Generalized Hybrid Viscosity-Type Forward-Backward Splitting Method with Application to Convex Minimization and Image Restoration Problems

An Accelerated Halpern-Type Algorithm for Solving Variational Inclusion Problems With Applications

“…In this section will state some important results used in the proof of our main Theorem 3.5. We will assume that the basic notions used are known by the reader (otherwise, see, e.g., page 5 of [21]). The first lemma we will state is the famous subdifferential inequality whose proof can be found in this monograph [22].…”

“…Remark 2.9. The analytic representations of duality maps and κ q are known in L p (Λ) and L q (Λ) spaces, Λ ⊂ R, for p > 1 and q > 1 such that 1 p + 1 q = 1 (see, e.g., page 7 of [21]).…”

“…λn is nonexpansive (see, e.g., [21]). Now, using Remark 2.4 (i) and the nonexpansivity of W A,B λn , we have Thus, using inequality (3.1), we obtain…”

Approximation method for monotone inclusion problems in real Banach spaces with applications

“…However, if the operator maps E to its dual space, E * and satisfies the same property as in the setting of real Hilbert spaces, the name monotone is retained. In the literature, extensions of the inclusion problem (1) involving accretive operators have been studied by many authors (see, e.g., [30][31][32][33][34][35]). However, there are only a few results in the monotone sense.…”

A parallel method for common variational inclusion and common fixed point problems with applications

“…Moudafi and Oliny [15] in 2003 introduced the inertial proximal algorithm to solve the problem (1.1), which was developed from the forwardbackward splitting algorithm with the inertial extrapolation technique. Some very recent results on the modified forward-backward splitting method have also been in [1,5,6,14]. Many real-world problems necessitate finding a solution that satisfies several constraints.…”