Retraction algorithms for solving variational inequalities, pseudomonotone equilibrium problems, and fixed-point problems in Banach spaces

Strong convergence theorems for variational inequalities and fixed point problems in Banach spaces

“…Furthermore, the theorems proved are analogue of the result of Khanh, [32] in that if D = H, a real Hilbert space, the normalized duality map is the identity on D. Hence, the both theorems coincide. Finally, the class of η-strongly J-pseudo-monotone maps considered, contains the class J-monotone maps studied in [26].…”

“…Definition 2.2. [26] Let M be a nonempty, closed and convex subset of Q. The monovariational inequality is to find an element u ∈ M , such that ψ(u), Jz − Ju ≥ 0, ∀ z ∈ M, where ψ : M → Q.…”

“…In this paper, we study the mono-variational inequality problem of Jouymandil and Moradloul [26] and J-fixed points for a countable family of generalized non-expansivetype maps in L p spaces, 2 ≤ p < ∞.…”

A subgradient extragradient algorithm for solving split equilibrium and fixed point problems in reflexive Banach spaces

“…In 2016, Dihn et al [18] studied the split equilibrium problem involving pseudomonotone and monotone bifunctions and nonexpansive mappings in real Hilbert spaces. Jouymandi and Moradlou [19] extended this study to the framework of Banach space. They considered a single EP involving a pseudomonotone bifunction.…”

Extragradient and linesearch methods for solving split feasibility problems in Hilbert spaces

“…In the recent years, many authors applied extragradient algorithms for solving ( EP ) by using auxiliary equilibrium problem where the convergence of the presented methods requires f to satisfy a certain Lipschitz‐type condition. () In Lipschitz‐type condition, two positive parameters c 1 and c 2 must be determined and have a fundamental role, which in some cases, they are unknown and their estimate is difficult. To dominate this difficulty, researchers applied the linesearch method to afford algorithms for solving ( EP ).…”