Common fixed points for generalized (v,o)-weak contractions in ordered cone metric spaces

• Nashine, Hemant Kumar ^[2] ; Aydi, Hassen ^[1]
  1. [1] University of Sousse

     University of Sousse

     Túnez

     
  2. [2] Disha Institute of Management and Technology
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 13, Nº. 2, 2012, págs. 151-166
• Idioma: inglés
• DOI: 10.4995/agt.2012.1626
• Enlaces
  • Texto completo
• Resumen

  • The purpose of this paper is to establish coincidence point and common fixed point results for four maps satisfying generalized (v,o)-weak contractions in partially ordered cone metric spaces. Also, some illustrative examples are presented.

• Referencias bibliográficas
  • M. Abbas and G. Jungck, Common fixed point results for noncommuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl....
  • M. Abbas, T. Nazir and S. Radenovic, Common fixed point of four maps in partially ordered metric spaces, Appl. Math. Lett. 24 (2011), 1520–1526....
  • M. Abbas and B. E. Rhoades, Fixed and periodic point results in cone metric spaces, Appl. Math. Lett. 22 (2009), 511–515. http://dx.doi.org/10.1016/j.aml.2008.07.001
  • R. P. Agarwal, Contraction and approximate contraction with an application to multipoint boundary value problems, J. Comput. Appl. Appl. Math....
  • R. P. Agarwal, M. A. El-Gebeily and D. O’Regan, Generalized contractions in partially ordered metric spaces, Applicable Anal. 87 (2008), 109–116.
  • I. Altun and H. Simsek, Some fixed point theorems on ordered metric spaces and application, Fixed Point Theory Appl. 2010(2010) Article ID...
  • H. Aydi, H. K. Nashine, B. Samet and H. Yazidi, Coincidence and common fixed point results in partially ordered cone metric spaces and applications...
  • I. Beg and A.R. Butt, Fixed point for set-valued mappings satisfying an implicit relation in partially ordered metric spaces, Nonlinear Anal....
  • B. S. Choudhury and N. Metiya, The point of coincidence and common fixed point for a pair of mappings in cone metric spaces, Comput. Math....
  • Lj. B. Ciric, N. Cakic, M. Rajovic and J. S. Ume, Monotone generalized nonlinear contractions in partially ordered metric spaces, Fixed Point...
  • Lj. B. Ciric, B. Samet, N. Cakic and B. Damjanovic, Coincidence and fixed point theorems for generalized ( , _)-weak nonlinear contraction...
  • W.-S. Du, A note on cone metric fixed point theory and its equivalence, Nonlinear Anal. 72 (2010), 2259–2261. http://dx.doi.org/10.1016/j.na.2009.10.026
  • L. G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007), 1468–1476....
  • D. Ilic and V. Rakoèevic, Common fixed points for maps on cone metric space, J. Math. Anal. Appl. 341 (2008), 876–882. http://dx.doi.org/10.1016/j.jmaa.2007.10.065
  • E. Karapinar, Couple fixed point theorems for nonlinear contractions in cone metric spaces, Comput. Math. Appl. 59, no. 12 (2010), 3656–3668....
  • E.M. Mukhamadiev and V.J. Stetsenko, Fixed point principle in generalized metric space, Izvestija AN Tadzh. SSR, fiz.-mat. igeol.-chem. nauki....
  • H.K. Nashine and I. Altun, Fixed point theorems for generalized weakly contractive condition in ordered metric spaces, Fixed Point Theory...
  • H. K. Nashine and M. Abbas, Common fixed point point of mappings satisfying implicit contractive conditions in TVS-valued ordered cone metric...
  • H. K. Nashine and B. Samet, Fixed point results for mappings satisfying ( , ')-weakly contractive condition in partially ordered metric...
  • H. K. Nashine, B. Samet and C. Vetro, Monotone generalized nonlinear contractions and fixed point theorems in ordered metric spaces, Math....
  • H .K. Nashine and W. Shatanawi, Coupled common fixed point theorems for pair of commuting mappings in partially ordered complete metric spaces,...
  • J. J. Nieto and R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordianry differential equations,...
  • J. O. Olaleru, Some generalizations of fixed point theorems in cone metric spaces, Fixed Point Theory Appl. 2009 (2009), Article ID 657914,...
  • A. I. Perov, The Cauchy problem for systems of ordinary differential equations, in: Approximate Methods of Solving Differential Equations,...
  • A. I. Perov and A.V. Kibenko, An approach to studying boundary value problems, Izvestija AN SSSR, Ser. Math. 30, no. 2 (1966), 249–264 (in...
  • A. C. M. Ran and M. C. B. Reurings, A fixed point thm in partially ordered sets and some applications to matrix equations, Proc. Amer. Math....
  • D. O’regan and A. Petrusel, Fixed point theorems for generalized contractions in ordered metric spaces, J. Math. Anal. Appl. 341 (2008), 241–1252....
  • Sh. Rezapour and R. Hamlbarani, Some notes on the paper: cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal....
  • B. Samet, Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces, Nonlinear Anal. 72 (2010),...
  • B. Samet, Common fixed point theorems involving two pairs of weakly compatible mappings in K-metric spaces, Appl. Math. Lett. 24 (2011), 1245–1250....
  • W. Shatanawi, Partially ordered cone metric spaces and coupled fixed point results, Comput. Math. Appl. 60 (2010), 2508–2515. http://dx.doi.org/10.1016/j.camwa.2010.08.074
  • W. Shatanawi and B. Samet, On ( , _)-weakly contractive condition in partially ordered metric spaces, Comput. Math. Appl. 62 (2011), 3204–3214...
  • J. S. Vandergraft, Newton’s method for convex operators in partially ordered spaces, SIAM J. Numer. Anal. 4 (1967), 406–432. http://dx.doi.org/10.1137/0704037
  • P. P. Zabrejko, K-metric and K-normed linear spaces: survey, Collect. Math. 48 (1997), 825–859.