A fixed point theorem of generalized weakly contractive maps in orbitally complete metric spaces. (English) Zbl 1259.54017

Summary: We prove the existence of fixed points of a generalized weakly contractive map in \(T\)-orbitally complete metric spaces. This result generalizes the results of G.V.R.Babu and G.N.Alemayehu [“Point of coincidence and common fixed points of a pair of generalized weakly contractive maps”, J. Adv. Res. Pure Math. 2, No. 2, 89–106 (2010)] and B. E. Rhoades [Nonlinear Anal., Theory Methods Appl. 47, No. 4, 2683–2693 (2001; Zbl 1042.47521)] when the space under consideration is bounded.


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


Zbl 1042.47521
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