1998 年度実績報告書

分数微積分の単葉・多葉関数の族への応用の研究

研究課題

研究課題/領域番号	09640238
研究機関	福岡大学
研究代表者	西郷恵福岡大学, 理学部, 教授 (10040403)
研究分担者	斎藤斉群馬工業高等専門学校, 教授 (10042607) 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)
キーワード	分数微積分 / 単葉関数 / 多葉関数 / 星型関数 / 凸型関数 / Gauss超幾何関数 / Appell超幾何関数 / サブオーデイネーション
研究概要	前年に引き続き,次のような研究をそれぞれ行った.西郷は分数微積分の応用として,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行った.本年は特に,Appellの超幾何関数F_3を核に含むものについて,その指数定理の検証が行われ,利用された.さらに,G-関数を含むKiryakova型の分数微積分の単葉関数への応用についても,いくつかの結果が得られ現在投稿準備中である.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.尾和は単位円板内の正規化された解析関数に対するSalageanの微分作用素,Ruscheweyhの微分作用素などを中心に,これらの作用素の単葉性,星型性,凸型性などについての研究を行った.また単位円板内の一様凸型関数の諸性質を考察するとともに一般化された超幾何関数の一様星型性や,一様凸型性なども考察した.斎藤は2階線形微分方程式W″+aW′+bW=0の解の単葉性,星型性について研究を行った.また応用として,Weber微分方程式の解の星型性についても調べた.これらの研究は古くから知られているNehariやRobertsonの結果とも関連がある.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,尾和が2回,斎藤が1回福岡大学に出張し,本研究グループとの研究連絡を行った.また,尾和が山口市に出張し,研究発表をし他の研究者との研究打ち合わせを行った.さらに宮崎大学.川野日郎を福岡大学に招き共同研究を行った.さらに本研究の協力者として,福岡大学大学院学生.池田彰を,伊勢市での研究集会に派遣した.一方,吉田が韓国・安東大学における第6回有限または無限次元複素解析研究集会での講演のために出張した.

研究成果

(22件)

すべてその他

すべて文献書誌 (22件)

[文献書誌] Megumi Saigo and A.A. Kil-bas: "On Mittag-Leffler type function and applications" Integral Transforms and Special Functions. 7(1-2). 97-112 (1998)
[文献書誌] S.A. Shlapakov, Megumi Saigo and A.A. Kilbas: "On inversion of H-transform in L_v,_r-spaces" International Journal of Mathematics and Mathematical Sciences. 21(4). 713-722 (1998)
[文献書誌] V.S. Kiryakova, Megumi Saigo and H.M.Srivastava: "Some criteria univalence of analytic functions involving generalized fractional cal-culus" Fractional Calculus & Applied Analysis. 1(1). 79-104 (1998)
[文献書誌] J.H. Choi and Megumi Saigo: "Starlike and convex functions of complex order involving a certain fractional integral operator" Fukuoka University Science Reports. 28(2). 29-40 (1998)
[文献書誌] A.A. Kilbas and Megumi: "Fractional calculus of the H-function" Fukuoka University Science Reports. 28(2). 41-51 (1998)
[文献書誌] Megumi Saigo and R.K.Sax-ena: "Expansions of _4F_3 when the upper parameters differ by integers" Kyungpook Mathematical Journal. 38(2). 293-299 (1998)
[文献書誌] A.A. Kilbas and Megumi Saigo: "Application of fractional calculus to solve Abel-Volterra nonlinear and linear integral equations" Proceedings of second International Workshop, Transform Methods and Special Functions,Varna'96. 236-263 (1998)
[文献書誌] Megumi Saigo and Nobuyuki Maeda: "More generalization of fractional calculus" Proceedings of Second International Workshop,Transform Methods and Special Functions, Varna'96. 386-400 (1998)
[文献書誌] Vu Kim Tuan and Megumi Saigo: "Modified fractional integral operators in L_p space with power-logarithmic weight" Mathematica Japonica. 49(1). 145-150 (1999)
[文献書誌] A.A. Kilbas and Megumi Saigo: "On solution of nonlinear Abel-Volterra ingegral equation" Journal of Mathematical Analysis and Applications. 239(1). 41-60 (1999)
[文献書誌] Megumi Saigo and A.A. Kil-bas: "Generalized fractional calculus of the H-function" Fukuoka University Science Reports. 29(1). 31-45 (1999)
[文献書誌] N.E. Cho, I.H. Kim, M. Nunokawa and S.Owa: "Angular estimations of certain analytic functions" Indian Journal Pure and Applied Mathematics. 29(3). 321-331 (1998)
[文献書誌] N. Niwa, T. Jimbo and S. Owa: "Hardy class of functions defined by the Salagean operator" Annales Polonici Mathematici. 69(1). 25-30 (1998)
[文献書誌] J.L. Li and S. Owa: "Properties of the Salagean operator" Georgian Mathematical Journal. 5(4). 361-366 (1998)
[文献書誌] S. Owa and H. M. Srivastava: "Distortion inequalities for Ruscheweyh derivatives" Mathematical Inequalities and Applications. 1(2). 239-246 (1998)
[文献書誌] S.Owa: "On uniformly convex functions" Mathematica Japonica. 48(3). 377-384 (1998)
[文献書誌] S.Owa: "Generalization properties for certain analytic functions" International Journal of Mathematics and Mathematical Sciences. 21(4). 707-712 (1998)
[文献書誌] S.Owa: "Some properties of Ruscheweyh derivatives" Kyungpook Mathematical Journal. 38(1). 99-104 (1998)
[文献書誌] H.Saitoh: "On certain subclasses of analytic functions involving a linear operator" Proceedings of Second International Workshop,Transform Methods and Special Functions,Varna'96. 401-411 (1998)
[文献書誌] H.Saitoh: "Starlikeness of certain integrals" Mathematical Sciences Research Hot-Line. 2(1). 23-26 (1998)
[文献書誌] T.Honda, M. Miyagi, M.Nishihara and M. Yoshida: "Topologies on the space of all n-homogeneous polynomials of nitegral type on locally convex spaces" Proceedings of the Sixth International colloquium on Finite or Infinte Dimensional Complex Analysis,Andong,Korea July 27-July 30. 70-73 (1998)
[文献書誌] M.Yoshida: "On some bilinear forms" Proceedins of the Sixth International Colloquium of Finite or Infinte Dimensional complex Analysis,Andong,Korea July 27-July 30. 184-187 (1998)

1998 年度 実績報告書

分数微積分の単葉・多葉関数の族への応用の研究

研究代表者

西郷 恵 福岡大学, 理学部, 教授 (10040403)

研究成果

[文献書誌] Megumi Saigo and A.A. Kil-bas: "On Mittag-Leffler type function and applications" Integral Transforms and Special Functions. 7(1-2). 97-112 (1998)

[文献書誌] S.A. Shlapakov, Megumi Saigo and A.A. Kilbas: "On inversion of H-transform in L_v,_r-spaces" International Journal of Mathematics and Mathematical Sciences. 21(4). 713-722 (1998)

[文献書誌] V.S. Kiryakova, Megumi Saigo and H.M.Srivastava: "Some criteria univalence of analytic functions involving generalized fractional cal-culus" Fractional Calculus & Applied Analysis. 1(1). 79-104 (1998)

[文献書誌] J.H. Choi and Megumi Saigo: "Starlike and convex functions of complex order involving a certain fractional integral operator" Fukuoka University Science Reports. 28(2). 29-40 (1998)

[文献書誌] A.A. Kilbas and Megumi: "Fractional calculus of the H-function" Fukuoka University Science Reports. 28(2). 41-51 (1998)

[文献書誌] Megumi Saigo and R.K.Sax-ena: "Expansions of _4F_3 when the upper parameters differ by integers" Kyungpook Mathematical Journal. 38(2). 293-299 (1998)

[文献書誌] A.A. Kilbas and Megumi Saigo: "Application of fractional calculus to solve Abel-Volterra nonlinear and linear integral equations" Proceedings of second International Workshop, Transform Methods and Special Functions,Varna'96. 236-263 (1998)

[文献書誌] Megumi Saigo and Nobuyuki Maeda: "More generalization of fractional calculus" Proceedings of Second International Workshop,Transform Methods and Special Functions, Varna'96. 386-400 (1998)

[文献書誌] Vu Kim Tuan and Megumi Saigo: "Modified fractional integral operators in L_p space with power-logarithmic weight" Mathematica Japonica. 49(1). 145-150 (1999)

[文献書誌] A.A. Kilbas and Megumi Saigo: "On solution of nonlinear Abel-Volterra ingegral equation" Journal of Mathematical Analysis and Applications. 239(1). 41-60 (1999)

[文献書誌] Megumi Saigo and A.A. Kil-bas: "Generalized fractional calculus of the H-function" Fukuoka University Science Reports. 29(1). 31-45 (1999)

[文献書誌] N.E. Cho, I.H. Kim, M. Nunokawa and S.Owa: "Angular estimations of certain analytic functions" Indian Journal Pure and Applied Mathematics. 29(3). 321-331 (1998)

[文献書誌] N. Niwa, T. Jimbo and S. Owa: "Hardy class of functions defined by the Salagean operator" Annales Polonici Mathematici. 69(1). 25-30 (1998)

[文献書誌] J.L. Li and S. Owa: "Properties of the Salagean operator" Georgian Mathematical Journal. 5(4). 361-366 (1998)

[文献書誌] S. Owa and H. M. Srivastava: "Distortion inequalities for Ruscheweyh derivatives" Mathematical Inequalities and Applications. 1(2). 239-246 (1998)

[文献書誌] S.Owa: "On uniformly convex functions" Mathematica Japonica. 48(3). 377-384 (1998)

[文献書誌] S.Owa: "Generalization properties for certain analytic functions" International Journal of Mathematics and Mathematical Sciences. 21(4). 707-712 (1998)

[文献書誌] S.Owa: "Some properties of Ruscheweyh derivatives" Kyungpook Mathematical Journal. 38(1). 99-104 (1998)

[文献書誌] H.Saitoh: "On certain subclasses of analytic functions involving a linear operator" Proceedings of Second International Workshop,Transform Methods and Special Functions,Varna'96. 401-411 (1998)

[文献書誌] H.Saitoh: "Starlikeness of certain integrals" Mathematical Sciences Research Hot-Line. 2(1). 23-26 (1998)

[文献書誌] M.Yoshida: "On some bilinear forms" Proceedins of the Sixth International Colloquium of Finite or Infinte Dimensional complex Analysis,Andong,Korea July 27-July 30. 184-187 (1998)

1998 年度実績報告書

西郷恵福岡大学, 理学部, 教授 (10040403)