%0 Journal Article %T Non-self multivariate contraction mapping principle in Banach spaces %A Tang, Yanxia %A Guan, Jinyu %A Xu, Yongchun %A Su, Yongfu %J Journal of Nonlinear Sciences and Applications %D 2017 %V 10 %N 9 %@ ISSN 2008-1901 %F Tang2017 %X The purpose of this article is to prove the non-self multivariate contraction mapping principle in a Banach space. The main result is the following: let \(C\) be a nonempty closed convex subset of a Banach space \((X,\|\cdot\|)\). Let \(T: C \rightarrow X\) be a weakly inward \(N\)-variables non-self contraction mapping. Then \(T\) has a unique multivariate fixed point \(p\in C\). That is, there exists a unique element \(p \in C\) such that \(T(p,p,\cdots ,p)=p\). In order to get the non-self multivariate contraction mapping principle, the inward and weakly inward \(N\)-variables non-self mappings are defined. In addition, the meaning of \(N\)-variables non-self contraction mapping \(T: C \rightarrow X\) is the following: \[ \|Tx-Ty\|\leq h \nabla (\|x_1-y_1\|, \|x_2-y_2\|,\cdots ,\|x_N-y_N\|) \] for all \(x=(x_1,x_2, \cdots, x_N), \ y=(y_1,y_2, \cdots, y_N)\in C^N\), where \(h \in (0,1)\) is a constant, and \(\nabla\) is an \(N\)-variables real function satisfying some suitable conditions. The results of this article improve and extend the previous results given in the literature. %9 journal article %R 10.22436/jnsa.010.09.13 %U http://dx.doi.org/10.22436/jnsa.010.09.13 %P 4704--4712 %0 Book %T Fixed point theory for Lipschitzian-type mappings with applications %A R. Agarwal %A D. Regan %A D. Rahu %D 2009 %I Springer %C New York %F Agarwal2009 %0 Journal Article %T A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations %A A. Amini-Harandi %A H. Emami %J Nonlinear Anal. %D 2010 %V 72 %F Amini-Harandi2010 %0 Journal Article %T On nonlinear contractions %A D. W. Boyd %A J. S. W. Wong %J Proc. Amer. Math. Soc. %D 1969 %V 20 %F Boyd1969 %0 Journal Article %T On the convergence of successive approximations for nonlinear functional equations %A F. E. Browder %J Nederl. Akad. Wetensch. Proc. Ser. A 71, Indag. Math. %D 1968 %V 30 %F Browder1968 %0 Journal Article %T Fixed point theorem for mappings satisfying inwardness conditions %A J. Caristi %J Tran. Amer. Math. Soc. %D 1976 %V 215 %F Caristi 1976 %0 Journal Article %T On contractive mappings %A M. A. Geraghty %J Proc. Am. Math. Soc. %D 1973 %V 40 %F Geraghty1973 %0 Journal Article %T Fixed point theorems in partially ordered metric spaces and applications %A T. Gnana Bhaskar %A V. Lakshmikantham %J Nonlinear Anal. %D 2006 %V 65 %F Bhaskar2006 %0 Journal Article %T Fixed point theorems for weakly contraction mappings in partially ordered sets %A J. Harjani %A K. Sadarangni %J Nonlinear Anal. %D 2009 %V 71 %F Harjani2009 %0 Journal Article %T Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations %A J. Harjani %A K. Sadarangni %J Nonlinear Anal. %D 2010 %V 72 %F Harjani2010 %0 Journal Article %T Equivalence of some contractivity properties over metrical structures %A J. R. Jachymski %J Proc. Amer. Math. Soc. %D 1997 %V 125 %F Jachymski1997 %0 Journal Article %T Nonlinear contractive conditions: a comparison and related problems %A J. Jachymski %A I. Jóźwik %J in: Fixed Point Theory and its Applications, Banach Center Publisher %D 2007 %V 77 %F Jachymski2007 %0 Journal Article %T Fixed point 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 Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces %A V. Lakshmikantham %A L. Ciric %J Nonlinear Anal. %D 2009 %V 70 %F Lakshmikantham2009 %0 Journal Article %T Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations %A J. Nieto %A R. Rodriguez-López %J Order %D 2005 %V 22 %F Nieto2005 %0 Journal Article %T Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations %A J. J. Nieto %A R. Rodriguez-López %J Acta Math. Sin. %D 2007 %V 23 %F Nieto2007 %0 Journal Article %T Fixed point theorem for \(\alpha-\psi\)-contractive type mappings %A B. Samet %A C. Vetro %A P. Vetro %J Nonlinear Anal. %D 2012 %V 75 %F Samet2012 %0 Journal Article %T Multivariate fixed point theorems for contractions and nonexpansive mappings with applications %A Y. Su %A A. Petruşel %A J. Yao %J Fixed Point Theory and Appl. %D 2016 %V 2016 %F Su2016 %0 Journal Article %T Further generalized contraction mapping principle and best proximity theorem in metric spaces %A Y. Su %A J.-C. Yao %J Fixed Point Theory and Appl. %D 2015 %V 2015 %F Su2015 %0 Journal Article %T A new contraction mapping principle in partially ordered metric spaces and applications to ordinary differential equations %A F. Yan Y. Su %A Q. Feng %J Fixed Point Theory Appl. %D 2012 %V 2012 %F Su2012