본문 바로가기
KERD
논문KCI 등재

Certain New Families for Bi-univalent Functions Defined by a Known Operator

최준상|Abbas Kareem Wanas
영남수학회 (Youngnam Mathematical Society)|2021.05|East Asian Mathematical Journal|제37권 제3호|pp. 319-331

1

조회

0

다운로드

0

인용

0

참고문헌

키워드

Analytic functionsBi-univalent functionsCoefficient estimatesGeneralized Mittag-Leffler functionsFekete-Szeg\"{o} proble
주제분류수학

초록

In this paper, we aim to introduce two new families of analytic and bi-univalent functionsassociated with the Attiya's operator, which is defined by the Hadamard product ofa generalized Mittag-Leffler function and analytic functions on the open unit disk. Then we estimate the second and third coefficients of the Taylor-Maclaurin series expansions of functions belonging to these families. Also, we investigate Fekete-Szeg\"{o} problem for these families. Some relevant connections of certain special cases of the main results with those in several earlier works are also pointed out. Two naturally-arisen problems are given for further investigation.

Abstract

In this paper, we aim to introduce two new families of analytic and bi-univalent functionsassociated with the Attiya's operator, which is defined by the Hadamard product ofa generalized Mittag-Leffler function and analytic functions on the open unit disk. Then we estimate the second and third coefficients of the Taylor-Maclaurin series expansions of functions belonging to these families. Also, we investigate Fekete-Szeg\"{o} problem for these families. Some relevant connections of certain special cases of the main results with those in several earlier works are also pointed out. Two naturally-arisen problems are given for further investigation.

참고문헌 (44)

  1. C. Abirami, "Initial bounds for certain classes of bi-univalent functions defined by Horadam polynomials", Abstr. Appl. Anal., 2020, pp.8~ (2020)[DOI]
  2. Ebrahim Analouei Adegani, "Coefficient estimates for a subclass of analytic bi-univalent functions", 대한수학회보, 55(2), pp.405~413 (2018), 대한수학회
  3. A. G. Al-Amoush, "Certain subclasses of bi-univalent functions involving the Poisson distribution associated with Horadam polynomials", Malaya J. Mat, 7(4), pp.618~624 (2019)[DOI]
  4. R. M. Ali, "Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions", Appl. Math. Lett, 25(3), pp.344~351 (2012)[DOI]
  5. A. Alsoboh, "On Fekete-Szeg¨o problems for certain subclasses of an-alytic functions defined by differential operator involving q-Ruscheweyh operator", J. Funct. Spaces, 2020, pp.6~ (2020)[DOI]
  6. S¸. Altınkaya, "On the Chebyshev polynomial coefficient problem of some subclasses of bi-univalent functions", Gulf J. Math, 5(3), pp.34~40 (2017)
  7. H. Arikan, "Fekete-Szeg¨o inequality for a subclass of analytic functions defined by Komatu integral operator", AIMS Math, 5(3), pp.1745~1756 (2020)[DOI]
  8. A. A. Attiya, "Some applications of Mittag-Leffler function in the unit disk", Filomat, 30(7), pp.2075~2081 (2016)[DOI]
  9. D. A. Brannan, "Aspects of Contemporary Complex Analysis (Pro-ceedings of the NATO Advanced Study Institute held at the University of Durham, Durham; July 120, 1979)" (1980), Academic Press
  10. J. Choi, "A note on fractional integral operator associated with multiindex Mittag-Leffler functions", Filomat, 30(7), pp.1931~1939 (2016)[DOI]
  11. P. L. Duren, "Univalent Functions, Grundlehren der Mathematischen Wissenschaften" (1983), Springer Verlag
  12. A. Erd´elyi, "Higher Transcendental Functions, Vol. 3" (1955), McGraw-Hill Book Company
  13. M. Fekete, "Eine bemerkung uber ungerade schlichte funktionen", J. London Math. Soc, 2s1-8(2), pp.85~89 (1933)[DOI]
  14. B. A. Frasin, "Coefficient bounds for certain classes of bi-univalent functions", Hacet. J. Math. Stat, 43(3), pp.383~389 (2014)
  15. B. A. Frasin, "New subclasses of bi-univalent functions", Appl. Math. Lett, 24(9), pp.1569~1573 (2011)[DOI]
  16. H. ¨O. G¨uney, "Subclasses of bi-univalent func-tions related to shell-like curves connected with Fibonacci numbers", Acta Univ. Sapient. Math, 10(1), pp.70~84 (2018)[DOI]
  17. N. U. Khan, "Legendre-Gould Hopper-based Sheffer polynomials and operational methods", Symmetry, 12, pp.17~ (2020)[DOI]
  18. M. Lewin, "On a coefficient problem for bi-univalent functions", Proc. Amer. Math. Soc, 18(1), pp.63~68 (1967)
  19. Nanjundan Magesh, "Chebyshev polynomial coefficient estimates for a class of analytic bi-univalent functions related to pseudo-starlike functions", Afrika Matematika, 29(1-2), pp.203~209 (2018), Springer Science and Business Media LLC[DOI]
  20. G. M. Mittag-Leffler, "Sur la nouvelle function", C. R. Acad. Sci. Paris, 137, pp.554~558 (1903)
  21. G. M. Mittag-Leffler, "Sur la representation analytique dune function monogene (cin-quieme note)", Acta Math, 29, pp.101~181 (1905)[DOI]
  22. E. Netanyahu, "The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in |z| < 1", Arch. Rational Mech. Anal, 32, pp.100~112 (1969)
  23. A. Pfluger, "The Fekete-Szego inequality by a variational method", An. Acad. Scientiorum Fennicae Seria A. I, 10, pp.447~454 (1985)
  24. S. Roman, "The Umbral Calculus" (1984), Academic Press
  25. R. K. Saxena, "N-fractional calculus of generalized Mittag-Leffler func-tions", J. Fract. Calc, 37, pp.43~52 (2010)
  26. H. M. Srivastava, "Certain subclasses of bi-univalent functions associated with the Horadam polynomials", Iran. J. Sci. Technol. Trans. A Sci, 43, pp.1873~1879 (2019)[DOI]
  27. H. M. Srivastava, "Zeta and q-Zeta Functions and Associated Series and Integrals" (2012), Elsevier Science Publishers
  28. H. M. Srivastava, "Faber polynomial coef-ficient estimates for bi-univalent functions defined by the Tremblay fractional derivative operator", Bull. Iranian Math. Soc, 44(1), pp.149~157 (2018)[DOI]
  29. H. M. Srivastava, "Coefficient estimates for some general subclasses of analytic and bi-univalent functions", Afr. Mat, 28, pp.693~706 (2017)[DOI]
  30. H. M. Srivastava, "Certain subclasses of analytic and bi-univalent functions", Appl. Math. Lett, 23, pp.1188~1192 (2010)[DOI]
  31. H. M. Srivastava, "Fekete-Szegö inequality for classes of (p, q)-Starlike and (p, q)-convex functions", Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 113(4), pp.3563~3584 (2019), Springer Science and Business Media LLC[DOI]
  32. H. M. Srivastava, "Fractional calculus with an integral operator con-taining a generalized Mittag-Leffler function in the kernal", Appl. Math. Comp, 211(1), pp.198~210 (2009)[DOI]
  33. 스리바스타바, "Initial Maclaurin Coefficient Bounds for New Subclasses of Analytic and m-Fold Symmetric Bi-Univalent Functions Defined by a Linear Combination", Kyungpook Mathematical Journal, 59(3), pp.493~503 (2019), 경북대학교 자연과학대학 수학과[DOI]
  34. H. M. Srivastava, "Certain family of bi-univalent functions associated with Pascal distribution series based on Horadam polyno-mials", Surv. Math. Appl, 16, pp.193~205 (2021)
  35. S. R. Swamy, "Some special families of holomorphic and Sˇalˇagean type bi-univalent functions associated with (m,n)-Lucas polynomials", Commun. Math. Appl, 11(4), pp.563~574 (2020)[DOI]
  36. Eszter Szatmari, "Coefficient estimates and Fekete-Szegö inequality for a class of analytic functions satisfying subordinate condition associated with Chebyshev polynomials", Acta Universitatis Sapientiae, Mathematica, 11(2), pp.430~436 (2019), Walter de Gruyter GmbH[DOI]
  37. A. K. Wanas, "Bounds for initial Maclaurin coefficients for a new subclasses of analytic and m-fold symmetric bi-univalent functions", TWMS J. App. Eng. Math, 10(2), pp.305~311 (2020)[DOI]
  38. A. K. Wanas, "Applications of Chebyshev polynomials on λ-pseudo bi-starlike and λ-pseudo bi-convex functions with respect to symmetrical points", TWMS J. App. Eng. Math, 10(3), pp.568~573 (2020)
  39. A. K. Wanas, "Coefficient estimates of bi-starlike and bi-convex functions with respect to symmetrical points associated with the second kind Chebyshev polynomials", Earthline J. Math. Sci, 3, pp.191~198 (2020)[DOI]
  40. A. K. Wanas, "Applications of Horadam polynomials on Bazilevicˇ bi-univalent function satisfying subordinate conditions", J. Phys. : Conf. Ser, 1294, pp.032003~ (2019)[DOI]
  41. A. K. Wanas, "Chebyshev polynomial bounded for analytic and bi-univalent functions with respect to symmetric conjugate points", Appl. Math. E-Notes, 19, pp.14~21 (2019)[DOI]
  42. A. K. Wanas, "Initial coefficient estimates for a new subclasses of analytic and m-fold symmetric bi-univalent functions", Malaya J. Mat, 7, pp.472~476 (2019)[DOI]
  43. A. K. Wanas, "Coefficient estimates and Fekete-Szeg¨o inequality for family of bi-univalent functions defined by the second kind Chebyshev polynomial", Int. J. Open Problems. Compt. Math, 13(2), pp.25~33 (2020)
  44. P. Zaprawa, "On the Fekete-Szeg¨o problem for classes of bi-univalent functions", Bull. Belg. Math. Soc. Simon Stevin, 21, pp.169~178 (2014)[DOI]

관련 논문AI추천

Sharp bounds for the initial coefficients for certain families of bi-univalent functionsAhmad Motamednezhad, Safa Salehian대한수학회 · 대한수학회논문집2024 · 제39권 제4호Coefficient bounds for a subclass of bi-univalent functions associated with Dziok-Srivastava operatorMohammad Mehdi Shabani, Saeed Hashemi Sababe강원경기수학회 · 한국수학논문집2022 · 제30권 제1호COEFFICIENT ESTIMATES OF BI-UNIVALENT FUNCTIONS OF COMPLEX ORDER ASSOCIATED WITH RAFID-OPERATORG. Murugusundaramoorthy, T. Janani장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2015 · 제18권 제4호Application of Gegenbauer polynomials to certain classes of bi-univalent functions of order $\nu+i\varsigma$Ala Amourah, MASLINA DARUS, Omar Alnajar강원경기수학회 · 한국수학논문집2024 · 제32권 제1호Coefficient estimates for certain subclass for spirallike functions defined by means of generalized Attiya-Srivastava operatorTugba Yavuz대한수학회 · 대한수학회논문집2016 · 제31권 제4호Coefficient estimates for a new general subclass of analytic bi-univalent functionsSerap Bulut강원경기수학회 · 한국수학논문집2021 · 제29권 제3호

이 간행물의 다른 논문 (4건)

Degree of Approximation of Functions of Class $Zyg^{\omega}(\alpha,\gamma)$ by Cesaro means of Fourier series김재만pp. 289-293Efficiency Analysis of a Domain Decomposition Method for the Two-dimensional Telegraph Equations전윤배pp. 295-305An Intrinsic Criterion for the Type of Automorphisms of the Unit Disc이강혁pp. 307-317Comparative Study of the Performance of Support Vector Machines with Various Kernels김상일, 유용빈, 남성욱, 김현민pp. 333-354
원문 보기