### Coincidence and fixed point theorems with applications

DOI: http://dx.doi.org/10.12775/TMNA.2000.016

#### Abstract

In this paper, we first establish a coincidence theorem under the noncompact settings. Then we derive some fixed point theorems for a family of functions.

We apply our fixed point theorem to study nonempty intersection problems for sets with convex sections and obtain a social equilibrium

existence theorem. We also introduce a concept of a quasi-variational inequalities and prove an existence result for a solution to such a system.

We apply our fixed point theorem to study nonempty intersection problems for sets with convex sections and obtain a social equilibrium

existence theorem. We also introduce a concept of a quasi-variational inequalities and prove an existence result for a solution to such a system.

#### Keywords

Coincidence; fixed point; convex section; equilibrium; quasi-variational inequality

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