‎In this paper‎, ‎we introduce and study a class of generalized vector quasi-equilibrium problem‎, ‎which includes many vector equilibrium problems‎, ‎equilibrium problems‎, ‎vector variational inequalities and variational inequalities as special cases‎. ‎Using one person game theorems‎, ‎the concept of escaping sequences and without convexity assumptions‎, ‎we prove some existence results for ...

A concept of weak $f$-property for a set-valued mapping is introduced‎, ‎and then under some suitable assumptions‎, ‎which do not involve any information‎ ‎about the solution set‎, ‎the lower semicontinuity of the solution mapping to‎ ‎the parametric‎ ‎set-valued vector equilibrium-like problems are derived by using a density result and scalarization method‎, ‎where the‎ ‎constraint set $K$...

In this paper, we suggest and analyze some iterative methods for solving equilibrium problems with trifunction by using the auxiliary principle technique. We prove that the convergence of the proposed methods either requires only pseudomonotonicity or partially relaxed strongly monotonicity. We also consider the concept of well-posedness for equilibrium problems with trifunction and obtain some...

As Henri PoincarC once remarked, “solution of a mathematical problem” is a phrase of indefinite meaning. Pure mathematicians sometimes are satisfied with showing that the non-existence of a solution implies a logical contradiction, while engineers might consider a numerical result as thc only reasonable goal. Such one sided views seem to reflect human limitations rather than objective values. I...

We introduce a new class of equilibrium problems, known as mixed quasi invex equilibrium (or equilibrium-like) problems. This class of invex equilibrium problems includes equilibrium problems, variational inequalities, and variational-like inequalities as special cases. Several iterative schemes for solving invex equilibrium problems are suggested and analyzed using the auxiliary principle tech...

The aim of this work is to analyze lexicographic equilibrium problems on a topological Hausdorff vector space X, and their relationship with some other vector equilibrium problems. Existence results for the tangled lexicographic problem are proved via the study of a related sequential problem. This approach was already followed by the same authors in the case of variational inequalities.