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Two common fixed point theorems for weakly commuting mappings. (English) Zbl 0643.54041

In complete metric spaces, the authors establish two common fixed point theorems involving weakly commuting set-valued and single-valued mappings. The first theorem generalizes a result of the first author [Kyungpook Math. J. 25, 35-42 (1985; Zbl 0582.54032)].
Reviewer: S.Sessa

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)

Citations:

Zbl 0582.54032
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References:

[1] J. Daneš, Two fixed point theorems in topological and metric spaces,Bull. Austral. Math. Soc. 14 (1976), 259–265.MR 54: 6110 · Zbl 0318.54046
[2] B. Fisher, Common fixed point theorems for mappings and set-valued mappings,Rostock. Math. Kolloq. 18 (1981), 69–77.MR 83e: 54041 · Zbl 0479.54025
[3] B. Fisher, Common fixed points of four mappings,Bull. Inst. Math. Acad. Sinica 11 (1983), 103–113.MR 85c: 54079 · Zbl 0515.54029
[4] B. Fisher, Common fixed points of mappings and set-valued mappings on metric spaces,Kyungpook Math. J. 25 (1985), 35–42.MR 87a: 54060 · Zbl 0582.54032
[5] B. A. Meade andS. P. Singh, On common fixed point theorems,Bull. Austral. Math. Soc. 16 (1977), 49–53.MR 55: 11234 · Zbl 0351.54040
[6] S. Sessa, On a weak commutativity condition of mappings in fixed point considerations,Publ. Inst. Math. (Beograd)32 (46) (1982), 149–153.MR 85f: 54107 · Zbl 0523.54030
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[8] S. Sessa andB. Fisher, Common fixed points of weakly commuting mappings,Bull. Acad. Polon. Sci. 35 (1987), 341–349.Zbl 639: 54031 · Zbl 0639.54031
[9] S. Sessa, M. S. Khan andM. Imdad, Common fixed point theorem under a weak commutativity condition,Glasnik Mat. 21 (41) (1986), 225–235.Zbl 603: 54046 · Zbl 0603.54046
[10] S. Sessa, M. S. Khan andM. Imdad, On some weak conditions of commutativity in common fixed point theorems,Internat. J. Math. & Math. Sci. 11 (1988), 289–296.Zbl 642: 54045 · Zbl 0642.54045
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