On the approximation of fixed points of non-self strict pseudocontractions

Halpern–Ishikawa type iterative schemes for approximating fixed points of multi-valued non-self mappings

“…In addition, a Halpern-Ishikawa type iterative method for approximating fixed points of multivalued k-strictly pseudocontractive mappings is introduced and strong convergence results of the scheme are obtained without the end point condition. Our results extend and generalize many of the results in the literature (see, e.g., [6,7,22,23,25,[27][28][29]). More particularly, Theorem 3.2 extends Theorem 3.2 of Zegeye and Tufa [28] from single-valued mapping to multi-valued mapping.…”

“…Recently, Zegeye and Tufa [28] constructed a Halpern-Ishikawa type iterative scheme for single-valued Lipschitz pseudocontractive non-self mappings in Hilbert spaces and obtained strong convergence of the scheme to fixed points of the mappings under some mild conditions. Their result mainly extends the result of Colao et al [7] from k-strictly pseudocontractive to pseudocontractive mapping.…”

Halpern–Ishikawa type iterative method for approximating fixed points of non-self pseudocontractive mappings

“…Our results extend and generalize many results in the literature. More particularly, Theorem 3.1 extends Theorem 8 of Colao et al [5] in the sense that it provides a convergent scheme for approximating fixed points of Lipschitz pseudocontractive non-self mappings more general than that of k-strictly pseudocontractive non-self mappings.…”

“…Recently, Colao et al [5] extended this result of Colao and Marino [4] to a class of kstrictly pseudocontractive mappings. We observe that these results (the results obtained in [4] and [5]) provide a way forward to avoid the use of metric projection or sunny nonexpansive mapping in constructing algorithms for approximating fixed points of a more general class of non-self mappings.…”

“…Second, he proved the strong convergence of Halpern's scheme (5) in the framework of real uniformly smooth Banach spaces.…”