Iterative process with errors for fixed points of multivalued \(\Phi\)-hemicontractive operators in uniformly smooth Banach spaces (Q1570134)

The author considers a uniformly smooth Banach space and a (not necessarily continuous) multivalued \(\Phi\)-hemicontractive mapping \(T:E\to 2^E\). He proves that, under suitable conditions, the multivalued Ishikawa iterative sequence with errors strongly converges to the unique fixed point of \(T\). A related result deals with the strong convergence of the Ishikawa iterative sequence with errors to the solution of the equation \(f\in Tx\) when \(T: E\to 2^E\) is multivalued \(\Phi\)-strongly accretive.