Iterative process with errors for fixed points of multivalued Φ-hemicontractive operators in uniformly smooth Banach spaces

AbstractLet E be a uniformly smooth Banach space and T : E → 2E be a (not necessarily continuous) multivalued ø-hemicontractive mapping. This paper proves that, under suitable conditions, the multivalued Ishikawa iterative sequence with errors strongly converges to the unique fixed point of T. The related result deals with the strong convergence of the Ishikawa iterative sequence with errors to the unique solution of the equation f ∈ Tx when T : E → 2E is multivalued ø-strongly accretive. These results generalize the results of the author [1], Ding [2,3], Osilike [4,5], Zhou [6,7], and Chidume [8,9] into more general multivalued ø-hemicontractive operators without the continuous assumption on operators T