본문 바로가기
KERD
논문KCI 등재

Hypergeometric distribution series and its application of certain class of analytic functions based on special functions

Saurabh Porwal|Gangadharan Murugusundaramoorthy
대한수학회 (The Korean Mathematical Society)|2021.10|대한수학회논문집 (Communications of the KMS)|제36권 제4호|pp. 671-684|DOI 10.4134/CKMS.c200168

1

조회

0

다운로드

0

인용

0

참고문헌

키워드

univalent functionsAnalyticgeneralized hypergeometric functionuniformly convex functionsuniformly starlike functions
주제분류수학

초록

The tenacity of the current paper is to find connections between various subclasses of analytic univalent functions by applying certain convolution operator involving generalized hypergeometric distribution series. To be more specific, we examine such connections with the classes of analytic univalent functions $k-\mathcal{UCV}^{*}\left( \beta \right)$, $k-\mathcal{S}_p^{*}\left( \beta \right)$, $\mathcal{R}\left( \beta \right)$, $\mathcal{R}^{\tau}(A,B)$, $k-\mathcal{PUCV}^{*}\left( \beta \right)$ and $k -\mathcal{PS}_p^{*}\left( \beta \right)$ in the open unit disc $\mathbb{U}$.

Abstract

The tenacity of the current paper is to find connections between various subclasses of analytic univalent functions by applying certain convolution operator involving generalized hypergeometric distribution series. To be more specific, we examine such connections with the classes of analytic univalent functions $k-\mathcal{UCV}^{*}\left( \beta \right)$, $k-\mathcal{S}_p^{*}\left( \beta \right)$, $\mathcal{R}\left( \beta \right)$, $\mathcal{R}^{\tau}(A,B)$, $k-\mathcal{PUCV}^{*}\left( \beta \right)$ and $k -\mathcal{PS}_p^{*}\left( \beta \right)$ in the open unit disc $\mathbb{U}$.

참고문헌 (22)

  1. M. S. Ahmad, "An application of a Hypergeometric distribution series on certain analytic functions", Sci. Int, 27(4,), pp.2989~2992 (2015)
  2. S. Altınkaya, "Poisson distribution series for analytic univalent functions", Complex Anal. Oper. Theory, 12(5), pp.1315~1319 (2018)[DOI]
  3. K. K. Dixit, "On subclass of univalent functions with positive coefficients", Aligarh Bull. Math, 27(2), pp.87~93 (2008)
  4. K. K. Dixit, "On a class of univalent functions related to complex order", Indian J. Pure Appl. Math, 26(9), pp.889~896 (1995)
  5. K. K. Dixit, "A new class of analytic functions with positive coefficients", Indian J. Pure Appl. Math, 34(2,), pp.209~218 (2003)
  6. K. K. Dixit, "On a new class of close-to-convex functions with positive coefficients", Bull. Calcutta Math. Soc, 97(6,) (2005)
  7. K. K. Dixt, "A new subclass of univalent functions with positive coefficients", Bessel J. Math, 3(2,), pp.125~135 (2013)
  8. B. A. Frasin, "On certain subclasses of analytic functions associated with Poisson distribution series", Acta Univ. Sapientiae Math, 11(1), pp.78~86 (2019)[DOI]
  9. W. Nazeer, "An application of binomial distribution series on certain analytic functions", J. Comput. Anal. Appl, 26(1), pp.11~17 (2019)
  10. Saurabh Porwal, "An application of certain convolution operator involving Poisson distribution series", Asian-European Journal of Mathematics, 09(04), pp.1650085~ (2016), World Scientific Pub Co Pte Ltd[DOI]
  11. Saurabh Porwal, "Confluent Hypergeometric Distribution and Its Applications on Certain Classes of Univalent Functions of Conic Regions", Kyungpook Mathematical Journal, 58(3), pp.495~505 (2018), 경북대학교 자연과학대학 수학과
  12. S. Porwal, "An application of certain convolution operator involving hypergeometric functions", J. Rajasthan Acad. Phys. Sci, 9(2), pp.173~186 (2010)
  13. S. Porwal, "An application of generalized Bessel functions on certain analytic functions", Acta Univ. M. Belii Ser. Math, 21, pp.55~61 (2013)
  14. S. Porwal, "On a subclass of analytic function defined by convolution", Gen. Math, 19(3), pp.57~65 (2011)
  15. S. Porwal, "Some properties of convolution for hypergeometric distribution type series on certain analytic univalent functions", Acta Univ. Apulensis Math. Inform, pp.69~80 (2018)[DOI]
  16. E. D. Rainville, "Special Functions" (1960), The Macmillan Co
  17. Malcolm I. S. Robertson, "On the Theory of Univalent Functions", The Annals of Mathematics, 37(2), pp.374~408 (1936), JSTOR[DOI]
  18. A. K. Sharma, "Class mappings properties of convolutions involving certain univalent functions associated with hypergeometric functions", Electronic J. Math. Anal. Appl, 1(2), pp.326~333 (2013)
  19. H. Silverman, "Univalent functions with negative coefficients", Proc. Amer. Math. Soc, 51, pp.109~116 (1975)[DOI]
  20. R. Themangani, "Generalized hypergeometric distribution and its applications on univalent functions", J. Inequal. Appl, 249 (2020)[DOI]
  21. B. A. Uralegaddi, "Univalent functions with positive coefficients", Tamkang J. Math, 25(3), pp.225~230 (1994)
  22. B. A. Uralegaddi, "Close-to-convex functions with positive coefficients", Studia Univ. Babe¸s-Bolyai Math, 40(4), pp.25~31 (1995)

관련 논문AI추천

Subclasses of Starlike and Convex Functions Associated with Pascal Distribution SeriesAbbas Kareem Wanas, Basem Aref Frasin, Sondekola Rudra Swamy경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2021 · 제61권 제1호Applications of the Gaussian hypergeometric function to some subclasses of analytic functionsAbeer O. Badghaish, Amani Z. Bajamal강원경기수학회 · 한국수학논문집2024 · 제32권 제1호Some inclusion relations of certain subclasses of harmonic univalent functions associated with generalized distribution seriesNanjundan Magesh, Rajavadivelu Themangani, Saurabh Porwal대한수학회 · 대한수학회논문집2020 · 제35권 제3호Univalent functions with positive coefficients involving Pascal distribution seriesGangadharan Murugusundaramoorthy, Teodor Bulboaca대한수학회 · 대한수학회논문집2020 · 제35권 제3호Pascal Distribution Series Connected with Certain Subclasses of Univalent FunctionsJacek Dziok, Sheeza M. El-Deeb, Teodor Bulboaca경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2019 · 제59권 제2호PROPERTIES OF HYPERGEOMETRIC FUNCTIONS RELATED TO UNIFORMLY CONVEX AND UNIFORMLY STARLIKE FUNCTIONS이효정, G. Murugusundaramoorthy, J. H. Park, N. E. Choi장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2015 · 제18권 제1호

이 간행물의 다른 논문 (14건)

On automorphisms in prime rings with applicationsMohd Arif Razapp. 641-650Slice regular Besov spaces of hyperholomorphic functions and composition operatorsSanjay Kumar, Khalid Manzoorpp. 651-669A Cameron--Storvick theorem on $C_{a,b}^2[0,T]$ with applicationsDavid Skoug, 최재길pp. 685-704An extension of the Whittaker functionKottakkaran Sooppy Nisar, 최준상, Gauhar Rahmanpp. 705-714Some results concerned with Hankel determinant for $\mathcal{N}\left( \mathcal{\alpha }\right)$ classGizem Atli, Bulent Nafi Ornekpp. 715-727
원문 보기