A Modified Halpern's Iterative Scheme for Solving Split Feasibility Problems

Abstract

The purpose of this paper is to introduce and study a modified Halpern's iterative scheme for solving the split feasibility problem SFP in the setting of infinite-dimensional Hilbert spaces. Under suitable conditions a strong convergence theorem is established. The main result presented in this paper improves and extends some recent results done by Xu Iterative methods for the split feasibility problem in infinite-dimensional Hilbert space, Inverse Problem 26 2010 105018 and some others.

Multiple-Set Split Feasibility Problems forκ-Strictly Pseudononspreading Mapping in Hilbert Spaces

“…Osilike and Isiogugu [11] introduced a class of nonspreading type mappings which is more general than that of the mappings studied in [12] in Hilbert spaces and proved some weak and strong convergence theorems in real Hilbert spaces. Recently, the split feasibility problem also was considered in the work by Deepho and Kumam [13,14] and Sunthrayuth et al [15], and some weak and strong convergence theorems are proved in real Hilbert spaces.…”

Strong convergence result of split feasibility problems in Banach spaces

“…Hence, our algorithm (17) appears more efficient and implementable than the algorithm of Wang [25]. and Kumam [7] are dispensed with in our result even in higher Banach spaces than Hilbert where the result of Deepho and Kumam [7] was proved.…”

“…2. In implementing the algorithm (7), one has to calculate, at each iteration, the Bregman projection onto the intersection of two half spaces but in this our iterative algorithm (17), one does not have to calculate, at each iteration, the Bregman projection onto the intersection of two half spaces. Hence, our algorithm (17) appears more efficient and implementable than the algorithm of Wang [25].…”

“…Using the idea in the work of Nakajo and Takahashi [14], he proved the following strong convergence theorem in p-uniformly convex Banach spaces which is also uniformly smooth. be generated by (7). Then {x n } ∞ n=1 converges strongly to the Bregman projection ofx onto the solution set Ω.…”

Extragradient methods for split feasibility problems and generalized equilibrium problems in Banach spaces

“…Recently, it has been found that the S F P can also be used to study of intensity‐modulated radiation therapy, see Censor et al,() and it has been studied by many researchers. ()…”