A projection method for solving nonlinear problems in reflexive Banach spaces

作者：Reich Simeon^*; Sabach Shoham

来源：Journal of Fixed Point Theory and Applications, 2011, 9(1): 101-116.

DOI：10.1007/s11784-010-0037-5

• Banach space
• Bregman distance
• Bregman firmly nonexpansive operator
• Bregman inverse strongly monotone mapping
• Bregman projection
• convex feasibility problem
• equilibrium problem
• fixed point
• iterative algorithm
• Legendre function
• monotone mapping
• totally convex function

We study the convergence of an iterative algorithm for finding common fixed points of finitely many Bregman firmly nonexpansive operators in reflexive Banach spaces. Our algorithm is based on the concept of the so-called shrinking projection method and it takes into account possible computational errors. We establish a strong convergence theorem and then apply it to the solution of convex feasibility and equilibrium problems, and to finding zeroes of two different classes of nonlinear mappings.

• 出版日期2011-3