Geodesic
Applications of the Fixed Point Index in Menger PN-Spaces
Matematičeskie zametki, Tome 91 (2012) no. 5, pp. 773-779.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, applications of the fixed-point index of a nonlinear operator in Menger PN-spaces are given. Theorems on the existence of fixed points of a compact continuous operator are obtained. At the same time, the existence of the solution of a class of differential equations in a complete Menger PN-space is studied, and the theorem on the existence of the solution of a class of differential equations is obtained.
Keywords: fixed-point index, probabilistic normed space, Menger PN-space, completeness, distribution function.
Mots-clés : $T$-retraction 
@article{MZM_2012_91_5_a12,
     author = {Chuanxi Zhu and Qiuying Li},
     title = {Applications of the {Fixed} {Point} {Index} in {Menger} {PN-Spaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {773--779},
     publisher = {mathdoc},
     volume = {91},
     number = {5},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_91_5_a12/}
}
TY  - JOUR
AU  - Chuanxi Zhu
AU  - Qiuying Li
TI  - Applications of the Fixed Point Index in Menger PN-Spaces
JO  - Matematičeskie zametki
PY  - 2012
SP  - 773
EP  - 779
VL  - 91
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2012_91_5_a12/
LA  - ru
ID  - MZM_2012_91_5_a12
ER  - 
%0 Journal Article
%A Chuanxi Zhu
%A Qiuying Li
%T Applications of the Fixed Point Index in Menger PN-Spaces
%J Matematičeskie zametki
%D 2012
%P 773-779
%V 91
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2012_91_5_a12/
%G ru
%F MZM_2012_91_5_a12
Chuanxi Zhu; Qiuying Li. Applications of the Fixed Point Index in Menger PN-Spaces. Matematičeskie zametki, Tome 91 (2012) no. 5, pp. 773-779. http://geodesic.mathdoc.fr/item/MZM_2012_91_5_a12/

[1] Kiuing Li, Chuangsi Zhu, “Indeks nepodvizhnoi tochki nelineinogo operatora v PN-prostranstvakh Mengera”, Matem. zametki, 90:1 (2011), 104–112

[2] S. S. Chang, J. C. Yeol, M. K. Shi, Probabilistic Metric Spaces and Nonlinear Operator Theory, Sichuan Univ. Press, Chengdu, 1994

[3] S. Zhang, Y. Chen, “Topological degree theory and fixed point theorems in probabilistic metric spaces”, Appl. Math. Mech. (English Ed.), 10:6 (1989), 495–505 | DOI | MR | Zbl

[4] M. Y. Ye, Research on Some Problems of Nonlinear Operators in the PM-Space, Master's degree thesis, Nanchang University, 2006

[5] S. S. Chang, B. S. Lee, Y. J. Cho, Y. Q. Chen, S. M. Kang, J. S. Jung, “Generalized contraction mapping principle and differential equations in probabilistic metric spaces”, Proc. Amer. Math. Soc., 124:8 (1996), 2367–2376 | DOI | MR | Zbl

[6] Q. Li, C. Zhu, “Some new fixed points in a Z-P-S space”, J. Systems Sci. Math. Sci., 28:4 (2008), 400–405 | MR | Zbl

[7] C. Zhu, “Several nonlinear operator problems in the Menger PN space”, Nonlinear Anal., 65:7 (2006), 1281–1284 | DOI | MR | Zbl

[8] C. Zhu, “Generalizations of Krasnoselskii's theorem and Petryshyn's theorem”, Appl. Math. Lett., 19:7 (2006), 628–632 | DOI | MR | Zbl

[9] C. X. Zhu, Z. B. Xu, “A class of random operator equations in the Hilbert space”, Acta Math. Sinica (Chin. Ser.), 47:4 (2004), 641–646 | MR | Zbl

[10] C. X. Zhu, “Some theorems in the X-M-PN Space”, Appl. Math. Mech. (English Ed.), 21:2 (2000), 181–184 | MR | Zbl

[11] C. Zhu, Z. Xu, “Inequalities and solution of an operator equation”, Appl. Math. Lett., 21:6 (2008), 607–611 | DOI | MR | Zbl

[12] C. Zhu, C. Chen, “Calculations of random fixed point index”, J. Math. Anal. Appl., 339:2 (2008), 839–844 | DOI | MR | Zbl