본문 바로가기
KERD
논문KCI 등재

A subclass of harmonic univalent mappings with a restricted analytic part

Priyabrat Gochhayat|Bikash Kumar Chinhara|Sudhananda Maharana
대한수학회 (The Korean Mathematical Society)|2019.07|대한수학회논문집 (Communications of the KMS)|제34권 제3호|pp. 841-854|DOI 10.4134/CKMS.c180272

0

조회

0

다운로드

0

인용

0

참고문헌

키워드

coefficient estimatesharmonic univalent mappingBloch's constantgrowth theoremdistortion theoremcovering theoremarea theorem
주제분류수학

초록

In this article, a subclass of univalent harmonic mapping is introduced by restricting its analytic part to lie in the class $\mathcal{S}^{\delta}[\alpha]$, $0\leq \alpha < 1$, $-\infty < \delta < \infty$ which has been introduced and studied by Kumar \cite{Kumar87} (see also \cite{Mishra95}, \cite{MishraChoudhury95}, \cite{MishraDas96}, \cite{MishraGochhayat06}). Coefficient estimations, growth and distortion properties, area theorem and covering estimates of functions in the newly defined class have been established. Furthermore, we also found bound for the Bloch's constant for all functions in that family.

Abstract

In this article, a subclass of univalent harmonic mapping is introduced by restricting its analytic part to lie in the class $\mathcal{S}^{\delta}[\alpha]$, $0\leq \alpha < 1$, $-\infty < \delta < \infty$ which has been introduced and studied by Kumar \cite{Kumar87} (see also \cite{Mishra95}, \cite{MishraChoudhury95}, \cite{MishraDas96}, \cite{MishraGochhayat06}). Coefficient estimations, growth and distortion properties, area theorem and covering estimates of functions in the newly defined class have been established. Furthermore, we also found bound for the Bloch's constant for all functions in that family.

참고문헌 (27)

  1. A. G. Akritas, "Improving the performance of the continued fractions method using new bounds of positive roots", Nonlinear Anal. Model. Control, 13(3), pp.265~279 (2008)
  2. A. Alesina, "Vincent's theorem from a modern point of view", Rend. Circ. Mat. Palermo (2), (64), pp.179~191 (2000)
  3. Huaihui Chen, "Bloch constants for planar harmonic mappings", Proceedings of the American Mathematical Society, 128(11), pp.3231~3241 (2000), American Mathematical Society (AMS)[DOI]
  4. Sh. Chen, "Bloch constant and Landau's theorem for planar p-harmonic mappings", Journal of Mathematical Analysis and Applications, 373(1), pp.102~110 (2011), Elsevier BV[DOI]
  5. J. Clunie, "Harmonic univalent functions", Annales Academiae Scientiarum Fennicae Series A I Mathematica, 9, pp.3~25 (1984), Finnish Academy of Science and Letters[DOI]
  6. Flavia Colonna, "The Bloch constant of bounded harmonic mappings", Indiana University Mathematics Journal, 38(4), pp.829~ (1989), Indiana University Mathematics Journal[DOI]
  7. P. Duren, "Univalent Functions" (1983), Springer-Verlag
  8. P. Duren, "Harmonic Mappings in the Plane" (2004), Cambridge University Press
  9. M. O. Gonzalez, "Complex Analysis: Selected Topics" (1992), Marcel Dekker, INC
  10. A. W. Goodman, "Univalent Functions. Vol. I and Vol. II" (1983), Mariner Publishing Co., Inc
  11. I. Graham, "Geometric Function Theory in One and Higher Dimensions", pp.1201~ (2003), Marcel Dekker, Inc
  12. I. Hotta, "Locally one-to-one harmonic functions with starlike analytic part", Bull. Soc. Sci. Lett. Lodz Ser. Rech. Deform, 64(2), pp.19~27 (2014)
  13. Stanislawa Kanas, "Harmonic mappings related to functions with bounded boundary rotation and norm of the pre-Schwarzian derivative", 대한수학회보, 51(3), pp.803~812 (2014), 대한수학회
  14. S. Kanas, "Coefficient Estimates and Bloch’s Constant in Some Classes of Harmonic Mappings", Bulletin of the Malaysian Mathematical Sciences Society, 39(2), pp.741~750 (2016), Springer Science and Business Media LLC[DOI]
  15. D. Klimek-Smet, "Univalent anti-analytic perturbations of the identity in the unit disc", Sci. Bull. Che lm, 1, pp.67~76 (2006)
  16. D. Klimek-Smet, "Univalent anti-analytic perturbations of convex analytic mappings in the unit disc", Ann. Univ. Mariae Curie-Sk lodowska Sect. A, 61, pp.39~49 (2007)
  17. Vinod Kumar, "Quasi-Hadamard product of certain univalent functions", Journal of Mathematical Analysis and Applications, 126(1), pp.70~77 (1987), Elsevier BV[DOI]
  18. Hans Lewy, "On the non-vanishing of the Jacobian in certain one-to-one mappings", Bulletin of the American Mathematical Society, 42(10), pp.689~693 (1936), American Mathematical Society (AMS)[DOI]
  19. MingSheng Liu, "Estimates on Bloch constants for planar harmonic mappings", Science in China Series A: Mathematics, 52(1), pp.87~93 (2009), Springer Science and Business Media LLC[DOI]
  20. A. K. Mishra, "Quasi-Hadamard product of analytic functions related to univalent func-tions", Math. Student, 64(1-4), pp.221~225 (1995)
  21. A. K. Mishra, "A class of multivalent functions with negative Taylor coecients", Demonstratio Math, 28(1), pp.223~234 (1995)
  22. A. K. Mishra, "Fractional integral operators and distortion theorems for a class of multivalent functions with negative coecients", J. Anal, 4, pp.185~199 (1996)
  23. A. K. Mishra, "Coecients of inverse functions in a nested class of starlike functions of positive order", J. Ineq. Pure and Appl. Math, 7(3) (2006)
  24. Malcolm I. S. Robertson, "On the Theory of Univalent Functions", The Annals of Mathematics, 37(2), pp.374~ (1936), JSTOR[DOI]
  25. E. C. Titchmarsh, "The Theory of Functions" (1939), Oxford University Press
  26. A. J. H. Vincent, "Sur la resolution des equations numeriques", J. Math. Pures Appl, 1, pp.341~372 (1836)
  27. M. Zhu, "The distortion theorems for harmonic mappings with analytic parts convex or starlike functions of order", J. Math, pp.1~6 (2015)[DOI]

관련 논문AI추천

New Subclasses of Harmonic Starlike and Convex FunctionsKaushal Kishore Dixit, Saurabh Porwal경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2013 · 제53권 제3호Multivalent Harmonic Uniformly Starlike FunctionsNaveneet Sangle, Om Ahuja, Santosh Joshi경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2009 · 제49권 제3호Mapping properties of a family of planar harmonic functionsManju Yadav, Sukhjit Singh, Sushma Gupta대한수학회 · 대한수학회보2025 · 제62권 제3호Radius of fully starlikeness and fully convexity of harmonic linear differential operatorSaminathan Ponnusamy, ZhiHong Liu대한수학회 · 대한수학회보2018 · 제55권 제3호Coefficient Bounds for a Subclass of Harmonic Mappings Con vex in One DirectionMaryam Yazdi, Mohammad Mehdi Shabani, Saeed Hashemi Sababe경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2021 · 제61권 제2호A subclass of harmonic functions associated with wright hypergeometric functionsG. Murugusundaramoorthy, K. Vijaya장전수학회 · Advanced Studies in Contemporary Mathematics2009 · 제18권 제1호

이 간행물의 다른 논문 (24건)

The $U$-projective resolution of modules over path algebras of types $A_n$ and $\tilde{A}_n$Karin Baur, Intan Muchtadi-Alamsyah, Yudi Mahatmapp. 701-718On partial-Armendariz rings윤상조, Zhelin Piao, 남상복pp. 719-727On prime submodules of a finitely generated projective module over a commutative ringZahra Pourshafiey, Reza Nekooeipp. 729-741Module amenability and module Arens regularity of weighted semigroup algebrasAbasalt Bodaghi, DAVOOD EBRAHIMI BAGHA, Gholamreza Asgaripp. 743-755Heat equation with a geometric rough path potential in one space dimension: existence and regularity of solutionHyun-Jung Kim, Sergey V. Lototskypp. 757-769
원문 보기