본문 바로가기
KERD
논문KCI 등재

CONSTRUCTION OF SUBCLASSES OF UNIVALENT HARMONIC MAPPINGS

V. Ravichandran|Sumit Nagpal
대한수학회 (The Korean Mathematical Society)|2014.05|대한수학회지 (Journal of the KMS)|제51권 제3호|pp. 567-592

2

조회

0

다운로드

1

인용

0

참고문헌

키워드

starlikeconvexconvolutionintegral operators.coefficient estimatesclose-to-convexconvex combinationunivalent harmonic mappingsgrowth estimate
주제분류수학

초록

Complex-valued harmonic functions that are univalent and sense-preserving in the open unit disk are widely studied. A new method- ology is employed to construct subclasses of univalent harmonic mappings from a given subfamily of univalent analytic functions. The notions of harmonic Alexander operator and harmonic Libera operator are intro- duced and their properties are investigated.

Abstract

Complex-valued harmonic functions that are univalent and sense-preserving in the open unit disk are widely studied. A new method- ology is employed to construct subclasses of univalent harmonic mappings from a given subfamily of univalent analytic functions. The notions of harmonic Alexander operator and harmonic Libera operator are intro- duced and their properties are investigated.

참고문헌 (37)

  1. J.W. Alexander, "Functions which map the interior of the unit circle upon simple regions", Ann. of Math. (2), 17(1), pp.12~22 (1915)
  2. R. M. Ali, "Convolution of certain analytic functions", J. Anal, 18, pp.1~8 (2010)
  3. Y. Avci, "On harmonic univalent mappings", Ann. Univ. Mariae Curie-Sk lodowska Sect. A, 44, pp.1~7 (1990)
  4. D. M. Campbell, "Valence properties of the solution of a differential equation", Pacific J. Math, 84(1), pp.29~33 (1979)
  5. P. N. Chichra, "New subclasses of the class of close-to-convex functions", Proc. Amer. Math. Soc, 62(1), pp.37~43 (1976)
  6. M. Chuaqui, "Curvature properties of planar harmonic map-pings", Comput. Methods Funct. Theory, 4(1), pp.127~142 (2004)
  7. J. Clunie, "Harmonic univalent functions", Ann. Acad. Sci. Fenn. Ser. A I Math, 9, pp.3~25 (1984)
  8. M. Dorff, "Convolutions of planar harmonic convex mappings", Complex Variables Theory Appl, 45(3), pp.263~271 (2001)
  9. M. Dorff, "Convolutions of harmonic convex mappings", Complex Var. Elliptic Equ, 57(5), pp.489~503 (2012)
  10. P. Duren, "Harmonic Mappings in the Plane" (2004), Cambridge Univ. Press
  11. C. Y. Gao, "On the starlikeness of the Alexander integral operator", Proc. Japan Acad. Ser. A Math. Sci, 68(10), pp.330~333 (1992)
  12. M. R. Goodloe, "Hadamard products of convex harmonic mappings", Complex Var. Theory Appl, (2), pp.81~92 (2002)
  13. A. W. Goodman, "Univalent functions and nonanalytic curves", Proc. Amer. Math. Soc, 8, pp.598~601 (1957)
  14. A. W. Goodman, "Univalent Functions. Vol. I and II" (1983), Mariner
  15. R. Hernandez, "Stable geometric properties of analytic and harmonic functions", Math. Proc. Cambridge Philos. Soc, 155, pp.343~359 (2013)
  16. J. Krzyz, "The radius of close-to-convexivity within the family of univalent functions", Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys, 10, pp.201~204 (1962)
  17. J. Krzyz, "On the integral of univalent functions", Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys, 11, pp.447~448 (1963)
  18. R. J. Libera, "Some classes of regular univalent functions", Proc. Amer. Math. Soc, 16, pp.755~758 (1965)
  19. T. H. MacGregor, "Functions whose derivative has a positive real part", Trans. Amer. Math. Soc, 104, pp.532~537 (1962)
  20. T. H. MacGregor, "A class of univalent functions", Proc. Amer. Math. Soc, 15, pp.311~317 (1964)
  21. E. P. Merkes, "On the univalence of a certain integral", Proc. Amer. Math. Soc, 27, pp.97~100 (1971)
  22. S. S. Miller, "Differential Subordinations" (2000), Dekker
  23. P. T. Mocanu, "Sufficient conditions of univalency for complex functions in the class C¹", Anal. Numer. Theor. Approx, 10(1), pp.75~79 (1981)
  24. P. T. Mocanu, "On starlikeness of Libera transform", Mathematica (Cluj), 28(2), pp.153~155 (1986)
  25. P. T. Mocanu, "Injectivity conditions in the complex plane", Complex Anal. Oper. Theory, 5(3), pp.759~766 (2011)
  26. S. Nagpal, "A subclass of close-to-convex harmonic mappings", Complex Var. Elliptic Equ, 59(2), pp.204~216 (2014)
  27. S. Nagpal, "Fully starlike and fully convex harmonic mappings of order", Ann. Polon. Math, 108(1), pp.85~107 (2013)
  28. S. Nagpal, "Univalence and convexity in one direction of the convolution of harmonic map- pings", Complex Var. Elliptic Equ (2013)[DOI]
  29. S. Ponnusamy, "On harmonic close-to-convex functions", Comput. Methods Funct. Theory, 12, pp.669~685 (2012)
  30. S. Ponnusamy, "Variability regions for certain families of harmonic univalent mappings", Complex Var. Elliptic Equ, 58(1), pp.23~34 (2013)
  31. J. S. Ratti, "The radius of convexity of certain analytic functions", Indian J. Pure Appl. Math, 1(1), pp.30~36 (1970)
  32. S. Ruscheweyh, "Convolutions in Geometric Function Theory" (1982), Presses Univ. Montreal
  33. S. Ruscheweyh, "On the preservation of direction-convexity and the Goodman-Saff conjecture", Ann. Acad. Sci. Fenn. Ser. A I Math, 14(1), pp.63~73 (1989)
  34. H. Silverman, "Univalent functions with negative coefficients", Proc. Amer. Math. Soc, 51, pp.109~116 (1975)
  35. H. Silverman, "Harmonic univalent functions with negative coefficients", J. Math. Anal. Appl, 220(1), pp.283~289 (1998)
  36. R. Singh, "Starlikeness and convexity of certain integrals", Ann. Univ. Mariae Curie-Sk lodowska Sect. A, 35, pp.145~148 (1984)
  37. R. Singh, "Convolution properties of a class of starlike functions", Proc. Amer. Math. Soc, 106(1), pp.145~152 (1989)

관련 논문AI추천

Mapping properties of a family of planar harmonic functionsManju Yadav, Sukhjit Singh, Sushma Gupta대한수학회 · 대한수학회보2025 · 제62권 제3호Multivalent Harmonic Uniformly Starlike FunctionsNaveneet Sangle, Om Ahuja, Santosh Joshi경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2009 · 제49권 제3호Convolution on a Generalized Class of Harmonic Univalent FunctionsKaushal Kishore Dixit, Saurabh Porwal경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2015 · 제55권 제1호Mapping Properties of Some Harmonic FunctionsManju Yadav, Sukhjit Singh, Sushma Gupta경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2025 · 제65권 제4호HARMONIC MAPPINGS WITH ANALYTIC FUNCTIONS전숙희강원경기수학회 · 한국수학논문집2012 · 제20권 제4호On A Subclass of Harmonic Multivalent Functions Dened by a Certain Linear OperatorAbdel Moneim Yousof Lashin, Hanan Elsayed Darwis, Suliman Mohammed Sowileh경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2019 · 제59권 제4호

이 간행물의 다른 논문 (10건)

A RECURRENCE RELATION FOR THE JONES POLYNOMIALAbdul Rauf Nizami, Barbu Berceanupp. 443-462SEMICENTRAL IDEMPOTENTS IN A RING이양, 한준철, 박상원pp. 463-472EXISTENCE AND GLOBAL EXPONENTIAL STABILITY OF POSITIVE ALMOST PERIODIC SOLUTIONS FOR A DELAYED NICHOLSON’S BLOWFLIES MODELYanli Xupp. 473-493ANNIHILATORS IN ONE-SIDED IDEALS GENERATED BY COEFFICIENTS OF ZERO-DIVIDING POLYNOMIALS곽태근, 이동수, 이양pp. 495-507w-INJECTIVE MODULES AND w-SEMI-HEREDITARY RINGS김환구, Fanggui Wangpp. 509-525
원문 보기