Yosida Approximation Iterative Methods for Split Monotone Variational Inclusion Problems

Abstract

In this paper, we present two iterative algorithms involving Yosida approximation operators for split monotone variational inclusion problems ( S p MVIP ). We prove the weak and strong convergence of the proposed iterative algorithms to the solution of S p MVIP in real Hilbert spaces. Our algorithms are based on Yosida approximation operators of monotone mappings such that the step size does not require the precalculation of the operator norm. To show the reliability and accuracy of the proposed algorithms, a numerical example is also constructed.

A Modified Viscosity-Type Self-Adaptive Iterative Algorithm for Common Solution of Split Problems with Multiple Output Sets in Hilbert Spaces

“…Since then, various successive approximation methods for solving the SCFP (1) have been established and studied; see [4][5][6][7][8][9][10][11][12][13][14][15][16]. Some commonly investigated generalizations of the SCFP (1) are multiple set split feasibility problems (MSSFPs) [9], split common fixed point problems (SCFPPs) [17], split variational inequality problems (SVIPs) [8], split monotone variational inclusion problems (SMVIPs) [18,19], and split common null point problems (SCNPPs) [20][21][22].…”

Modified Iterative Schemes for a Fixed Point Problem and a Split Variational Inclusion Problem

“…where ψ is a contraction mapping, α ∈ (0, 1), µ ∈ (0, 1 L ), L is the spectral radius of A * A, α n ∈ (0, 1) is a real sequence, and λ > 0. Inspired by the work of [8][9][10], many authors have studied (S p VIP) and (FPP) in diverse directions using different techniques (see, for example, [11][12][13][14][15][16][17][18][19][20]).…”

Tseng‐Type Algorithms for the Split Variational Inclusion

“…It should be pointed out that the operators h and φ in (10) were assumed to be inverse strongly monotone. e split variational inclusion (7) has been studied extensively, see [24,28,[30][31][32][33][34][35][36].…”