General Split Feasibility Problems in Hilbert Spaces

Abstract

Introducing a general split feasibility problem in the setting of infinite-dimensional Hilbert spaces, we prove that the sequence generated by the purposed new algorithm converges strongly to a solution of the general split feasibility problem. Our results extend and improve some recent known results.

Feasible iterative algorithms and strong convergence theorems for bi-level fixed point problems

“…As special cases, we shall utilize our results to study the Bi-lever split equilibrium problems, Bi-level split convex optimization problems and Bi-level split variational inequality problems. The results presented in the paper extend and improve the corresponding results announced by Censor et al [4,5,6,7,8], Moudafi et al [23,24,25], Eslamian and Latif [19], Chen et al [17], Chuang [18], Chang and wang [13], Chang and Agarwal [10] and Chang et al [14], Naraghirad [26], He and Du [21], Ansari and Rehan [1].…”

“…Very recently, Eslamian et al [19], Chen et al [17], Chuang [18] and Chang et al [10,13,14] introduced and studied some kinds of general split feasibility problem, general split equality problem, general split equality variational inclusion problems and general split equality optimization problems in real Hilbert spaces. Under suitable conditions some strong convergence theorems are proved.…”

Some Results for Split Equality Equilibrium Problems in Banach Spaces

“…Some iteration algorithms have been proposed for finding a solution of these problems (see, for instance, ref. [20][21][22][23] and the references therein). Especially, the split equality mixed equilibrium problem was investigated in [24] and the convergence results on solutions were obtained in Hilbert spaces.…”

Strong convergence for generalized multiple-set split feasibility problem

“…Recently, it has been found that the SFP can also be applied to study intensity-modulated radiation therapy; see, e.g., [6,8,10] and the references therein. In the recent past, a wide variety of iterative methods have been used in signal processing and image reconstruction and for solving the SFP and MSSPP; see, e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] and the references therein.…”