Monotone hybrid methods for a common solution problem in Hilbert spaces

A Weak-to-strong Convergence Principle for Fej Er-monotone Methods in Hilbert Spaces

A Weak-to-Strong Convergence Principle for Fejé-Monotone Methods in Hilbert Spaces

where Pi denotes the projector onto Si and where the mod m function takes values in 0 m−1 , converges weakly to a point in S =⋂mi=1 Si. In Gubin et al. (1967) (see also Bauschke 1995, Bauschke and Borwein 1996, Bauschke et al. 1997, and Combettes 1997), certain regularity conditions on the sets were described that guaranteed strong convergence of the iterations. To this day, however, it remains...

A Hybrid Proximal Point Algorithm for Resolvent operator in Banach Spaces

Equilibrium problems have many uses in optimization theory and convex analysis and which is why different methods are presented for solving equilibrium problems in different spaces, such as Hilbert spaces and Banach spaces. The purpose of this paper is to provide a method for obtaining a solution to the equilibrium problem in Banach spaces. In fact, we consider a hybrid proximal point algorithm...

Hybrid algorithm for common solution of monotone inclusion problem and fixed point problem and applications to variational inequalities

The aim of this paper is to investigate hybrid algorithm for a common zero point of the sum of two monotone operators which is also a fixed point of a family of countable quasi-nonexpansive mappings. We point out two incorrect proof in paper (Hecai in Fixed Point Theory Appl 2013:11, 2013). Further, we modify and generalize the results of Hecai's paper, in which only a quasi-nonexpansive mappin...

Backward-forward Algorithms for Structured Monotone Inclusions in Hilbert Spaces

In this paper, we study the backward-forward algorithm as a splitting method to solve structured monotone inclusions, and convex minimization problems in Hilbert spaces. It has a natural link with the forward-backward algorithm and has the same computational complexity, since it involves the same basic blocks, but organized differently. Surprisingly enough, this kind of iteration arises when st...