Moreover, comparing to [9] (which also considers upper semicontinuous multifunctions), we imposed only the upper semicontinuity with respect to the second argument, along with a jointly measurability condition.
A trimapping is generalized pseudo-contractive with respect to in the first argument of with constant and generalized -pseudo-contractive wito respect to in the second argument of with constant, Lipschitz continuous with respect to the first, second, and third arguments with positive constants respectively.
A trimapping is generalized pseudo-contractive with respect to map in first argument of with constant and generalized -pseudo-contractive wito respect to in the second argument of with constant, Lipschitz continuous with respect to first, second, and third arguments with positive constants, respectively.
Assume that, are Lipschitz continuous with constants, and, respectively, is g-generalized pseudocontractive with constant with respect to in the second argument, and is cocoercive with constant.
Let and be mappings such that is -strongly monotone with respect to in the first argument with constant, -monotone with respect to in the second argument, is Lipschitz continuous with constant and and are -hemicontinuous with respect to and in.
Let T i : H × H → H and g i : H → H be mappings such that T i is relaxed ( ω i, t i ) -cocoercive, μ i -Lipschitz continuous with respect to the first argument, γ i -Lipschitz continuous with respect to the second argument and g i is η i -Lipschitz continuous, ζ i -strongly monotone mapping for i = 1, 2. Assume that the following assumptions hold: where κ = ∑ i = 1 2 1 − 2 ζ i + η i 2 < 1.
Assume that, are Lipschitz continuous with constants and, respectively, is relaxed Lipschitz with constant, and is relaxed Lipschitz with constant with respect to in the second argument.
Let be a -strongly monotone with respect to the first argument and -Lipschitz mapping and be a -strongly monotone with respect to the second argument and -Lipschitz mapping.
Furthermore, the truncation operators are continuous, uniformly bounded, and Lipschitz continuous with respect to the second argument.
