Abstract
In this paper, we establish a strong convergence theorem for hierarchical problems, an equivalent relation between a multiple sets split feasibility problem and a fixed point problem. As applications of our results, we study the solution of mathematical programming with fixed point and multiple sets split feasibility constraints, mathematical programming with fixed point and multiple sets split equilibrium constraints, mathematical programming with fixed point and split feasibility constraints, mathematical programming with fixed point and split equilibrium constraints, minimum solution of fixed point and multiple sets split feasibility problems, minimum norm solution of fixed point and multiple sets split equilibrium problems, quadratic function programming with fixed point and multiple set split feasibility constraints, mathematical programming with fixed point and multiple set split feasibility inclusions constraints, mathematical programming with fixed point and split minimax constraints.
Highlights
1 Introduction The split feasibility problem (SFP) in finite dimensional Hilbert spaces was first introduced by Censor and Elfving [ ] for modeling inverse problems which arise from phase retrievals and in medical image reconstruction
We establish a strong convergence theorem for hierarchical problems, an equivalent relation between a multiple sets split feasibility problem and a fixed point problem
As applications of our results, we study the solution of mathematical programming with fixed point and multiple sets split feasibility constraints, mathematical programming with fixed point and multiple sets split equilibrium constraints, mathematical programming with fixed point and split feasibility constraints, mathematical programming with fixed point and split equilibrium constraints, minimum solution of fixed point and multiple sets split feasibility problems, minimum norm solution of fixed point and multiple sets split equilibrium problems, quadratic function programming with fixed point and multiple set split feasibility constraints, mathematical programming with fixed point and multiple set split feasibility inclusions constraints, mathematical programming with fixed point and split minimax constraints
Summary
The split feasibility problem (SFP) in finite dimensional Hilbert spaces was first introduced by Censor and Elfving [ ] for modeling inverse problems which arise from phase retrievals and in medical image reconstruction. Xu [ ] studied the following minimization problem over the set of fixed points of a nonexpansive operator T on a real Hilbert space H: min Bx, x – a, x , x∈Fix(T). [ ] Let C be a nonempty closed convex subset of a real Hilbert space H, and let T : C → C be a mapping. For solving the equilibrium problem, let us assume that the bifunction g : C × C → R satisfies the following conditions:. [ ] Let C be a nonempty closed convex subset of a real Hilbert space H. [ ] Let C be a nonempty closed convex subset of a real Hilbert space H, and let g : C × C → R be a function satisfying conditions (A )-(A ).
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