×

zbMATH — the first resource for mathematics

Dynamic processes and fixed points of set-valued nonlinear contractions in cone metric spaces. (English) Zbl 1203.54042
Summary: Investigations concerning the existence of dynamic processes convergent to fixed points of set-valued nonlinear contractions in cone metric spaces are initiated. The conditions guaranteeing the existence and uniqueness of fixed points of such contractions are established. Our theorems generalize recent results obtained by L.-G. Huang and X. Zhang [J. Math. Anal. Appl. 332, No. 2, 1468–1476 (2007; Zbl 1118.54022)] for cone metric spaces and by D. Klim and D. Wardowski [J. Math. Anal. Appl. 334, No. 1, 132–139 (2007; Zbl 1133.54025)] for metric spaces. The examples and remarks provided show an essential difference between our results and those mentioned above.

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
54C60 Set-valued maps in general topology
26A18 Iteration of real functions in one variable
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Banach, S., Sur LES opérations dans LES ensembles abstraits et leur applications aux équations intégrales, Fund. math., 3, 133-181, (1922) · JFM 48.0201.01
[2] Klim, D.; Wardowski, D., Fixed point theorems for set-valued contractions in complete metric spaces, J. math. anal. appl., 334, 1, 132-139, (2007) · Zbl 1133.54025
[3] Huang, L.-G.; Zhang, X., Cone metric spaces and fixed point theorems of contractive maps, J. math. anal. appl., 332, 1467-1475, (2007)
[4] Deimling, K., Nonlinear functional analysis, (1985), Springer-Verlag · Zbl 0559.47040
[5] Aubin, J.P.; Siegel, J., Fixed points and stationary points of dissipative multivalued maps, Proc. amer. math. soc., 78, 391-398, (1980) · Zbl 0446.47049
[6] Aubin, J.P.; Ekeland, I., Applied nonlinear analysis, (1984), John Wiley and Sons, Inc.
[7] Berge, C., Topological spaces, (1963), Oliver and Boyd · Zbl 0114.38602
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.