Geodesic
On order-Lipschitz mappings in Banach spaces without normalities of involving cones
Li, Zhilong1 ; Jiang, Shujun2 ; Lazovic, Rade3
1 School of Statistics, Jiangxi University of Finance and Economics, Nanchang, 330013, China;Research Center of Applied Statistics, Jiangxi University of Finance and Economics, Nanchang, 330013, China
2 Department of Mathematics, Jiangxi University of Finance and Economics, Nanchang, 330013, China
3 Faculty of Organizational Sciences, University of Belgrade, Jove Ilica 154, Belgrade, Serbia
Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 1, p. 27-33.

Voir la notice de l'article provenant de la source International Scientific Research Publications

We prove a new fixed point theorem of order-Lipschitz mappings in Banach spaces without assumption of normalities of the involving cones, which presents a positive answer to a problem raised in [S. Jiang, Z. Li, Fixed Point Theory Appl., 2016 (2016), 10 pages] and improves the corresponding results of Krasnoselskii and Zabreiko’s and Zhang and Sun’s since the normality of the involving cone is removed.
DOI : 10.22436/jnsa.010.01.03
Classification : 06A07, 47H10
Keywords: Fixed point theorem, order-Lipschitz mapping, Picard-completeness, non-normal cone.

Li, Zhilong 1 ; Jiang, Shujun 2 ; Lazovic, Rade 3

1 School of Statistics, Jiangxi University of Finance and Economics, Nanchang, 330013, China;Research Center of Applied Statistics, Jiangxi University of Finance and Economics, Nanchang, 330013, China
2 Department of Mathematics, Jiangxi University of Finance and Economics, Nanchang, 330013, China
3 Faculty of Organizational Sciences, University of Belgrade, Jove Ilica 154, Belgrade, Serbia 
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Li, Zhilong; Jiang, Shujun; Lazovic, Rade. On order-Lipschitz mappings in Banach spaces without normalities of involving cones. Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 1, p. 27-33. doi : 10.22436/jnsa.010.01.03. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.01.03/

[1] Deimling, K. Nonlinear functional analysis, Springer-Verlag, Berlin, 1985

[2] Jiang, S.; Li, Z. Extensions of Banach contraction principle to partial cone metric spaces over a non-normal solid cone, Fixed Point Theory Appl., Volume 2013 (2013 ), pp. 1-9 | DOI | Zbl

[3] Jiang, S.; Li, Z. Fixed point theorems of order-Lipschitz mappings in Banach algebras, Fixed Point Theory Appl., Volume 2016 (2016 ), pp. 1-10 | DOI | Zbl

[4] Krasnosel’skiĭ, M. A.; Zabreĭko, P. P. Geometrical methods of nonlinear analysis, Springer-Verlag, Berlin, 1984 | DOI

[5] Li, Z.; Jiang, S. Common fixed point theorems of contractions in partial cone metric spaces over nonnormal cones, Abstr. Appl. Anal., Volume 2014 (2014 ), pp. 1-8

[6] Sun, J.-X. Iterative solutions of nonlinear operator, (Chinese) J. Engin. Math., Volume 6 (1989), pp. 12-17

[7] Zhang, X. Y.; Sun, J. X. Existence and uniqueness of solutions for a class of nonlinear operator equations and its applications, (Chinese) Acta Math. Scientia, Volume 25 (2005), pp. 846-851

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