×

Multivalued generalized nonlinear contractive maps and fixed points. (English) Zbl 1206.54050

Summary: We introduce some notions of generalized nonlinear contractive maps and prove some fixed point results for such maps. Consequently, several known fixed point results are either improved or generalized including the corresponding recent fixed point results of L. B. Ćirić [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 7–8, A, 2716–2723 (2009; Zbl 1179.54053)], D. Klim and D. Wardowski [J. Math. Anal. Appl. 334, No. 1, 132–139 (2007; Zbl 1133.54025)], Y. Feng and S. Liu [ibid. 317, No. 1, 103–112 (2006; Zbl 1094.47049)] and N. Mizoguchi and W. Takahashi [ibid. 141, No. 1, 177–188 (1989; Zbl 0688.54028)].

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54C60 Set-valued maps in general topology
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Nadler, S. B., Multivalued contraction mappings, Pacific J. Math., 30, 475-488 (1969) · Zbl 0187.45002
[2] Mizoguchi, N.; Takahashi, W., Fixed point theorems for multivalued mappings on complete metric spaces, J. Math. Anal. Appl., 141, 177-188 (1989) · Zbl 0688.54028
[3] Feng, Y.; Liu, S., Fixed point theorems for multivalued contractive mappings and multivalued Caristi type mappings, J. Math. Anal. Appl., 317, 103-112 (2006) · Zbl 1094.47049
[4] Klim, D.; Wardowski, D., Fixed point theorems for set-valued contractions in complete metric spaces, J. Math. Anal. Appl., 334, 132-139 (2007) · Zbl 1133.54025
[5] Ciric, L. B., Multivalued nonlinear contraction mappings, Nonlinear Anal., 71, 2716-2723 (2009) · Zbl 1179.54053
[6] Kada, O.; Susuki, T.; Takahashi, W., Nonconvex minimization theorems and fixed point theorems in complete metric spaces, Math. Japon., 44, 381-391 (1996) · Zbl 0897.54029
[7] Takahashi, W., Nonlinear Functional Analysis: Fixed Point Theory and its Applications (2000), Yokohama Publishers · Zbl 0997.47002
[8] Lin, L. J.; Du, W. S., Some equivalent formulations of the generalized Ekland’s variational principle and their applications, Nonlinear Anal., 67, 187-199 (2007) · Zbl 1111.49013
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.