Coincidence and fixed point theorems with applications

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 quasivariational inequalities and prove an existence result for a solution to such a system.

Fixed point theorems for generalized multivalued nonlinear F -contractions

“…We say that T is monotone increasing, if T y T z, for all y, z ∈ X , for which y z. There are many applications in differential and integral equations of monotone mappings in ordered metric spaces (see [2,7,16,17] and references therein). In this section, from Sections 2 and 3, we derive the following new results in partially ordered metric spaces.…”

Collective fixed points and maximal elements with applications to abstract economies

“…In the recent past the existence theorems for a maximal element for a family of multivalued maps have been used to prove the existence of a solution of system of variational inequalities and system of equilibrium problems, see for example [2,[10][11][12]19] and references therein. It can be easily seen that the maximal elements theory for the family of multivalued maps is useful to study the following qualitative game.…”

“…In the last decade, the theory of fixed points and maximal elements for a family of multivalued maps defined on a product space has been investigated by many authors, see for example [1,2,[4][5][6][10][11][12]19] and references therein. It has many applications in abstract economies, nonlinear analysis and other branches of mathematics.…”

Existence of solutions of systems of generalized implicit vector quasi-equilibrium problems

“…By using different types of maximal element theorems for a family of multivalued maps and different types of fixed point theorems for a multivalued map, several authors studied the existence of solutions of different kinds of systems of (vector) quasi-equilibrium problems. See, for example, [3][4][5][6][7]16,[18][19][20]26,[28][29][30]36,37] and references therein.…”