## Some fixed point results in Menger spaces using a control function.(English)Zbl 1180.54054

Summary: Here we prove a probabilistic contraction mapping principle in Menger spaces. This is in line with research in fixed point theory using control functions which was initiated by M. S. Khan, M. Swaleh and S. Sessa [Bull. Aust. Math. Soc. 30, 1–9 (1984; Zbl 0553.54023)] in metric spaces and extended by B. S. Choudhury and K. Das [Acta Math. Sin., Engl. Ser. 24, No. 8, 1379–1386 (2008; Zbl 1155.54026)] in probabilistic metric spaces. An example has also been constructed.

### MSC:

 54H25 Fixed-point and coincidence theorems (topological aspects) 54E70 Probabilistic metric spaces

### Keywords:

Menger space; p-convergence; $$\Phi$$-function; fixed point

### Citations:

Zbl 0553.54023; Zbl 1155.54026
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