Multi-Step Inertial Regularized Methods for Hierarchical Variational Inequality Problems Involving Generalized Lipschitzian Mappings

Abstract

In this paper, we construct two multi-step inertial regularized methods for hierarchical inequality problems involving generalized Lipschitzian and hemicontinuous mappings in Hilbert spaces. Then we present two strong convergence theorems and some numerical experiments to show the effectiveness and feasibility of our new iterative methods.

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

“…Then, by the boundedness of {w n }, this implies that lim n→∞ φ(w, w n ) exists. Thus, from inequality (14), we obtain that…”

“…It is well known that iterative methods involving monotone operators have slow convergence properties. In the literature, the study of convergence properties of iterative algorithms has become an area of contemporary interest (see, e.g., [11][12][13][14][15][16][17]). One method that is now studied enormously is the inertial extrapolation technique which dates back to the early result of Polyak [18] in the context of convex minimization.…”

Higher Transcendental Functions and Their Multi-Disciplinary Applications

“…The geographical distribution of the contributors to this Special Issue is remarkably widely-scattered. Their contributions (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]) originated in many different countries on every continent of the world.…”

“…The subject matter of the first 16 publications (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]) dealt extensively with analytic, univalent, multivalent, and harmonic functions of complex analysis and their quantum or basic (or q-) extensions, the Euler-Poisson-Darboux partial differential equation, approximation theory and associated summability methods, variational inequalities, linear and nonlinear integro-differential equations, growth results involving Dirichlet series, theory and applications of wavelet transforms, analysis of ordinary and partial differentialdifference equations, and several other topics listed in the preceding section.…”