Geodesic
Fixed point theorems of nondecreasing order-Ćirić-Lipschitz mappings in normed vector spaces without normalities of cones
Li, Zhilong1 ; Jiang, Shujun2
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
Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 1, p. 18-26.

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

We introduce the concept of order-Ćirić-Lipschitz mappings, and prove some fixed point theorems for such kind of mappings in normed vector spaces without assuming the normalities of cones by using upper and lower solutions method, which improve many existing results of order-Lipschitz mappings in Banach spaces or Banach algebras. It is worth mentioning that even in the setting of normal cones, the main results in this paper are still new since the sum of spectral radius or the sum of restricted constants may be greater than or equal to 1.
DOI : 10.22436/jnsa.010.01.02
Classification : 06A07, 47H10
Keywords: Fixed point, order-C´ iric´-Lipschitz mapping, Picard-complete, w-complete.

Li, Zhilong 1 ; Jiang, Shujun 2

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 
@article{JNSA_2017_10_1_a1,
     author = {Li, Zhilong and Jiang, Shujun},
     title = {Fixed point theorems of nondecreasing {order-\'Ciri\'c-Lipschitz} mappings in normed vector spaces without normalities of cones},
     journal = {Journal of nonlinear sciences and its applications},
     pages = {18-26},
     publisher = {mathdoc},
     volume = {10},
     number = {1},
     year = {2017},
     doi = {10.22436/jnsa.010.01.02},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.01.02/}
}
TY  - JOUR
AU  - Li, Zhilong
AU  - Jiang, Shujun
TI  - Fixed point theorems of nondecreasing order-Ćirić-Lipschitz mappings in normed vector spaces without normalities of cones
JO  - Journal of nonlinear sciences and its applications
PY  - 2017
SP  - 18
EP  - 26
VL  - 10
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.01.02/
DO  - 10.22436/jnsa.010.01.02
LA  - en
ID  - JNSA_2017_10_1_a1
ER  - 
%0 Journal Article
%A Li, Zhilong
%A Jiang, Shujun
%T Fixed point theorems of nondecreasing order-Ćirić-Lipschitz mappings in normed vector spaces without normalities of cones
%J Journal of nonlinear sciences and its applications
%D 2017
%P 18-26
%V 10
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.01.02/
%R 10.22436/jnsa.010.01.02
%G en
%F JNSA_2017_10_1_a1
Li, Zhilong; Jiang, Shujun. Fixed point theorems of nondecreasing order-Ćirić-Lipschitz mappings in normed vector spaces without normalities of cones. Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 1, p. 18-26. doi : 10.22436/jnsa.010.01.02. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.01.02/

[1] S. Banach Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fundam. Math., Volume 3 (1922), pp. 133-181

[2] S. K. Chatterjea Fixed point theorems, C. R. Acad. Bulgare Sci., Volume 25 (1972), pp. 727-730

[3] Ćirić, L. B. Generalized contractions and fixed-point theorems, Publ. Inst. Math., Volume 12 (1971), pp. 19-26

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

[5] 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

[6] Jiang, 6] 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

[7] Kannan, R. Some results on fixed points, Bull. Calcutta Math. Soc., Volume 60 (1968), pp. 71-76

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

[9] 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

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

[11] 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

Cité par Sources :