1999 Fiscal Year Annual Research Report

分数微積分の単葉・多葉関数の族への応用の研究

Research Project

Project/Area Number	09640238
Research Institution	FUKUOKA UNIVERSITY
Principal Investigator	西郷恵福岡大学, 理学部, 教授 (10040403)
Co-Investigator(Kenkyū-buntansha)	尾和重義近畿大学, 理工学部, 教授 (50088506) 福嶋幸生福岡大学, 理学部, 助教授 (40099007) 吉田守福岡大学, 理学部, 教授 (60078607) 斎藤斉群馬工業高等専門学校, 教授 (10042607)
Keywords	分数微積分 / 単葉関数 / p-葉関数 / 星型関数 / 凸型関数 / Gauss超幾何関数 / H-関数 / H-変換
Research Abstract	前年に引き続き,次のような研究をそれぞれ行った. 西郷は単葉関数および多葉関数の単葉性,星型性,凸型性などについての研究を前年に引き続き行った.本年は特に,単葉関数に対する Marx-Strohhackerの定理をp-葉関数に拡張した.また,H-変換についての研究を継続し,特殊関数を含む変換のいくつかについて,既に得られたH-変換の結果を適用して興味あるものが得られた.吉田は弱型多項式や弱型正則関数が有界集合上弱連続であれば弱一様連続であることを,双対空間の双対空間に拡張して解決した.福嶋は正則関数と調和関数との関係を多変数の関数論,無限次元の関数論,Quaternion AnalysisやClifford Analysisで展開することを研究した.尾和は負係数を持つ解析関数族の問題について,これらの関数族の殆どが関数の係数不等式によって特徴付けられることに注目して,関数の係数不等式を保存しながら,負係数を持つ解析関数の一般化を試みて,様々な結果を得た.斎藤はある有界な関数族を導入して,2階線型微分方程式の解の幾何学的性質を研究した.この研究において,よく知られているエルミートの微分方程式,エアリーの微分方程式,ウェーバーの微分方程式などの解の単葉性と量型性について調べた. 以上の研究のために,この研究グループのメンバーは旅費を使用して相互に研究連絡,および研究集会での報告発表を行った.すなわち,尾和,斎藤が福岡大学に出張し,本研究グループの福岡大学メンバーとの研究連絡を行った.また,和歌山大学.福井誠一を福岡大学に招き共同研究を行った.そして,吉田が神奈川県葉山市における研究集会に出席した.さらに西郷がブルガリア・Blagoevgrad のAmerican University of Bulgariaにおける第3回「積分変換法と特殊関数」研究集会での招待講演のために出張した.

Research Products

(18 results)

All Other

All Publications (18 results)

[Publications] A.kilbas and M.Saigo: "On the H-function"Journal of Applied Mathmatics and Stochastic Analysis. 12-2. 191-204 (1999)
[Publications] Vu K.T.and M.Saigo: "Modified fractional integral operators in L_p space with power-logarithmic weight"Mathematica Japonica. 49-1. 145-150 (1999)
[Publications] A.A.Kilbas and M.Saigo: "On solution of nonlinear Abel-Volterra integral equation"Journal of Mathematical Analysis and Applications. 239-1. 41-60 (1999)
[Publications] M.Saigo and A.A.Kilbas: "Generalized factional calculus of the H-function"Fukuoka University Science Reports. 29-1. 31-45 (1999)
[Publications] A.A.Kilbas,R.K.Raina,M.Saigo and H.M.Srivastava: "0n Solution of Abel's type multidimensional hypergeometric integral equations(Russian)"Doklady Natsional'noi Akademii Nauk Belarusi. 43-2. 23-26 (1999)
[Publications] A.A.Kilbas,M.Saigo and H.-J.Glaeske: "Modified Bessel type integral transform and its compositions with fractional integration and differentiation operators (Russian)"Doklady Natsional'noi Akademii Nauk Belarusi. 43-4. 26-30 (1999)
[Publications] M.Saigo and R.K.Saxena: "Unified fractional integral formulas for the multivariable H-function"Journal of Fractional Calculus. 15. 91-107 (1999)
[Publications] S.Fukui,M.Saigo and A.Ikeda: "On the Marx-Strohhacker theorem in p-valently analytic functions(in Japanese)"京都大学数理解析研究所講究録. 1112. 17-25 (1999)
[Publications] M.Saigo and R.K.Saxena: "Unified fractional integral forrmulas for the multivariable H-function.II"Journal of Fractional Calculus. 16. 99-110 (1999)
[Publications] A.A.Kilbas,M.Saigo and A.N.Borovco: "Lommel-Maitland transform on L_<v,r>-space"Fractional Calculus & Applied Analysis. 2-4. 429-444 (1999)
[Publications] T.Honda,M.Miyagi,M.Nishihara and M.Yoshida: "Integral representations of continuous linear functions on a space of polynomials on any locally convex space and the dual of the space of approximable polynomials"Fukuoka Universit Science Reports. 29. 1-6 (1999)
[Publications] M.Yoshida: "On some bilinear forms"Proceeding of the Seventh International Colloquium on Finite or Infinite Dimensional Complex Analysis. 184-187 (1999)
[Publications] T.Honda,M.Miyagi,M.Nishihara and M.Yoshida: "On continuities of the Borel transforms on the duals of spaces of continuous n-homogeneous polynomials on locally convex spaces"Fukuoka Unibersity Science Reports. 30(in press). (2000)
[Publications] T.Sekine and S.Owa: "Coefficient inequalities for certain univalent functions"Mathematical Inequalities and Applications. 2-4. 535-544 (1999)
[Publications] H.Saitoh: "Univalence and starlikeness of solutions of W''+aW'+bW=0"Annales Universitaties Mariae Curie-Sklodowska Sect.A. 53. 209-216 (1999)
[Publications] M.Nunkawa,S.Owa,H.Saitoh and O.P.Ahuja: "On the quotient of the analytic representations of convex and starlike functions"京都大学数理解析研究講究録. 1112. 63-69 (1999)
[Publications] M.Nunokawa,H.Saitoh,S.Owa and H.M.Srivastav: "Close-to-convexity,starlikeness and convexity"京都大学数理解析研究講究録. 1112. 98-105 (1999)
[Publications] H.Saitoh: "Univalence and starlikeness of W''+aW'+bW=0"京都大学数理解析研究講究録. 1112. 113-123 (1999)

1999 Fiscal Year Annual Research Report

分数微積分の単葉・多葉関数の族への応用の研究

Principal Investigator

西郷 恵 福岡大学, 理学部, 教授 (10040403)

Research Products

[Publications] A.kilbas and M.Saigo: "On the H-function"Journal of Applied Mathmatics and Stochastic Analysis. 12-2. 191-204 (1999)

[Publications] Vu K.T.and M.Saigo: "Modified fractional integral operators in L_p space with power-logarithmic weight"Mathematica Japonica. 49-1. 145-150 (1999)

[Publications] A.A.Kilbas and M.Saigo: "On solution of nonlinear Abel-Volterra integral equation"Journal of Mathematical Analysis and Applications. 239-1. 41-60 (1999)

[Publications] M.Saigo and A.A.Kilbas: "Generalized factional calculus of the H-function"Fukuoka University Science Reports. 29-1. 31-45 (1999)

[Publications] A.A.Kilbas,R.K.Raina,M.Saigo and H.M.Srivastava: "0n Solution of Abel's type multidimensional hypergeometric integral equations(Russian)"Doklady Natsional'noi Akademii Nauk Belarusi. 43-2. 23-26 (1999)

[Publications] A.A.Kilbas,M.Saigo and H.-J.Glaeske: "Modified Bessel type integral transform and its compositions with fractional integration and differentiation operators (Russian)"Doklady Natsional'noi Akademii Nauk Belarusi. 43-4. 26-30 (1999)

[Publications] M.Saigo and R.K.Saxena: "Unified fractional integral formulas for the multivariable H-function"Journal of Fractional Calculus. 15. 91-107 (1999)

[Publications] S.Fukui,M.Saigo and A.Ikeda: "On the Marx-Strohhacker theorem in p-valently analytic functions(in Japanese)"京都大学数理解析研究所講究録. 1112. 17-25 (1999)

[Publications] M.Saigo and R.K.Saxena: "Unified fractional integral forrmulas for the multivariable H-function.II"Journal of Fractional Calculus. 16. 99-110 (1999)

[Publications] A.A.Kilbas,M.Saigo and A.N.Borovco: "Lommel-Maitland transform on L_<v,r>-space"Fractional Calculus & Applied Analysis. 2-4. 429-444 (1999)

[Publications] T.Honda,M.Miyagi,M.Nishihara and M.Yoshida: "Integral representations of continuous linear functions on a space of polynomials on any locally convex space and the dual of the space of approximable polynomials"Fukuoka Universit Science Reports. 29. 1-6 (1999)

[Publications] M.Yoshida: "On some bilinear forms"Proceeding of the Seventh International Colloquium on Finite or Infinite Dimensional Complex Analysis. 184-187 (1999)

[Publications] T.Honda,M.Miyagi,M.Nishihara and M.Yoshida: "On continuities of the Borel transforms on the duals of spaces of continuous n-homogeneous polynomials on locally convex spaces"Fukuoka Unibersity Science Reports. 30(in press). (2000)

[Publications] T.Sekine and S.Owa: "Coefficient inequalities for certain univalent functions"Mathematical Inequalities and Applications. 2-4. 535-544 (1999)

[Publications] H.Saitoh: "Univalence and starlikeness of solutions of W''+aW'+bW=0"Annales Universitaties Mariae Curie-Sklodowska Sect.A. 53. 209-216 (1999)

[Publications] M.Nunkawa,S.Owa,H.Saitoh and O.P.Ahuja: "On the quotient of the analytic representations of convex and starlike functions"京都大学数理解析研究講究録. 1112. 63-69 (1999)

[Publications] M.Nunokawa,H.Saitoh,S.Owa and H.M.Srivastav: "Close-to-convexity,starlikeness and convexity"京都大学数理解析研究講究録. 1112. 98-105 (1999)

[Publications] H.Saitoh: "Univalence and starlikeness of W''+aW'+bW=0"京都大学数理解析研究講究録. 1112. 113-123 (1999)

西郷恵福岡大学, 理学部, 教授 (10040403)