Coupled Random Fixed Point Theorems for Nonlinear Contractions in Partially Ordered Metric Spaces

REFERENCES

• Agarwal , R.P. , El-Gebeily , M.A. , and O'Regan , D. 2008 . Generalized contractions in partially ordered metric spaces . Appl. Anal. 87 : 109 – 116 .
   Web of Science ®Google Scholar
• Agarwal , R.P. , O'Regan , D. , and Sambandham , M. 2004 . Random and deterministic fixed point theory for generalized contractive maps . Appl. Anal. 83 : 711 – 725 .
   Google Scholar
• Agarwal , R.P. , El-Gebeily , M.A. , and O'Regan , D. 2008 . Generalized contractions in partially ordered metric spaces . Appl. Anal. 87 : 1 – 8 .
   Google Scholar
• Beg , I. , and Shahzad , N. 1994 . Random fixed point theorems for nonexpansive and contractive-type random operators on Banach spaces . J. Appl. Math. Stochastic Anal. 7 : 569 – 580 .
   Google Scholar
• Bhaskar , T.G. , and Lakshmikantham , V. 2006 . Fixed point theorems in partially ordered metric spaces and applications . Nonlinear Anal.—Theor. 65 : 1379 – 1393 .
   Web of Science ®Google Scholar
• Bhaskar , T.G. , Lakshmikantham , V. , and Vasundhara Devi , J. 2007. Monotone iterative technique for functional differential equations with retardation and anticipation. Nonlinear Anal. Theor. 66(10):2237–2242.
   Google Scholar
• Ćirić , Lj.B. , Cakić , N. , Rajović , M. , and Ume , J.S. 2008 . Monotone generalized nonlinear contractions in partially ordered metric spaces . Fixed Point Theory Appl. 2008 : 11 . Article ID 131294 .
   Google Scholar
• Ćirić , Lj.B. , Ješić , S.N. , and Ume , J.S. 2006 . On random coincidence for a pair of measurable mappings . J. Inequal. Appl. 2006 : 1 – 12 . Article ID 81045 .
   Google Scholar
• Ćirić , Lj.B. , Milovanović-Arandjelović , M.M. , and Nikolić , N.T. 2008 . On random coincidence and fixed points for a pair of multi-valued and single-valued mappings . Italian J. Pure Applied Math. 23 : 37 – 44 .
   Google Scholar
• Guo , D. , and Lakshmikantham , V. 1988 . Nonlinear Problems in Abstract Cones . Academic Press , New York .
   Google Scholar
• Hadzić , O. 1979 . A random fixed point theorem for multi valued mappings of Ćirić's type . Mat. Vesnik 3 (16) (31)4 : 397 – 401 .
   Google Scholar
• Han[sbreve] , O. 1957 . Reduzierende Zufällige transformationen . Czech. Math. J. 7 : 154 – 158 .
   Google Scholar
• Han[sbreve] , O. 1961 . Random operator equations . Proc. 4th Berkeley Symp. Mathematical Statistics and Probability . Vol. II, Part I , University of California Press , Berkeley , pp. 185 – 202 .
   Google Scholar
• Heikkila , S. , and Lakshmikantham , V. 1994 . Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations . Marcel Dekker , New York .
   Google Scholar
• Himmelberg , C.J. 1975 . Measurable relations . Fund. Math. 87 : 53 – 72 .
   Google Scholar
• Huang , N.J. 1999 . A principle of randomization of coincidence points with applications . Applied Math. Lett. 12 : 107 – 113 .
   Google Scholar
• Hussain , N. 2008 . Common fixed points in best approximation for Banach operator pairs with Ćirić Type I-contractions . J. Math. Anal. Appl. 338 : 1351 – 1363 .
   Web of Science ®Google Scholar
• Itoh , S. 1977 . A random fixed point theorem for a multi-valued contraction mapping . Pacific J. Math. 68 : 85 – 90 .
   Google Scholar
• Ladde , G.S. , Lakshmikantham , V. , Vatsala , A.S. 1985 . Monotone Iterative Techniques for Nonlinear Differential Equations . Pitman , Cambridge .
   Google Scholar
• Lakshmikantham , V. , and Ćirić , Lj.B. 2009 . Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces . Nonlinear Anal. Theor. 70 ( 12 ): 4341 – 4349 .
   Google Scholar
• Lakshmikantham , V. , Bhaskar , T.G. , and Vasundhara Devi , J. 2005 . Theory of Set Differential Equations in Metric Spaces . Cambridge Scientific Publishers , Cambridge , UK .
   Google Scholar
• Lakshmikantham , V. , and Mohapatra , R.N. 2003 . Theory of Fuzzy Differential Equations and Inclusions . Taylor & Francis , London .
   Google Scholar
• Lakshmikantham , V. , and Koksal , S. 2003 . Monotone Flows and Rapid Convergence for Nonlinear Partial Differential Equations . Taylor & Francis , London .
   Google Scholar
• Lakshmikantham , V. , and Vatsala , A.S. 2008 . General uniqueness and monotone iterative technique for fractional differential equations . Appl. Math. Lett. 21 ( 8 ): 828 – 834 .
   Web of Science ®Google Scholar
• Lin , T.C. 1988 . Random approximations and random fixed point theorems for non-self maps . Proc. Am. Math. Soc. 103 : 1129 – 1135 .
   Web of Science ®Google Scholar
• McShane , E.J. , and Warfield , Jr. , R.B. 1967. On Filippov's implicit functions lemma. Proc. Am. Math. Soc. 18:41–47.
   Web of Science ®Google Scholar
• Nieto , J.J. , and Rodriguez-Lopez , R. 2005 . Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations . Order 22 : 223 – 239 .
   Web of Science ®Google Scholar
• Nieto , J.J. , Pouso , R.L. , and Rodriguez-Lopez , R. 2007 . Fixed point theorems in ordered abstract spaces . Proc. Amer. Math. Soc. 135 : 2505 – 2517 .
   Web of Science ®Google Scholar
• Papageorgiou , N.S. 1984 . Random fixed point theorems for multifunctions . Math. Japonica 29 : 93 – 106 .
   Google Scholar
• Papageorgiou , N.S. 1986 . Random fixed point theorems for measurable multifunctions in Banach spaces . Proc. Amer. Math. Soc. 97 : 507 – 514 .
   Web of Science ®Google Scholar
• Ran , A.C.M. , and Reurings , M.C.B. 2004 . A fixed point theorem in partially ordered sets and some applications to matrix equations . Proc. Amer. Math. Soc. 132 : 1435 – 1443 .
   Web of Science ®Google Scholar
• Rockafellar , R.T. 1969 . Measurable dependence of convex sets and functions in parameters . J. Math. Anal. Appl. 28 : 4 – 25 .
   Web of Science ®Google Scholar
• Sehgal , V.M. , and Singh , S.P. 1985 . On random approximations and a random fixed point theorem for set valued mappings . Proc. Am. Math. Soc. 95 : 91 – 94 .
   Web of Science ®Google Scholar
• Shahzad , N. , and Hussian , N. 2006 . Deterministic and random coincidence point results for f-nonexpansive maps . J. Math. Anal. Appl. 323 : 1038 – 1046 .
   Web of Science ®Google Scholar
• Shahzad , N. , and Latif , A. 2000 . A random coincidence point theorem . J. Math. Anal. Appl. 245 : 633 – 638 .
   Web of Science ®Google Scholar
• [Sbreve]paček , A. 1955 . Zufällige Gleichungen . Czech. Math. J. 5 : 462 – 466 .
   Google Scholar
• Tan , K.K. , Yuan , X.Z. , and Huang , N.J. 1994 . Random fixed point theorems and approximations in cones . J. Math. Anal. Appl. 185 : 378 – 390 .
   Web of Science ®Google Scholar
• Wagner , D.H. 1977 . Survey of measurable selection theorems . SIAM J. Control Optim. 15 : 859 – 903 .
   Web of Science ®Google Scholar