Abstract : In this paper, we introduce some hybrid iterative schemes (Picard-Ishikawa, Picard-AK, Picard-S hybrid iterative schemes) in line with Picard-Mann scheme and establish some strong convergence results for generalized contractive-like inequality operators introduced by Imoru and Olatinwo [10] in a Banach space. We also compare the convergence speed of CR, SP, Picard-Mann hybrid iterative schemes with our results (Picard-S, Picard-AK, Picard-Ishikawa hybrid iterative shemes). It is shown that one of our results (Picard-S iterative scheme) converges faster than others (CR, SP, Picard-AK, Picard- Ishikawa, Picard-Mann hybrid iterative schemes) for increasing functions, while the Picard-AK scheme is faster than CR scheme for decreasing function. Our results generalize and extend multitude of results in the literature, including the results of Khan [13].
Full article