2001 Fiscal Year Annual Research Report

解析関数の部分和の性質についての研究

Research Project

Project/Area Number	11640188
Research Institution	Kinki University
Principal Investigator	尾和重義近畿大学, 理工学部, 教授 (50088506)
Co-Investigator(Kenkyū-buntansha)	西郷恵福岡大学, 理学部, 教授 (10040403) 青木貴史近畿大学, 理工学部, 教授 (80159285) 泉脩藏近畿大学, 理工学部, 教授 (80025410) 布川護群馬大学, 教育学部, 教授 (00008137)
Keywords	単葉関数 / 星型関数 / 凸型関数 / 部分和 / 積分作用素 / 微分作用素 / 有理型関数 / 超幾何関数
Research Abstract	単位円板内で定義された解析関数f(z)=z+a_2z^2+a_3z^3+・・・の単葉性質・星型性質・凸型性質および有理型関数f(z)=1/z+a_1z+a_2z^2+・・・の星型性質・凸型性質などを中心に、解析関数・有理型関数の様々な性質を微分作用素・積分作用素・合成積・サブオーディネーション・微分方程式などの概念を用いて研究した。一般に星型関数や凸型関数f(z)の部分和fn(z)=z+a_2z^2+a_3z^3+・・・+a_nz^nは星型性質・凸型性質を保存しない。論文『Partial sums of certain analytic functions, International Journal of Mathematics and Mathematical Sciences, Internat. J. Math. Math. Sci. Vol.25, No.12 (2001), 771-775』では星型関数の極値関数f(z)=z/(1-z)^2=z+2z^2+3z^3+・・・や凸型関数の極値関数f(z)=z/(1-z)=z+z^2+z^3+・・・の部分和f_3(z)=z+2z^2+3z^3およびf_3(z)=z+z^2+z^3の星型半径・凸型半径を求めることができた。しかしながら、f_4(z)の星型性質や凸型性質についての考察はf_3(z)の考察と同様には求められない。ところが、最近になって、部分和の研究に対する新たな研究の方向を発見し、特別な関数の部分和ではなく、一般的な解析関数の部分和を論じる可能性が出てきた。このことによって、部分和の研究に対して、f_n(z)=z+a_2z^2+a_3z^3+・・・+a_nz^nという形の一般的な解析関数の部分和の性質を研究するための大きなきっかけが得られた。さらにははこれらの部分和の研究を1変数の解析関数のみならず、多変数の解析関数の部分和の問題へと拡張しつつある。したがって、解析関数の部分和に対する今後の課題は、上述の部分和に対する新しい議論によって、解析関数の部分和についての一般的な性質を考察すること、および、多変数の解析関数の部分和の研究へと拡張することにある。上記以外の研究から、J.E.Littlewoodによる論文『On inequalities in the theory of functions, Proc. London Math. Soc. Vol.23 (1925), 481-519』の中の結果が、解析関数の部分和に関係づけられることが分かり、解析関数の微分作用素や積分作用素と部分和に関する研究についても、新たな展開が可能になってきた。

Research Products
(17 results)

All Other

All Publications (17 results)

[Publications] S.Owa: "Partial sums of certain analytic functions"International Journal of Mathematics and Mathematical Sciences. 25・12. 771-775 (2001)
[Publications] N.E.Cho, S.Owa: "Sufficient conditions for meromorphic starlikeness and close-to-convexity of order α"International Journal of Mathematics and Mathematical Sciences. 26・5. 317-319 (2001)
[Publications] M.Obradovic, S.Owa: "Analytic functions of non-Bazilevic type and starlikeness"International Journal of Mathematics and Mathematical Sciences. 26・11. 701-706 (2001)
[Publications] J.H.Choi, Y.C.Kim, S.Owa: "Fractional calculus operator and its applications in the univalent functions"Fractional Calculus and Applied Analysis. 4・3. 367-378 (2001)
[Publications] N.E.Cho.S.Y.Woo, S.Owa: "Argument estimates of certain meromorphic functions"Mathematica Balkanica. 15・3/4. 285-295 (2001)
[Publications] S.Saita, S.Owa: "Convolutions of certain analytic functions"Algebras, Groups and Geometries. 18・4. 375-383 (2001)
[Publications] O.S.Kwon, S.Owa: "The radius of β-convexity for the classes of λ-spirallike order α functions"Scientiae Mathematicae Japonicae. 5・11. 531-539 (2001)
[Publications] H.Kitamura, S.Owa: "On starlikeness and convexity of certain analytic functions International"International Journal of Applied Mathematics. 8・1. 25-59 (2002)
[Publications] S.Owa, M.Nunokawa, H.Saitoh, H.M.Srivastava: "Close-to-convexity, starlikeness, and convexity of certain analytic functions"Applied Mathematics Letters. 15・1. 63-69 (2002)
[Publications] S.Owa, S.Saita: "Generalization properties of convolutions"International Journal of Applied Mathematics. 8・4. 425-440 (2002)
[Publications] V.Pescar, S.Owa: "Sufficient conditions for univalence of certain integral operators"Indian Journal of Mathematics. 44・4. 1-5 (2002)
[Publications] J.Nishiwaki, S.Owa: "Coefficient inequalities for certain analytic functions"International Journal of Mathematics and Mathematical Sciences. 29・5. 285-290 (2002)
[Publications] R.K.Raina, H.M.Srivastava, A.A.Kilbas, M.Saigo: "Solvability of some Abel-type integral equations involving the Gauss hypergeometric function as kernels in the spaces of summable functions"ANZIAM Journal. 43・2. 291-320 (2001)
[Publications] M.Nunokawa, O.P.Ahuja: "On meromorphic starlike and convex functions"Indian Journal of Pure and Applied Mathematics. 32・7. 1027-1032 (2001)
[Publications] M.Nunokawa: "On close-to-concave functions"Science Reports of Faculty of Education, Gunma University. 49. 1-6 (2001)
[Publications] M.Nunokawa, S.Owa, A.Ikeda: "On the strongly starlikeness of multivalently convex functions of order α"International Journal of Mathematics and Mathematical. Sciences. 28・1. 51-56 (2001)
[Publications] O.S.Kwon, S.Owa: "Radius of strongly starlikeness for certain analytic functions"International Journal of Mathematics and Mathematical Sciences. 29・5. 271-278 (2002)

2001 Fiscal Year Annual Research Report

解析関数の部分和の性質についての研究

Principal Investigator

尾和 重義 近畿大学, 理工学部, 教授 (50088506)

Research Products

[Publications] S.Owa: "Partial sums of certain analytic functions"International Journal of Mathematics and Mathematical Sciences. 25・12. 771-775 (2001)

[Publications] N.E.Cho, S.Owa: "Sufficient conditions for meromorphic starlikeness and close-to-convexity of order α"International Journal of Mathematics and Mathematical Sciences. 26・5. 317-319 (2001)

[Publications] M.Obradovic, S.Owa: "Analytic functions of non-Bazilevic type and starlikeness"International Journal of Mathematics and Mathematical Sciences. 26・11. 701-706 (2001)

[Publications] J.H.Choi, Y.C.Kim, S.Owa: "Fractional calculus operator and its applications in the univalent functions"Fractional Calculus and Applied Analysis. 4・3. 367-378 (2001)

[Publications] N.E.Cho.S.Y.Woo, S.Owa: "Argument estimates of certain meromorphic functions"Mathematica Balkanica. 15・3/4. 285-295 (2001)

[Publications] S.Saita, S.Owa: "Convolutions of certain analytic functions"Algebras, Groups and Geometries. 18・4. 375-383 (2001)

[Publications] O.S.Kwon, S.Owa: "The radius of β-convexity for the classes of λ-spirallike order α functions"Scientiae Mathematicae Japonicae. 5・11. 531-539 (2001)

[Publications] H.Kitamura, S.Owa: "On starlikeness and convexity of certain analytic functions International"International Journal of Applied Mathematics. 8・1. 25-59 (2002)

[Publications] S.Owa, M.Nunokawa, H.Saitoh, H.M.Srivastava: "Close-to-convexity, starlikeness, and convexity of certain analytic functions"Applied Mathematics Letters. 15・1. 63-69 (2002)

[Publications] S.Owa, S.Saita: "Generalization properties of convolutions"International Journal of Applied Mathematics. 8・4. 425-440 (2002)

[Publications] V.Pescar, S.Owa: "Sufficient conditions for univalence of certain integral operators"Indian Journal of Mathematics. 44・4. 1-5 (2002)

[Publications] J.Nishiwaki, S.Owa: "Coefficient inequalities for certain analytic functions"International Journal of Mathematics and Mathematical Sciences. 29・5. 285-290 (2002)

[Publications] R.K.Raina, H.M.Srivastava, A.A.Kilbas, M.Saigo: "Solvability of some Abel-type integral equations involving the Gauss hypergeometric function as kernels in the spaces of summable functions"ANZIAM Journal. 43・2. 291-320 (2001)

[Publications] M.Nunokawa, O.P.Ahuja: "On meromorphic starlike and convex functions"Indian Journal of Pure and Applied Mathematics. 32・7. 1027-1032 (2001)

[Publications] M.Nunokawa: "On close-to-concave functions"Science Reports of Faculty of Education, Gunma University. 49. 1-6 (2001)

[Publications] M.Nunokawa, S.Owa, A.Ikeda: "On the strongly starlikeness of multivalently convex functions of order α"International Journal of Mathematics and Mathematical. Sciences. 28・1. 51-56 (2001)

[Publications] O.S.Kwon, S.Owa: "Radius of strongly starlikeness for certain analytic functions"International Journal of Mathematics and Mathematical Sciences. 29・5. 271-278 (2002)

尾和重義近畿大学, 理工学部, 教授 (50088506)