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Original Articles

Fixed Point Theorems in Partially Ordered Metric Spaces and Existence Results for Integral Equations

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Pages 1304-1320 | Received 05 Dec 2010, Accepted 09 Mar 2012, Published online: 10 Oct 2012

REFERENCES

  • R. P. Agarwal , M. A. El-Gebeily , and D. O'Regan ( 2008 ). Generalized contractions in partially ordered metric spaces . Appl. Anal. 87 : 109 – 116 .
  • I. Altun and H. Simsek ( 2010 ). Some fixed point theorems on ordered metric spaces and application . Fixed Point Theory Appl. Article ID 621492 , p. 17 .
  • A. Amini-Harandi and H. Emami ( 2010 ). A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations . Nonlinear Anal. 72 : 2238 – 2242 .
  • S. Banach ( 1922 ). Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales . Fund. Math. 3 : 133 – 181 .
  • V. Berinde and F. Vetro ( 2002 ). Common fixed points of mappings satisfying implicit contractive conditions . Fixed Point Theory Appl. 105 .
  • T. G. Bhaskar and V. Lakshmikantham ( 2006 ). Fixed point theorems in partially ordered metric spaces and applications . Nonlinear Anal. 65 : 1379 – 1393 .
  • A. Branciari ( 2002 ). A fixed point theorem for mapping satisfying a general contractive condition of integral type . Int. J. Math. Math. Sci. 10 : 531 – 536 .
  • Lj. B. Ćirić , N. Cakić , M. Rajović , and J. S. Ume ( 2008 ). Monotone generalized nonlinear contractions in partially ordered metric spaces . Fixed Point Theory Appl. ID131294 , p. 11 .
  • B. C. Dhage , D. O'Regan , and R. P. Agrawal ( 1977 ). Common fixed point theorems for a pair of countably condensing mappings in ordered Banach spaces . J. Appl. Math. Stoch. Anal. 62 : 344 – 348 .
  • Z. Drici , F. A. McRae , and J. Vasundhara Devi ( 2007 ). Fixed point theorems in partially ordered metric spaces for operators with PPF dependence . Nonlinear Anal. 67 : 641 – 647 .
  • J. Harjani and K. Sadarangani ( 2008 ). Fixed point theorems for weakly contractive mappings in partially ordered sets . Nonlinear Anal. 71 : 3403 – 3410 .
  • J. Harjani and K. Sadarangani ( 2010 ). Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations . Nonlinear Anal. 72 : 1188 – 1197 .
  • G. Jungck ( 1986 ). Compatible mappings and common fixed points . Int. J. Math. Math. Sci. 9 : 771 – 779 .
  • H. K. Nashine ( 2011 ). Fixed point results for mappings satisfying (ψ, ϕ)-weakly contractive condition in partially ordered metric spaces . Nonlinear Anal. 74 : 2201 – 2209 .
  • H. K. Nashine , B. Samet , and J. K. Kim (2011). Fixed point results for contractions involving generalized altering distances in ordered metric spaces. Fixed Point Theory Appl. 2011:5.
  • J. J. Nieto and R. Rodríguez-López ( 2005 ). Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations . Order 22 : 223 – 239 .
  • J. J. Nieto and R. Rodríguez-López ( 2007 ). Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations . Acta Math. Sin. (Engl. Ser.) 23 : 2205 – 2212 .
  • J. J. Nieto , R. L. Pouso , and R. Rodríguez-López ( 2007 ). Fixed point theorems in partially ordered sets . Proc. Amer. Math. Soc. 132 : 2505 – 2517 .
  • A. C. M. Ran and M. C. B. Reurings ( 2004 ). A fixed point theorem in partially ordered sets and some applications to matrix equations . Proc. Amer. Math. Soc. 132 : 1435 – 1443 .
  • D. O'Regan and A. Petrutel ( 2008 ). Fixed point theorems for generalized contractions in ordered metric spaces . J. Math. Anal. Appl. 341 : 1241 – 1252 .
  • S. Reich ( 1974 ). Some fixed point problems . Atti. Accad. Naz. Lincei 57 : 194 – 198 .
  • B. Samet ( 2010 ). Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces . Nonlinear Anal. 72 : 4508 – 4517 .

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