Some Modified Extragradient Methods for Solving Split Feasibility and Fixed Point Problems

Abstract EN

We consider and study the modified extragradient methods for finding a common element of the solution set Γ of a split feasibility problem (SFP) and the fixed point set Fix(S) of a strictly pseudocontractive mapping S in the setting of infinite-dimensional Hilbert spaces.

We propose an extragradient algorithm for finding an element of Fix(S)∩Γ where S is strictly pseudocontractive.

It is proven that the sequences generated by the proposed algorithm converge weakly to an element of Fix(S)∩Γ.

We also propose another extragradient-like algorithm for finding an element of Fix(S)∩Γ where S:C→C is nonexpansive.

It is shown that the sequences generated by the proposed algorithm converge strongly to an element of Fix(S)∩Γ.