A modified extragradient method for inverse-monotone operators in Banach spaces

1. Alber Ya.I.: Metric and generalized projection operators in banach spaces: properties and applications In: Kartsatos A. (eds). Theory and applications of nonlinear operators of monotone and accretive type, pp. 15–50. Marcel Dekker, New York (1996)

   Google Scholar 

2. Barbu V., Precupanu Th.: Convexity and Optimization in Banach Spaces. Romania International Publishers, Bucuresti (1978)

   Google Scholar 

3. Butnariu D., Iusem A.N.: Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization. Kluwer Academic Publishers , Dordrecht (2000)

   Google Scholar 

4. Butnariu D., Iusem A.N., Zalinescu C.: On uniform convexity, total convexity and convergence of the proximal point and outer Bregman projection algorithms in Banach spaces. J. Convex Anal. 10, 35–61 (2003)

   Google Scholar 

5. Butnariu D., Resmerita E.: Bregman distances, totally convex functions and a method for solving operator equations in Banach spaces. Abstr. Appl. Anal. 84919, 39 (2006)

   Google Scholar 

6. Burachik R.S., Scheimberg S.: A proximal point method for the variational inequality problem in Banach spaces. SIAM J. Control Optim. 39(5), 1633–1649 (2001)

   Article  Google Scholar 

7. Herings P.J., Koshevoy G.A., Talman A.J., Yang Z.: General existence theorem of zero points. J. Optim. Theory Appl. 120, 375–394 (2004)

   Article  Google Scholar 

8. Iiduka H., Takahashi W.: Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings. Nonlinear Anal. 61, 341–350 (2005)

   Article  Google Scholar 

9. Kamimura S., Kohsaka F., Takahashi W.: Weak and strong convergence theorem for maximal monotone operators in a Banach space. Set-Valued Anal. 12, 417–429 (2004)

   Article  Google Scholar 

10. Kamimura S., Takahashi W.: Strong convergence of a proximal-type algorithm in a Banach space. SIAM J. Optim. 13, 938–945 (2003)

    Article  Google Scholar 

11. Li L., Song W.: A hybrid of extragradient method and proximal point algorithm for inverse strongly-monotone operators and maximal monotone operators in Banach spaces. Nonlinear Anal. Hybrid Syst. 1, 398–413 (2007)

    Article  Google Scholar 

12. Matsushita S., Takahashi W.: On the existence of zeros of monotone operators in reflexive Banach spaces. J. Math. Anal. Appl. 323, 1354–1364 (2006)

    Article  Google Scholar 

13. Minty G.: On a “monotonicity” method for the solution of nonlinear equations in Banach spaces. Proc. Natl. Acad. Sci. USA 50, 1038–1041 (1963)

    Article  Google Scholar 

14. Rockafellar R.T.: On the maximality of sums of nonlinear monotone operators. Trans. Am. Math. Soc. 149, 75–88 (1970)

    Article  Google Scholar 

15. Takahashi W.: Nonlinear Functional Analysis. Yokohama Publishers, Yokohama (2000)

    Google Scholar 

16. Xu H.K.: Inequalities in Banach spaces with applications. Nonlinear Anal. 16, 1127–1138 (1991)

    Article  Google Scholar 

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