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

Babu, G. V. R.; Sailaja, P. D.

Thai J. Math. 9, No. 1, 1-10 (2011).

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.

MSC:

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

Keywords:

weakly contractive maps; generalized weakly contractive maps; Fixed point; \(T\)-orbitally complete metric spaces

Citations:

Zbl 1042.47521