Iterative methods for generalized nonlinear variational inequalities

Completely generalized multivalued nonlinear quasi‐variational inclusions

“…We also establish four existence theorems of solutions for the class of completely generalized multivalued nonlinear quasi-variational inclusions involving strongly monotone, relaxed Lipschitz and generalized pseudocontractive multivalued mappings, and give some convergence results of iterative sequences generated by the algorithms. Our results extend, improve and unify a lot of results due to Adly [1], Huang [2,3,4], Jou and Yao [5], Kazmi [6], M. A. Noor [8,9,10], M. A. Noor and Al-Said [11], M. A. Noor and K. I. Noor [12], M. A. Noor et al [13], Shim et al [14], Siddiqi and Ansari [15,16], Verma [18,19], Yao [20], and Zhang [21].…”

“…which is known as the generalized multivalued quasi-variational inequality, introduced and studied by M. A. Noor [9]. For appropriate and suitable choices of the mappings g, h, A, B, C, D, E, N, M, W , the element f ∈ H, a number of known classes of variational inequalities, quasi-variational inequalities, and quasi-variational inclusions, studied by several researchers including Aldly [1], Huang [2,3], Jou and Yao [5], Kazmi [6], M. A. Noor [7,8], M. A. Noor and Al-Said [11], Siddiqi and Ansari [15,16], Uko [17], Verma [18,19], Yao [20], and Zhang [21], can be obtained as special cases of problem (2.1). This reveals that the completely generalized multivalued nonlinear quasi-variational inclusion (2.1) is the more general and unifying one.…”

Existence and algorithm of solutions for general set-valued Noor variational inequalities with relaxed (μ,ν)-cocoercive operators in Hilbert spaces

“…(see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] and references therein, for examples). Equally important is the study of the equations known as the Wiener-Hopf equations, whose origin can be traced back to Shi [16] and Robinson [13], independently in different areas.…”