Tykhonov Well-Posedness for Quasi-Equilibrium Problems

Vector parametric quasi-equilibrium problems for the sum of two set-valued mappings

“…In this work, we study also constraint parametric equilibrium problems. Different types of equilibrium problems for set-valued maps in various spaces were intensively studied and many results on the existence of solutions for equilibrium problems were obtained, see [9,10,11,12,13,14,15,16]. Moreover, equilibrium problems for the sum of two set-valued mappings were studied in [15,17].…”

“…then we obtain parametric generalized vector quasi-variational-like inequality problem in [21]; (iv) if for each x, y ∈ A and p ∈ P, we define G(x, y, p) = 0, then (a) Problem (P β (p)) reduces to vector parametric equilibrium problems, which has been considered in, e.g., [9,10,11,12,13,17,22]; (b) if F(x, y, p) = H(y, p) − H(x, p), that H : A × P −→ 2 Z then, we have vector parametric optimization problem (see [16,18,23]); (c) if F(x, y, p) =< w, y − x >, such that T : A × P −→ 2 L(X,Z) and w ∈ T (x, p) then we obtain vector parametric variational inequality (see [23,24]).…”