CONVERGENCE OF A DOUBLE-SEQUENCE RANDOM ITERATION SCHEMES TO A RANDOM FIXED POINT

Abstract

In this paper, we introduce the concept of double-sequence random Ishikawa iteration schemes and prove that if the random sequence generated by this random iteration scheme is convergent, then the limit is a random fixed point of continuous random operator T. We also prove that when the operator T is semi-compact and continuous, the double-sequence random Ishikawa iteration scheme is reliably convergent.