Dutta, P. N.; Choudhury, B. S.; Das, Krishnapada Some fixed point results in Menger spaces using a control function. (English) Zbl 1180.54054 Surv. Math. Appl. 4, 41-52 (2009). 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. Cited in 24 Documents 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 PDFBibTeX XMLCite \textit{P. N. Dutta} et al., Surv. Math. Appl. 4, 41--52 (2009; Zbl 1180.54054) Full Text: EuDML EMIS