Convergence Theorems for Fixed Points of Multivalued Strictly Pseudocontractive Mappings in Hilbert Spaces

Abstract

LetKbe a nonempty, closed, and convex subset of a real Hilbert spaceH. Suppose thatT:K→2Kis a multivalued strictly pseudocontractive mapping such thatF(T)≠∅. A Krasnoselskii-type iteration sequence{xn}is constructed and shown to be an approximate fixed point sequence ofT; that is,limn→∞d(xn,Txn)=0holds. Convergence theorems are also proved under appropriate additional conditions.

Strong andΔ-Convergence Theorems for Common Fixed Points of a Finite Family of Multivalued Demicontractive Mappings in CAT(0)Spaces

“…Thus, our result is applicable to all classes of demicontractive mappings. Furthermore, our theorems extend and improve the results of Chidume and Ezeora [18], Chidume et al [17], and Isiogugu and Osilike [19] and complement the results of Dhompongsa and Panyanak [16], Dhompongsa et al [9], Leustean [11], Shahzad and Markin [13], and Sokhuma [20] and results of a host of other authors on iterative approximation of fixed points in CAT(0) spaces.…”

“…Very recently, Chidume and Ezeora extended the result of Chidume et al [17] to a finite family of multivaluedstrictly pseudocontractive mappings in real Hilbert spaces. The following theorem is their main result.…”

“…In [17], Chidume et al introduced the class of multivalued -strictly pseudocontractive mappings which is a generalization of the class of multivalued nonexpansive mappings in Hilbert spaces. They constructed a Krasnoselskii-type algorithm sequence and showed that it is an approximate fixed point sequence of the map.…”

Algorithms of common solutions for a fixed point of hemicontractive-type mapping and a generalized equilibrium problem

“…Several authors have studied iterative algorithms for approximating fixed points of various classes of nonlinear mappings (including hemicontractive mapping); see, for example, [5,8,14,15,21] and the references cited therein. In 2007, Rafiq [13] introduced the following Mann-type implicit iteration process and showed that the process converges strongly to a fixed point of a continuous hemicontractive mapping T from a compact and convex subset C of a real Hilbert space into itself:…”

Mann and Ishikawa-Type Iterative Schemes for Approximating Fixed Points of Multi-valued Non-Self Mappings

“…Consequently, the existence of fixed points and their approximations for multi-valued contraction and nonexpansive mappings and their generalizations have been studied by several authors (see, e.g., [1,3,4,6,9,[11][12][13]15] and the references therein).…”