%0 Journal Article %T Multivariate contraction mapping principle in Menger probabilistic metric spaces %A Guan, Jinyu %A Tang, Yanxia %A Xu, Yongchun %A Su, Yongfu %J Journal of Nonlinear Sciences and Applications %D 2017 %V 10 %N 9 %@ ISSN 2008-1901 %F Guan2017 %X The purpose of this paper is to prove the multivariate contraction mapping principle of \(N\)-variables mappings in Menger probabilistic metric spaces. In order to get the multivariate contraction mapping principle, the product spaces of Menger probabilistic metric spaces are subtly defined which is used as an important method for the expected results. Meanwhile, the relative iterative algorithm of the multivariate fixed point is established. The results of this paper improve and extend the contraction mapping principle of single variable mappings in the probabilistic metric spaces. %9 journal article %R 10.22436/jnsa.010.09.17 %U http://dx.doi.org/10.22436/jnsa.010.09.17 %P 4741--4750 %0 Book %T Nonlinear Operator Theory in Probabilitic Metric Spaces %A S.-S. Chang %A Y. J. Cho %A S.-M. Kang %D 2001 %I Nova Publisher %C New York %F Chang2001 %0 Journal Article %T Common fixed point theorems for weakly compatible mappings in fuzzy metric spaces %A S. Chauhan %A S. Bhatnagar %A S. Radenović %J Matematiche %D 2013 %V 68 %F Chauhan2013 %0 Journal Article %T A new contraction principle in Menger spaces %A B. Choudhury %A K. Das %J Acta Math. Sin. %D 2008 %V 24 %F Choudhury2008 %0 Journal Article %T A coincidence point result in Menger spaces using a control function %A B. S. Choudhury %A K. Das %J Chaos Solitons & Fractals %D 2009 %V 42 %F Choudhury2009 %0 Journal Article %T A fixed point result in Menger spaces using a real function %A B. S. Choudhury %A K. Das %A P. N. Dutta %J Acta Math. Hungar. %D 2009 %V 122 %F Choudhury2009 %0 Journal Article %T Common property (E.A) and existence of fixed points in Menger spaces %A S. Chauhan %A S. Dalal %A W. Sintunavarat %A J. Vujaković %J J. Inequal. Appl. %D 2014 %V 2014 %F Chauhan2014 %0 Journal Article %T Hybrid coincidence and common fixed point theorems in Menger probabilistic metric spaces under a strict contractive condition with an application %A S. Chauhan %A M. Imdad %A C. Vetro %A W. Sintunavarat %J Appl. Math. Comput. %D 2014 %V 239 %F Chauhan2014 %0 Journal Article %T Some integral type fixed point theorems in non-Archimedean Menger PM-spaces with common property (E.A) and application of functional equations in dynamic programming %A S. Chauhan %A S. Radenović %A M. Imdad %A C. Vetro %A %J Rev. R. Acad. Cienc. Exactas Fs. Nat. Ser. A Math. %D 2014 %V 108 %F Chauhan2014 %0 Journal Article %T On fixed point of generalized contractions on probabilistic metric spaces %A L. B. Ćirć %J Publ. Inst. Math. %D 1975 %V 18 %F Ćirć1975 %0 Journal Article %T Some fixed point results in Menger spaces using a control function %A P. N. Dutta %A B. S. Choudhury %A K. Das %J Surv. Math. Appl. %D 2009 %V 4 %F Dutta2009 %0 Journal Article %T Pair of non-self-mappings and common fixed points %A L. Gajić %A V. Rakoćević %J Appl. Math. Comput. %D 2007 %V 187 %F Gajić2007 %0 Book %T Fixed Point Theory in Probabilistic Metric Spaces %A O. Hadzic %A E. Pap %D 2001 %I Kluwer Academic %C Dordrecht %F Hadzic2001 %0 Journal Article %T Fixed points theorems by altering distances between the points %A M. S. Khan %A M. Swaleh %A S. Sessa %J Bull. Aust. Math. Soc. %D 1984 %V 30 %F Khan1984 %0 Journal Article %T Further generalization of fixed point theorems in Menger PM-spaces %A M. A. Kutbi %A D. Gopal %A C. Vetro %A W. Sintunavarat %J Fixed Point Theory and Appl. %D 2015 %V 2015 %F Kutbi2015 %0 Journal Article %T Multivariate coupled fixed point theorems on ordered partial metric spaces %A H. Lee %A S. Kim %J J. Korean Math. Soc. %D 2014 %V 51 %F Lee2014 %0 Journal Article %T Statistical metrics %A K. Menger %J Proc. Nat. Acad. Sci. U. S. A. %D 1942 %V 28 %F Menger1942 %0 Journal Article %T Probabilistic Geometry %A K. Menger %J Proc. Nat. Acad. Sci. U. S. A. %D 1951 %V 37 %F Menger 1951 %0 Journal Article %T Altering distances in probabilistic Menger spaces %A D. Miheţ %J Nonlinear Anal. %D 2009 %V 71 %F Miheţ 2009 %0 Book %T Probabilistic Metric Spaces %A B. Schweizer %A A. Sklar %D 1983 %I North-Holland Publishing Co. %C New York %F Schweizer1983 %0 Book %T Some Fixed Point Theorems in Functional Analysis and Probability %A V. Sehgal %D 1966 %I Ph.D. Dissertation, Wayne State University %C Michigan %F Sehgal1966 %0 Journal Article %T Fixed point of contraction mappings in PM-spaces %A V. Sehgal %A A. Bharucha-Reid %J Math. Syst. Theory. %D 1972 %V 6 %F Sehgal1972 %0 Journal Article %T Generalized contraction mapping principle and generalized best proximity point theorems in probabilistic metric spaces %A Y. Su %A W. Gao %A J. Yao %J Fixed Point Theory and Appl. %D 2015 %V 2015 %F Su2015 %0 Journal Article %T Multivariate fixed point theorems for contractions and nonexpansive mappings with applications %A Y. Su %A A. Petrusel %A J.-C. Yao %J Fixed Point Theory and Appl. %D 2016 %V 2016 %F Su2016 %0 Journal Article %T Fixed point and best proximity point theorems for contractions in new class of probabilistic metric spaces %A Y. Su %A J. Zhang %J Fixed Point Theory and Appl. %D 2014 %V 2014 %F Su2014 %0 Journal Article %T Various generalizations of metric spaces and fixed point theorems %A T. Van An %A N. Van Dung %A Z. Kadelburg %A S. Radenović %J Rev. R. Acad. Cienc. Exactas Fs. Nat. Ser. A Math. %D 2015 %V 109 %F An2015