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On fixed point generalizations of Suzuki’s method. (English) Zbl 1290.54024
Summary: In order to generalize the well-known Banach contraction theorem, many authors have introduced various types of contraction inequalities. In [Proc. Am. Math. Soc. 136, No. 5, 1861–1869 (2008; Zbl 1145.54026)], T. Suzuki introduced a new method which was then extended by some authors (see, for example, [S. Dhompongsa and H. Yingtaweesittikul, Fixed Point Theory Appl. 2009, Article ID 972395, 15 p. (2009; Zbl 1179.54055)], [M. Kikkawa and T. Suzuki, Fixed Point Theory Appl. 2008, Article ID 649749, 8 p. (2008; Zbl 1162.54019)] and [G. Moţ and A. Petruşel, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 70, No. 9, 3371–3377 (2009; Zbl 1213.54068)]). M. Kikkawa and T. Suzuki [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 69, No. 9, 2942–2949 (2008; Zbl 1152.54358)] extended the method and then G. Moţ and A. Petruşel further generalized it in [loc. cit.].
In this paper, we shall provide a new condition for \(T\) which guarantees the existence of its fixed point. Our results generalize some old results.

54H25 Fixed-point and coincidence theorems (topological aspects)
Full Text: DOI
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