). Coefficient Bounds for New Subclasses of Bi-Univalent Functions. Filomat, 27(7); 1165–1171
Cik Soh, S. (2009). A Generalized Class of Close-to-Convex Functions. Ph.D. Thesis, Universiti Teknologi MARA
Duren, P. L. (2001). Univalent Functions Volume 259. Springer Science & Business Media
Elhaddad, S. and M. Darus (2020). Coefficient Estimates for a Sub- class of Bi-Univalent Functions Defined by q-Derivative Operator. Mathematics, 8(3); 306
Fukui, S., S. Owa, S. Ogawa, and M. Nunokawa (1987). A Note on a Class of Analytic Functions Satisfying Re {f’(z) }> ????. Bulletin of The Faculty of Education, Wakayama University. Natural Science, 36; 13–17
Goel, R. (1967). A Class of Univalent Functions Whose Derivatives Have Positive Real Part in The Unit Disc. Nieuw Archief Voor Wiskunde, 15; 55–63
Goel, R. and B. S. Mehrok (1983). A Subclass of Univalent Functions. Journal of The Australian Mathematical Society, 35(1); 1–17
Goodman, A. (1983). Univalent Function Volume 1. Mariner Publishing Company, INC.
Kaharudin, N. (2011). On a Class of ????-Close-to-Convex Functions. Master’s Thesis, Universiti Teknologi MARA
Kaplan, W. (1952). Close-to-Convex Schlicht Functions. Michigan Mathematical Journal, 1(2); 169–185
MacGregor, T. H. (1962). Functions whose Derivative has a Positive Real Part. Transactions of The American Mathematical Society, 104(3); 532–537
MacGregor, T. H. (1964). A Class of Univalent Functions. Proceedings of The American Mathematical Society, 15(2); 311–317
Magesh, N. and J. Yamini (2013). Coefficient Bounds for Certain Subclasses of Bi-Univalent Functions. International Mathematical Forum, 8; 1337–1344
Mohamad, D. (1998). Functions Whose Derivative Maps The Unit Disc Into Half Plane. Ph.D. Thesis, University of Wales Swansea
Mohamad, D. (2000). On a Class of Functions Whose Derivatives Map The Unit Disc Into a Half Plane. Bulletin of The Malaysian Mathematical Sciences Society, 23(2); 163–167
Shaba, T. G. and A. K. Wanas (2022). Coefficient Bounds for a New Family of Bi-Univalent Functions Associated with (U , V )- Lucas Polynomials. International Journal of Nonlinear Analysis and Applications, 13(1); 615–626
Shashkin, Y. A. (1994). Local Degrees of Simplicial Mappings. Publi- cationes Mathematicae-Debrecen, 45(3-4); 407–413
Silverman, H. (1972). On a Class of Close-to-Convex Functions. Proceedings of The American Mathematical Society, 36(2); 477–484
Silverman, H. and E. Silvia (1996). On ????-Close-to-Convex Functions. Publicationes Mathematicae-Debrecen, 49; 305–316
Silverman, H. and D. Telage (1979). Extreme Points of Subclasses of Close-to-Convex Functions. Proceedings of The American Mathematical Society, 74(1); 59–65
Soh, S. C. and D. Mohamad (2006). On Extremal Properties for ????Close-to-Convex Functions. Proceeding of The 2nd IMT-GT Regional Conference on Mathematics, Statistics and Applications, ; 77–81
Wang, L. M. (2010). The Titled Carathodory Class and its Applications. arXiv Preprint arXiv:1003.1776
Yahya, A., S. C. Soh, and D. Mohamad (2014). Some Extremal Properties of a Generalised Close-to-Convex Function. International Journal of Mathematical Analysis, 8(39); 1931–1936
Akbarally, A., D. Mohamad, S. C. Soh, and N. Kaharudin (2011). On The Properties of a New Class of ????-Close-to-Convex Functions. International Journal of Mathematical Analysis, 5(8); 387–396
Brickman, L., D. Hallenbeck, T. MacGregor, and D. Wilken (1973). Convex Hulls and Extreme Points of Families of Starlike and Con- vex Mappings. Transactions of The American Mathematical Society, 185; 413–428
Çağlar, M., H. Orhan, and N. Yağmur (2013). Coefficient Bounds for New Subclasses of Bi-Univalent Functions. Filomat, 27(7); 1165–1171
Cik Soh, S. (2009). A Generalized Class of Close-to-Convex Functions. Ph.D. Thesis, Universiti Teknologi MARA
Duren, P. L. (2001). Univalent Functions Volume 259. Springer Science & Business Media
Elhaddad, S. and M. Darus (2020). Coefficient Estimates for a Sub- class of Bi-Univalent Functions Defined by q-Derivative Operator. Mathematics, 8(3); 306
Fukui, S., S. Owa, S. Ogawa, and M. Nunokawa (1987). A Note on a Class of Analytic Functions Satisfying Re {f’(z) }> ????. Bulletin of The Faculty of Education, Wakayama University. Natural Science, 36; 13–17
Goel, R. (1967). A Class of Univalent Functions Whose Derivatives Have Positive Real Part in The Unit Disc. Nieuw Archief Voor Wiskunde, 15; 55–63
Goel, R. and B. S. Mehrok (1983). A Subclass of Univalent Functions. Journal of The Australian Mathematical Society, 35(1); 1–17
Goodman, A. (1983). Univalent Function Volume 1. Mariner Publishing Company, INC.
Kaharudin, N. (2011). On a Class of ????-Close-to-Convex Functions. Master’s Thesis, Universiti Teknologi MARA
Kaplan, W. (1952). Close-to-Convex Schlicht Functions. Michigan Mathematical Journal, 1(2); 169–185
MacGregor, T. H. (1962). Functions whose Derivative has a Positive Real Part. Transactions of The American Mathematical Society, 104(3); 532–537
MacGregor, T. H. (1964). A Class of Univalent Functions. Proceedings of The American Mathematical Society, 15(2); 311–317
Magesh, N. and J. Yamini (2013). Coefficient Bounds for Certain Subclasses of Bi-Univalent Functions. International Mathematical Forum, 8; 1337–1344
Mohamad, D. (1998). Functions Whose Derivative Maps The Unit Disc Into Half Plane. Ph.D. Thesis, University of Wales Swansea
Mohamad, D. (2000). On a Class of Functions Whose Derivatives Map The Unit Disc Into a Half Plane. Bulletin of The Malaysian Mathematical Sciences Society, 23(2); 163–167
Shaba, T. G. and A. K. Wanas (2022). Coefficient Bounds for a New Family of Bi-Univalent Functions Associated with (U , V )- Lucas Polynomials. International Journal of Nonlinear Analysis and Applications, 13(1); 615–626
Shashkin, Y. A. (1994). Local Degrees of Simplicial Mappings. Publi- cationes Mathematicae-Debrecen, 45(3-4); 407–413
Silverman, H. (1972). On a Class of Close-to-Convex Functions. Proceedings of The American Mathematical Society, 36(2); 477–484
Silverman, H. and E. Silvia (1996). On ????-Close-to-Convex Functions. Publicationes Mathematicae-Debrecen, 49; 305–316
Silverman, H. and D. Telage (1979). Extreme Points of Subclasses of Close-to-Convex Functions. Proceedings of The American Mathematical Society, 74(1); 59–65
Soh, S. C. and D. Mohamad (2006). On Extremal Properties for ????Close-to-Convex Functions. Proceeding of The 2nd IMT-GT Regional Conference on Mathematics, Statistics and Applications, ; 77–81
Wang, L. M. (2010). The Titled Carathodory Class and its Applications. arXiv Preprint arXiv:1003.1776
Yahya, A., S. C. Soh, and D. Mohamad (2014). Some Extremal Properties of a Generalised Close-to-Convex Function. International Journal of Mathematical Analysis, 8(39); 1931–1936
Authors
Yahya, A., Najir Tokachil, M., Hamzah, H. H., Pirman, S. M. S. ., & Muhammad, S. A. C. . (2022). Coefficient Bound of a New Generalized Class of Tilted Analytic Univalent Functions. Science and Technology Indonesia, 7(1), 67–72. https://doi.org/10.26554/sti.2022.7.1.67-72
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