Topological degree for 1-set-contractive fields in M-PN spaces and its applications

Applied Mathematics-A Journal of Chinese Universities - Tập 25 Số 4 - Trang 463-474 - 2010
Zhaoqi Wu1, Chuanxi Zhu1
1Department of Mathematics, Zhejiang University, Hangzhou, China

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Tài liệu tham khảo

G Bocsan, G Constantin. The Kuratowski function and some applications to the probabilistic metric spaces, Atti Accad Naz Lincei, 1973, 55: 236–240.

S S Chang, Y Q Chen. Nonlinear operator theory in probabilistic metric spaces, Appl Math Mech, 1989, 10: 717–741.

S S Chang, Y J Cho, S M Kang. Nonlinear Operator Theory in Probabilistic Metric Spaces, Nova Science Publishers, 2001.

J R Egbert. Products and quotients of probabilistic metric spaces, Pacific J Math, 1968, 24: 437–455.

O Hadžić. Fixed point theory in topological vector spaces, Univerzitet u Novom Sadu, Institut za Matematiku, Novi Sad, 1984.

X Q Huang, M S Wang, C X Zhu. The topological degree of A-proper mapping in the Menger PN-space (I), Bull Austral Math Soc, 2006, 73:161–168.

G Z Li, X Y Xu, H G Duan. Fixed point theorems of 1-set-contractive operators in Banach spaces, Appl Math Letters, 2006, 19: 403–412.

R D Nussbaum. Degree theory for local condensing maps, J Math Anal Appl, 1972, 37: 741–766.

V V Obukhovskiĭ. On the topological degree of multi-valued mappings in probabilistic normed spaces, Nonlinear operators in global analysis, Novoe Global Anal, Voronezh Gos Univ, Voronezh, 1991, 164: 141–146. (In Russian)

W V Petryshyn. Remark on condensing and k-set-contractive mappings, J Math Anal Appl, 1972, 39: 717–741.

A N Šerstnev. On the concept of a stochastic normalized space, Dokl Akad Nauk SSSR, 1963, 149: 280–283. (In Russian)

S Y Xu. New fixed point theorems for 1-set-contractive operators in Banach spaces, Nonlinear Anal, 2007, 67: 938–944.

C X Zhu. Some new fixed point theorems in probabilistic metric spaces, Appl Math Mech, 1995, 16: 179–185.

C X Zhu, X Q Huang. The topological degree of A-proper mapping in the Menger PN-space (II), Bull Austral Math Soc, 2006, 73: 169–173.

C X Zhu. Generalizations of Krasnoselskii’s theorem and Petryshyn’s theorem, Appl Math Lett, 2006, 19: 628–632.

C X Zhu. Several nonlinear operator problems in the Menger PN space, Nonlinear Anal, 2006, 65: 1281–1284.

C X Zhu, Z B Xu. Inequalities and solution of an operator equation, Appl Math Lett, 2008, 21: 607–611.

C X Zhu. Research on some problems for nonlinear operators, Nonlinear Anal, 2009, 71: 4568–4571.