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Some fixed point theorems for weak contraction conditions of integral type. (English) Zbl 1224.54096

Summary: In this paper, we establish two fixed point theorems following the concept of A. Branciari [Int. J. Math. Math. Sci. 29, No. 9, 531–536 (2002; Zbl 0993.54040)] and B. E. Rhoades [ibid. 2003, No. 63, 4007–4013 (2003; Zbl 1052.47052)] and using weak contractions of integral type.
Our results are generalizations of the classical Banach fixed point theorem as well as extensions of some other results of V. Berinde [Bulletin for Applied and Computing Math., 183–192 (1999; per bibl.); Iterative approximation of fixed points. Baia Mare: Efemeride (2002; Zbl 1036.47037); Nonlinear Anal. Forum 9, No. 1, 43–53 (2004; Zbl 1078.47042); Iterative approximation of fixed points. Lecture Notes in Mathematics 1912. Berlin: Springer (2007; Zbl 1165.47047)], M. Berinde and V. Berinde [J. Math. Anal. Appl. 326, No. 2, 772–782 (2007; Zbl 1117.47039)], A. Branciari [op. cit.], S. K. Chatterjea [C. R. Acad. Bulg. Sci. 25, 727–730 (1972; Zbl 0274.54033)], R. Kannan [Bull. Calcutta Math. Soc. 60, 71–76 (1968; Zbl 0209.27104)] and T. Zamfirescu [Arch. Math. 23, 292–298 (1972; Zbl 0239.54030)].

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E50 Complete metric spaces
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