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New extension of some fixed point results in complete metric spaces. (English) Zbl 1455.54030

Summary: We provide some new fixed point results which are inspired by the works of T. Suzuki [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 64, No. 5, 971–978 (2006; Zbl 1101.54047); ibid 71, No. 11, 5313–5317 (2009; Zbl 1179.54071)] and R. Kannan [Bull. Calcutta Math. Soc. 60, 71–76 (1968; Zbl 0209.27104)]. The results are proved using the properties of sequentially convergent mappings and \(A\)-contractions. Existence and uniqueness of fixed points of self maps satisfying certain conditions are investigated in a complete metric space.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces
54E50 Complete metric spaces
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