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In this article, we offer two modifications of the modified forward‐backward splitting method based on inertial Tseng method and viscosity method for inclusion problems in real Hilbert spaces. Under standard assumptions, such as Lipschitz continuity and monotonicity (also maximal monotonicity), we establish weak and strong convergence of the proposed algorithms. We give the numerical experiments to show the efficiency and advantage of the proposed methods and we also used our proposed algorithm for solving the image deblurring and image recovery problems. Our result extends some related works in the literature and the primary experiments might also suggest their potential applicability. [ABSTRACT FROM AUTHOR]

We introduce a new iterative algorithm for finding a common element of a fixed point problem of amenable semigroups of nonexpansive mappings, the set solutions of a system of a general system of generalized equilibria in a real Hilbert space. Then, we prove the strong convergence of the proposed iterative algorithm to a common element of the above three sets under some suitable conditions. As applications, at the end of the paper, we apply our results to find the minimum-norm solutions which solve some quadratic minimization problems. The results obtained in this paper extend and improve many recent ones announced by many others. [ABSTRACT FROM AUTHOR]

We propose new iterative schemes for finding the common element of the set of common fixed points of countable family of nonexpansive mappings, the set of solutions of the variational inequality problem for relaxed cocoercive and Lipschitz continuous, the set of solutions of system of variational inclusions problem, and the set of solutions of equilibrium problems in a real Hilbert space by using the viscosity approximation method. We prove strong convergence theorem under some parameters. The results in this paper unify and generalize some well-known results in the literature. [ABSTRACT FROM AUTHOR]

This paper deals with new methods for approximating a solution to the fixed point problem; find x ∈ F(T), where H is a Hilbert space, C is a closed convex subset of H, f is a ρ-contraction from C into H, 0 < ρ < 1, A is a strongly positive linear-bounded operator with coefficient γ > 0, 0 < γ < γ/ρ, T is a nonexpansive mapping on C, and PF(T) denotes the metric projection on the set of fixed point of T.Under a suitable different parameter, we obtain strong convergence theorems by using the projection method which solves the variational inequality 〈(A-γf)x+τ(I-S)x, x- x) = 0 for x ∈ F(T), where τ ∈ [0,∞). Our results generalize and improve the corresponding results of Yao et al. (2010) and some authors. Furthermore, we give an example which supports our main theorem in the last part. [ABSTRACT FROM AUTHOR]

We introduce a new general iterative method for finding a common element of the set of solutions of fixed point for nonexpansive mappings, the set of solution of generalized mixed equilibrium problems, and the set of solutions of the variational inclusion for a β-inverse-strongly monotone mapping in a real Hilbert space. We prove that the sequence converges strongly to a common element of the above three sets under some mild conditions. Our results improve and extend the corresponding results of Marino and Xu (2006), Su et al. (2008), Klin-eam and Suantai (2009), Tan and Chang (2011), and some other authors. [ABSTRACT FROM AUTHOR]

We introduce a general composite iterative scheme for nonexpansive semigroups in Banach spaces. We establish some strong convergence theorems of the general iteration scheme under different control conditions. The results presented in this paper improve and extend the corresponding results of Marino and Xu (2006), and others, from Hilbert spaces to Banach spaces. [ABSTRACT FROM AUTHOR]