2000 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, 理工学部, 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f_n(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(印刷中)』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・凸型半径が考察された。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。部分和の研究に対する今後の課題は、解析関数の様々な性質を応用して、部分和に対する新しい考察の方法を発見することである。さらに、有理型星型関数や有理型凸型関数についても、それらの極値関数を求めて、部分和の諸性質を考察することが要求される。論文『Properties of certain integral operators,Southeast Asian Bulletin of Mathematics 24(2000),411-419』では、解析関数の積分作用素に対してガウスの超幾何関数_2F_1(z)の性質が応用されて、解析関数の積分作用素の様々な性質が導かれた。この種の問題に対しても、今後は有理型解析関数の積分作用素への拡張を考えなければならない。さらに、論文『Analytic functions of non-Bazilevic type and starlikeness,International Journal of Mathematics and Mathematical Sciences(掲載決定)』では、解析関数の部分族に対して新しい形の微分形式が適用されて、解析関数の新しい性質が考察された。この研究の方法は今後星型関数族や凸型関数族などの、様々な解析関数の族に応用されるものと考えられる。上述のように、本研究に対する研究成果が様々な方向から得られつつあるが、今後に対する新たな課題も現れつつある。

Research Products
(20 results)

All Other

All Publications (20 results)

[Publications] S.Owa and J.Patel: "Properties of certain integral operators"Southeast Asian Bulletin of Mathematics. 24・3. 411-419 (2000)
[Publications] N.E.Cho arid S.Owa: "Argument estimates of meromorphically multivalent functions"Journal of Inequalities and Applications. 5・5. 419-432 (2000)
[Publications] V.Pescar and S.Owa: "Univalence of certain integral operators"International Journal of Mathematics and Mathematical Sciences. 23・10. 697-701 (2000)
[Publications] M.Obradovic and S.Owa: "Some sufficient conditions for strongly starlikeness"International Journal of Mathematics and Mathematical Sciences. 24・9. 643-647 (2000)
[Publications] N.E.Cho and S.Owa: "Sufficient conditions for meromorphic starlikeness and close-to-convexuty of order α"International Journal of Mathematics and Mathematical Sciences. (inpress). (2001)
[Publications] S.Owa: "Partial sums of certain analytic functions"International Journal of Mathematics and Mathematical Sciences. (inpress). (2001)
[Publications] M.Obradovic and S.0wa: "Analytic functions of non-Bazilevic type and starlikeness"International Journal of Mathematics and Mathematical Sciences. (to appear).
[Publications] N.E.Cho,S,Y.Woo and S.Owa: "Argument estimatesof certain meromorphic functions"Mathematica Balkanica. (to appear).
[Publications] M.Saigo and A.A.Kilbas: "The solution of a class of linear differential equations via functions of the Mittag-Leffler"Differential Equations. 36・2. 168-176 (2000)
[Publications] Y.C.Kim,A.Lecko,J.H.Choi and M.Saigo: "Differential subordinations for fractional-linear transformations"International Journal of Mathematics and Mathematical Sciences. 23・2. 109-117 (2000)
[Publications] R.K.Saxena and M.Saigo: "An integral equation containing product of Gauss hypergeomentric function and the H-function in the kernel"Journal of Fractional Calculus. 17. 103-114 (2000)
[Publications] H.-J.Glaeske,A.A.Kilbas and M.Saigo: "A modified Bessel-type integral transform and its compositions with fractional calculus operators on the space F_p,μ and F'_p,μ"Journal of Computational and Applied Mathematics. 118. 151-168 (2000)
[Publications] V.K.Tuan,A.Ismail and M.Saigo: "Plancherel and Paley-Wiener theorems for an index integral transform"Journal of the Korean Mathematical Society. 37・4. 545-563 (2000)
[Publications] A.A.Kilbas and M.Saigo: "Modified H-transforms in Lv,r-spaces"Demonstratio Mathematica. 33・3. 603-625 (2000)
[Publications] Y.C.Kim,J.H.Choi and M.Saigo: "Some properties of convolution operators involving Carlson-Shaffer operator"PanAmerican Mathematical Journal. 10・2. 51-60 (2000)
[Publications] M.Saigo and A.A.Kilbas: "Modified G-transforms and generalized Stieltjes transform in Lv,r-space"Fukuoka University Science Reports. 30・2. 181-200 (2000)
[Publications] 0.P.Ahuja and M.Nunokawa: "Neighborhoods of analytic functions defined by Ruscheweyh derivatives"Mathematica Japonica. 51・3. 181-200 (2000)
[Publications] 布川護,関根忠行,高橋典宏: "凸型性と星型性に関する尾和予想について"群馬大学教育学部紀要. 48. 1-4 (2000)
[Publications] M.Nunokawa and S.Owa: "On certain conditions for starlikeness"Southeast Asian Bulletin of Mathematics. (to appear).
[Publications] M.Nunokawa,S.0wa and A.Ikeda: "On the strongly starlikeness of multivalently convex functions of order α"International Journal of Mathematics and Mathematical Sciences. (to appear).

2000 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 and J.Patel: "Properties of certain integral operators"Southeast Asian Bulletin of Mathematics. 24・3. 411-419 (2000)

[Publications] N.E.Cho arid S.Owa: "Argument estimates of meromorphically multivalent functions"Journal of Inequalities and Applications. 5・5. 419-432 (2000)

[Publications] V.Pescar and S.Owa: "Univalence of certain integral operators"International Journal of Mathematics and Mathematical Sciences. 23・10. 697-701 (2000)

[Publications] M.Obradovic and S.Owa: "Some sufficient conditions for strongly starlikeness"International Journal of Mathematics and Mathematical Sciences. 24・9. 643-647 (2000)

[Publications] N.E.Cho and S.Owa: "Sufficient conditions for meromorphic starlikeness and close-to-convexuty of order α"International Journal of Mathematics and Mathematical Sciences. (inpress). (2001)

[Publications] S.Owa: "Partial sums of certain analytic functions"International Journal of Mathematics and Mathematical Sciences. (inpress). (2001)

[Publications] M.Obradovic and S.0wa: "Analytic functions of non-Bazilevic type and starlikeness"International Journal of Mathematics and Mathematical Sciences. (to appear).

[Publications] N.E.Cho,S,Y.Woo and S.Owa: "Argument estimatesof certain meromorphic functions"Mathematica Balkanica. (to appear).

[Publications] M.Saigo and A.A.Kilbas: "The solution of a class of linear differential equations via functions of the Mittag-Leffler"Differential Equations. 36・2. 168-176 (2000)

[Publications] Y.C.Kim,A.Lecko,J.H.Choi and M.Saigo: "Differential subordinations for fractional-linear transformations"International Journal of Mathematics and Mathematical Sciences. 23・2. 109-117 (2000)

[Publications] R.K.Saxena and M.Saigo: "An integral equation containing product of Gauss hypergeomentric function and the H-function in the kernel"Journal of Fractional Calculus. 17. 103-114 (2000)

[Publications] H.-J.Glaeske,A.A.Kilbas and M.Saigo: "A modified Bessel-type integral transform and its compositions with fractional calculus operators on the space F_p,μ and F'_p,μ"Journal of Computational and Applied Mathematics. 118. 151-168 (2000)

[Publications] V.K.Tuan,A.Ismail and M.Saigo: "Plancherel and Paley-Wiener theorems for an index integral transform"Journal of the Korean Mathematical Society. 37・4. 545-563 (2000)

[Publications] A.A.Kilbas and M.Saigo: "Modified H-transforms in Lv,r-spaces"Demonstratio Mathematica. 33・3. 603-625 (2000)

[Publications] Y.C.Kim,J.H.Choi and M.Saigo: "Some properties of convolution operators involving Carlson-Shaffer operator"PanAmerican Mathematical Journal. 10・2. 51-60 (2000)

[Publications] M.Saigo and A.A.Kilbas: "Modified G-transforms and generalized Stieltjes transform in Lv,r-space"Fukuoka University Science Reports. 30・2. 181-200 (2000)

[Publications] 0.P.Ahuja and M.Nunokawa: "Neighborhoods of analytic functions defined by Ruscheweyh derivatives"Mathematica Japonica. 51・3. 181-200 (2000)

[Publications] 布川護,関根忠行,高橋典宏: "凸型性と星型性に関する尾和予想について"群馬大学教育学部紀要. 48. 1-4 (2000)

[Publications] M.Nunokawa and S.Owa: "On certain conditions for starlikeness"Southeast Asian Bulletin of Mathematics. (to appear).

[Publications] M.Nunokawa,S.0wa and A.Ikeda: "On the strongly starlikeness of multivalently convex functions of order α"International Journal of Mathematics and Mathematical Sciences. (to appear).

尾和重義近畿大学, 理工学部, 教授 (50088506)