Ishikawa Iteration Process for Nonlinear Lipschitz Strongly Accretive Mappings

Fixed point iteration for pseudocontractive maps

“…Let x * ∈ F(T). As in the proof of Theorem 1, we obtain inequality (8). Let L > 0 denote the Lipschitz constant of T .…”

“…Results which had been known only in Hilbert spaces and only for Lipschitz maps have been extended to more general Banach spaces (see e.g., [3]- [6], [7], [8], [9], [10], [11], [12], [13], [16], [21]- [24], [25], [26]- [28], [29], [30], [31], [32] and the references cited therein) and to more general classes of maps (see e.g., [4]- [6], [7], [8], [9], [10], [11], [12], [13], [14], [16], [18]- [20], [21]- [24], [26]- [28], [29], [30], [31], [32] and the references cited therein). This success, however, has not carried over to arbitrary Lipschitz pseudocontraction T even when the domain of the operator T is a a compact convex subset of a Hilbert space.…”

Global iteration schemes for strongly pseudo-contractive maps

“…The class of pseudocontractive maps has been studied extensively by various authors (see, for example, [1], [2], [4]- [6], [7], [8], [11]- [14], [15], [16], [20], [21]- [25], [26]- [28], [29]- [30], [34]). Interest in pseudo-contractive mappings stems mainly from their firm connection with the important class of accretive operators-a mapping U is called accretive if the inequality x − y ≤ x − y + s(U x − U y) (2) holds for every x, y ∈ D(U ) and for all s > 0.…”

“…Consequently, considerable effort has been devoted to developing constructive techniques for the determination of the kernels of accretive operators. Moreover, since a continuous accretive operator can be approximated well by a sequence of strongly accretive ones, particular attention has been devoted to the determination of the kernels of strongly accretive maps (see for example, [1], [2], [4]- [6], [7], [8], [11]- [14], [20], [21]- [25], [26]- [28], [29], [30], [31], [32], [34], [35] …”

Convergence of Picard-S Hybrid Iteration Process for Strongly Accretive Operator

“…The Banach fixed point theorem have been studied extensively by various authors for approximating fixed points of nonlinear operators in Banach space. C. E. Chidume [3], [5], [7], [8], [11], [13] and [16] are introduced and studied Mann and Ishikawa iteration process to approximate fixed points. Recently, in 1998 Chidume [4], Liue [15], Osilike [21] and Xu [25] introduced the concepts of Ishikawa and Mann iterative process with errors for nonlinear strongly accretive operators in uniformly smooth Banach spaces.…”