×

Some new results and generalizations in metric fixed point theory. (English) Zbl 1190.54030

Summary: The main purpose of this paper is the study of the generalization of some results given in [M.Berinde and V.Berinde, J. Math.Anal.Appl.326, No.2, 772–782 (2007; Zbl 1117.47039) and references therein]. Some generalizations of the Mizoguchi-Takahashi fixed point theorem, Kannan’s fixed point theorems and Chatterjea’s fixed point theorems are established by using our new fixed point theorems.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54C60 Set-valued maps in general topology

Citations:

Zbl 1117.47039
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Berinde, M.; Berinde, V., On a general class of multi-valued weakly Picard mappings, J. Math. Anal. Appl., 326, 772-782 (2007) · Zbl 1117.47039
[2] Daffer, P. Z.; Kaneko, H.; Li, W., On a conjecture of S. Reich, Proc. Amer. Math. Soc., 124, 3159-3162 (1996) · Zbl 0866.47040
[3] 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
[4] Suzuki, T., Mizoguchi-Takahashi’s fixed point theorem is a real generalization of Nadler’s, J. Math. Anal. Appl., 340, 752-755 (2008) · Zbl 1137.54026
[5] Reich, S., Some problems and results in fixed point theory, Contemp. Math., 21, 179-187 (1983) · Zbl 0531.47048
[6] Jachymski, J., On Reich’s question concerning fixed points of multimaps, Boll. Unione. Mat. Ital., 7, 9, 453-460 (1995) · Zbl 0863.54042
[7] Nadler, S. B., Multi-valued contraction mappings, Pacific J. Math., 30, 475-488 (1969) · Zbl 0187.45002
[8] Takahashi, W., Nonlinear Functional Analysis (2000), Yokohama Publishers: Yokohama Publishers Yokohama, Japan
[9] Alesine, A.; Massa, S.; Roux, D., Punti uniti di multifunzioni con condizioni di tipo Boyd-Wong, Boll. Un. Mat. Ital., 8, 4, 29-34 (1973), (in Italian) · Zbl 0274.54036
[10] Kada, O.; Suzuki, T.; Takahashi, W., Nonconvex minimization theorems and fixed point theorems in complete metric spaces, Math. Japon., 44, 381-391 (1996) · Zbl 0897.54029
[11] Lin, L.-J.; Du, W.-S., Ekeland’s variational principle, minimax theorems and existence of nonconvex equilibria in complete metric spaces, J. Math. Anal. Appl., 323, 360-370 (2006) · Zbl 1101.49022
[12] Lin, L.-J.; Du, W.-S., Some equivalent formulations of generalized Ekeland’s variational principle and their applications, Nonlinear Anal., 67, 187-199 (2007) · Zbl 1111.49013
[13] Lin, L.-J.; Du, W.-S., On maximal element theorems, variants of Ekeland’s variational principle and their applications, Nonlinear Anal., 68, 1246-1262 (2008) · Zbl 1133.58006
[14] Kannan, R., Some results on fixed point — II, Amer. Math. Monthly, 76, 405-408 (1969) · Zbl 0179.28203
[15] Shioji, N.; Suzuki, T.; Takahashi, W., Contractive mappings, Kannan mappings and metric completeness, Proc. Amer. Math. Soc., 126, 3117-3124 (1998) · Zbl 0955.54009
[16] Chatterjea, S. K., Fixed-point theorems, C.R. Acad. Bulgare Sci., 25, 727-730 (1972) · Zbl 0274.54033
[17] Du, W.-S., Fixed point theorems for generalized Hausdorff metrics, Int. Math. Forum, 3, 1011-1022 (2008) · Zbl 1158.54020
[18] Aubin, J.-P.; Cellina, A., Differential Inclusions (1994), Springer-Verlag: Springer-Verlag Berlin, Heidelberg, Germany
[19] Downing, D.; Kirk, W. A., Fixed point theorems for set-valued mappings in metric and Banach spaces, Math. Japon., 22, 99-112 (1977) · Zbl 0372.47030
[20] Ding, X. P.; He, Y. R., Fixed point theorems for metrically weakly inward set-valued mappings, J. Appl. Anal., 5, 2, 283-293 (1999) · Zbl 0949.47045
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.