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Strong and weak convergence theorems for asymptotically strict pseudocontractive mappings in intermediate sense. (English) Zbl 1195.49011
Summary: We first prove the strong convergence of viscosity approximation method for a modified Mann iteration process for asymptotically strict pseudocontractive mappings in intermediate sense, and then the strong convergence of general CQ algorithm for asymptotically strict pseudocontractive mappings in intermediate sense. We extend the concept of asymptotically strict pseudocontractive mappings in intermediate sense to Banach space setting, called nearly asymptotically $\kappa$-strict pseudocontractive mapping in intermediate sense. We establish weak convergence theorems for a fixed point of a nearly asymptotically $\kappa$-strict pseudocontractive mapping in intermediate sense which is not necessarily Lipschitzian.
MSC:
 49J40 Variational methods including variational inequalities 47J20 Inequalities involving nonlinear operators 47H10 Fixed point theorems for nonlinear operators on topological linear spaces 47J25 Iterative procedures (nonlinear operator equations) 49L25 Viscosity solutions (infinite-dimensional problems)