Pan et al. [19] introduced a general nonlinear mixed set-valued inclusion framework for the over-relaxed A-proximal point algorithm based on the ( A, η ) -accretive mapping and studied the approximation solvability of a general class of inclusion problems using the generalized resolvent operator technique associated with an ( A, η ) -accretive mapping.
Further, by using the generalized resolvent operator technique associated with ( A, η, m ) -maximal monotone operators, we discussed the approximation solvability of operator equation problems and the convergence of iterative sequences generated by the algorithm frameworks.
Furthermore, by using the generalized resolvent operator technique associated with ( A, η, m ) -monotone operators, the approximation solvability of operator inclusion problems and the convergence rate of iterative sequences generated by the algorithm were discussed.
Further, by using the generalized resolvent operator technique associated with ( A, η, m ) -monotone operators, the Lipschitz continuity and Liu's inequality, the existence of solution for the nonlinear operator inclusion problem and the graphical convergence of iterative sequences generated by the algorithm will be discussed.
Moreover, by using the generalized resolvent operator technique associated with relative ( A, η ) -maximal monotone operators, we also construct some new iterative algorithms for finding approximation solutions to the general systems of set-valued variational inclusions and prove convergence of the sequences generated by the algorithms.
Li and Lan [17] introduced and studied the over-relaxed ( A, η ) -proximal point algorithm framework for approximating the solutions of operator inclusions by using the generalized resolvent operator technique associated with ( A, η ) -monotone operators and by means of two different methods.
Exchange correlation was described using the generalized gradient approximation in the Perdew–Burke Ernzerhof implementation.
We computed chemical structure similarity scores of compounds by using the generalized Jaccard correlation coefficient.
Using the generalized f-projection method.
By using Liu's inequality and the generalized resolvent operator technique associated with ( A, η, m ) -monotone operators, we also prove the existence of solution for the nonlinear operator inclusions and discuss the graph-convergent analysis of iterative sequences generated by the algorithm.
A new class of generalized nonlinear variational inclusions involving -monotone mappings in the framework of Hilbert spaces is introduced and then based on the generalized resolvent operator technique associated with -monotonicity, the approximation solvability of solutions using an iterative algorithm is investigated.
