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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 63, 2014 - Issue 5
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Articles

Global optimization in metric spaces with partial orders

Pages 817-825 | Received 11 May 2011, Accepted 04 Apr 2012, Published online: 25 May 2012

References

  • Al-Thagafi , MA and Shahzad , N . 2008 . Best proximity sets and equilibrium pairs for a finite family of multimaps . Fixed Point Theory Appl. , : 10 Article ID 457069
  • Al-Thagafi , MA and Shahzad , N . 2009 . Best proximity pairs and equilibrium pairs for Kakutani multimaps . Nonlinear Anal. , 70 : 1209 – 1216 .
  • Al-Thagafi , MA and Shahzad , N . 2009 . Convergence and existence results for best proximity points . Nonlinear Anal. , 70 : 3665 – 3671 .
  • Anuradha , J and Veeramani , P . 2009 . Proximal pointwise contraction . Topol. Appl. , 156 : 2942 – 2948 .
  • DeMarr , R . 1964 . Common fixed points for isotone mappings . Colloquium Math. , 13 : 45 – 48 .
  • Di Bari , C , Suzuki , T and Vetro , C . 2008 . Best proximity points for cyclic Meir–Keeler contractions . Nonlinear Anal. , 69 : 3790 – 3794 .
  • Diviccaro , ML . 2004 . Common fixed points of commutative antitone operators in partially ordered sets . Radovi Math. , 12 : 123 – 128 .
  • Diviccaro , ML . 2005 . Fixed point properties of decomposable isotone operators in posets . Sarajevo J. Math. , 13 : 5 – 10 .
  • Diviccaro , ML and Sessa , S . 2008 . Common fixed points of increasing operators in posets and related semilattice properties . Int. Math. Forum , 3 : 2123 – 2128 .
  • Eldred , AA , Kirk , WA and Veeramani , P . 2005 . Proximinal normal structure and relatively nonexpanisve mappings . Studia Math. , 171 : 283 – 293 .
  • Eldred , AA and Veeramani , P . 2006 . Existence and convergence of best proximity points . J. Math. Anal. Appl. , 323 : 1001 – 1006 .
  • Fernadez-Leon , A . 2010 . Existence and uniqueness of best proximity points in geodesic metric spaces . Nonlinear Anal. , 73 : 915 – 921 .
  • Nieto , JJ and Rodriguez-Lopez , R . 2005 . Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations . Order , 22 : 223 – 229 .
  • Piatek , B . 2011 . On cyclic Meir-Keeler contractions in metric spaces . Nonlinear Anal. , 74 : 35 – 40 .
  • Ran , ACM and Reurings , MCB . 2004 . A fixed point theorem in partially ordered sets and some applications to matrix equations . Proc. Amer. Math. Soc. , 132 : 1435 – 1443 .
  • Sadiq Basha , S . 2010 . Extensions of Banach's contraction principle . Numer. Funct. Anal. Optim. , 31 : 569 – 576 .
  • Sadiq Basha , S . Common best proximity points: Global minimal solutions , TOP, DOI: 10.1007/s11750-011-0171-2
  • Sadiq Basha , S . Global optimal approximate solutions . Optim. Lett. , DOI: 10.1007/s11590-010-0227-5
  • Sadiq Basha , S . 2011 . Best proximity points: Global optimal approximate solution . J. Glob. Optim. , 49 : 15 – 21 .
  • Sadiq Basha , S . 2011 . Best proximity point theorems generalizing the contraction principle . Nonlinear Anal. , 74 : 5844 – 5850 .
  • Sadiq Basha , S . 2011 . Best proximity point theorems . J. Approx. Theory , 163 : 1772 – 1781 .
  • Sadiq Basha , S . Common best proximity points: Global minimization of multi-objective functions . J. Glob. Optim. , DOI: 10.1007/s10898-011-9760-8
  • Sadiq Basha , S , Shahzad , N and Jeyaraj , R . 2011 . Common best proximity points: Global optimization of multi-objective functions . Appl. Math. Lett. , 24 : 883 – 886 .
  • Sadiq Basha , S , Shahzad , N and Jeyaraj , R . 2011 . Optimal approximate solutions of fixed point equations . Abstract Appl. Anal. , 2011 : 9 (Article ID 174560, doi: 10.115/2011/174560)
  • Sadiq Basha , S and Veeramani , P . 2000 . Best proximity pair theorems for multifunctions with open fibres . J. Approx. Theory , 103 : 119 – 129 .
  • Sankar Raj , V . 2011 . A best proximity point theorem for weakly contractive non-self-mappings . Nonlinear Anal. , 74 : 4804 – 4808 .
  • Sankar Raj , V and Veeramani , P . 2009 . Best proximity pair theorems for relatively nonexpansive mappings . Appl. General Topol. , 10 : 21 – 28 .
  • Shahzad , N , Sadiq Basha , S and Jeyaraj , R . 2011 . Common best proximity points: Global optimal solutions . J. Optim. Theory Appl. , 148 : 69 – 78 .
  • Vetro , C . 2010 . Best proximity points: Convergence and existence theorems for p-cyclic mappings . Nonlinear Anal. , 73 : 2283 – 2291 .
  • Wlodarczyk , K , Plebaniak , R and Banach , A . 2009 . Best proximity points for cyclic and noncyclic set-valued relatively quasi-asymptotic contractions in uniform spaces . Nonlinear Anal. , 70 : 3332 – 3341 .
  • Wlodarczyk , K , Plebaniak , R and Banach , A . 2009 . Erratum to: “Best proximity points for cyclic and noncyclic set-valued relatively quasi-asymptotic contractions in uniform spaces” . Nonlinear Anal. , 71 : 3583 – 3586 .
  • Wlodarczyk , K , Plebaniak , R and Obczynski , C . 2010 . Convergence theorems, best approximation and best proximity for set-valued dynamic systems of relatively quasi-asymptotic contractions in cone uniform spaces . Nonlinear Anal. , 72 : 794 – 805 .

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