A new class of generalized f-projected dynamical system in Banach spaces

References

• Dupuis , P and Nagurney , A . 1993 . Dynamical systems and variational inequalities . Ann. Oper. Res. , 44 : 19 – 42 .
   Google Scholar
• Friesz , TL , Bernstein , DH , Mehta , NJ , Tobin , RL and Ganjlizadeh , S . 1994 . Day-to-day dynamic network disequilibria and idealized traveler information systems . Oper. Res. , 42 : 1120 – 1136 .
   Web of Science ®Google Scholar
• Raciti , F . 2004 . Equilibrium trajectories as stationary solution of infinite-dimensional projected dynamical systems . Appl. Math. Lett. , 17 : 153 – 158 .
   Web of Science ®Google Scholar
• Wu , KQ and Huang , NJ . 2006 . The generalized f-projection operator with an application . Bull. Austral. Math. Soc. , 73 : 307 – 317 .
   Web of Science ®Google Scholar
• Wu , KQ and Huang , NJ . 2007 . Properties of the generalized f-projection operator and its applications in Banach spaces . Comput. Math. Appl. , 54 : 399 – 406 .
   Web of Science ®Google Scholar
• Xu , HK . 1991 . Inequalities in Banach spaces with applications . Nonlinear Anal. TMA , 16 : 1127 – 1138 .
   Web of Science ®Google Scholar
• Zhang , D and Nagurney , A . 1995 . On the stability of projected dynamical systems . J. Optim. Theory Appl. , 85 : 97 – 124 .
   Web of Science ®Google Scholar
• Xia , YS and Vincent , TL . 2000 . On the stability of global projected dynamical systems . J. Optim. Theory Appl. , 106 : 129 – 150 .
   Web of Science ®Google Scholar
• Zou , YZ , Ding , K and Huang , NJ . 2006 . New global set-valued projected dynamical systems . Impul. Dyn. Sys. Appl. , 4 : 233 – 237 .
   Google Scholar
• Alber , Y . 1994 . Generalized projection operators in Banach spaces: Properties and applications . Funct. Differ. Eqns. , 1 : 1 – 21 .
   Google Scholar
• Li , J . 2005 . The generalized projection operator on reflexive Banach spaces and its application . J. Math. Anal. Appl. , 306 : 377 – 388 .
   Web of Science ®Google Scholar
• Wu , KQ and Huang , NJ . 2009 . The generalized f-projection operator and set-valued variational inequalities in Banach spaces . Nonlinear Anal. TMA , 71 : 2481 – 2490 .
   Web of Science ®Google Scholar
• Xia , YS . 2004 . Further results on global convergence and stability of global projected dynamical systems . J. Optim. Theory Appl. , 122 : 627 – 649 .
   Web of Science ®Google Scholar
• Alber , Y . 1996 . “ Metric and generalized projection operators in Banach spaces: Properties and applications ” . In Theory and Applications of Nonlinear Operators of Accretive and Monotone Type , Edited by: Kartsatos , AG . 15 – 50 . New York : Marcel Dekker .
   Google Scholar
• Alber , Y and Guerre-Delabriere , S . 2001 . On the projection methods for fixed point problems . Analysis , 21 : 17 – 39 .
   Google Scholar
• Alber , Y and Yao , JC . 2009 . Another version of the proximal point algorithm in a Banach space . Nonlinear Anal. TMA , 70 : 3159 – 3171 .
   Web of Science ®Google Scholar
• Fan , JH , Liu , X and Li , JL . 2009 . Iterative schemes for approximating solutions of generalized variational inequalities in Banach spaces . Nonlinear Anal. TMA , 70 : 3997 – 4007 .
   Web of Science ®Google Scholar
• Li , X , Huang , NJ and Zou , YZ . 2011 . On the stability of generalized f-projection operators with an application . Acta Math. Sinica, Chin. Ser. , 54 : 811 – 822 .
   Google Scholar