Graphical approximation of common solutions to generalized nonlinear relaxed cocoercive operator equation systems with (A, η)-accretive mappings
Fang Li, Heng-you Lan, Yeol Je Cho · Fixed Point Theory and Applications · 2012
Abstract In this paper, we develop a new perturbed iterative algorithm framework with errors based on the variational graphical convergence of operator sequences with (A, η)-accretive mappings in Banach space. By using the generalized resolvent operator technique associated with (A, η)-accretive mappings, we also prove the existence of solutions for a class of generalized nonlinear relaxed cocoercive operator equation systems and the variational convergence of the sequence generated by the perturbed iterative algorithm in q-uniformly smooth Banach spaces. The obtained results improve and generalize some well-known results in recent literatures. 2000 Mathematics Subject Classification: 47H05; 49J40