A hybrid iterative scheme for equilibrium problems, variational inequality problems, and fixed point problems in Banach spaces.
A new hybrid algorithm for variational inclusions, generalized equilibrium problems, and a finite family of quasi-nonexpansive mappings.
Convergence analysis for a system of equilibrium problems and a countable family of relatively quasi-nonexpansive mappings in Banach spaces.
Weak convergence theorems for a countable family of strict pseudocontractions in Banach spaces.
Convergence analysis for a system of generalized equilibrium problems and a countable family of strict pseudocontractions.
Inertial forward-backward splitting method in Banach spaces with application to compressed sensing
We propose a Halpern-type forward-backward splitting with inertial extrapolation step for finding a zero of the sum of accretive operators in Banach spaces. Strong convergence of the sequence of iterates generated by the method proposed is obtained under mild assumptions. We give some numerical results in compressed sensing to validate the theoretical analysis results. Our result is one of the few available inertial-type methods for zeros of the sum of accretive operators in Banach spaces.
Convergence results of iterative algorithms for the sum of two monotone operators in reflexive Banach spaces
The aim of this paper is to propose two modified forward-backward splitting algorithms for zeros of the sum of a maximal monotone operator and a Bregman inverse strongly monotone operator in reflexive Banach spaces. We prove weak and strong convergence theorems of the generated sequences by the proposed methods under some suitable conditions. We apply our results to study the variational inequality problem and the equilibrium problem. Finally, a numerical example is given to illustrate the proposed...
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