Maximal element theorems in product FC-spaces and generalized games

Some Maximal Elements’ Theorems in FC-Spaces

Let I be a finite or infinite index set, let X be a topological space, and let Yi, φNi i∈I be a family of FC-spaces. For each i ∈ I, letAi : X → 2i be a set-valued mapping. Some new existence theorems of maximal elements for a set-valued mapping and a family of set-valued mappings involving a better admissible set-valuedmapping are established under noncompact setting of FC-spaces. Our results ...

Coincidence Theorems on Product FC-spaces

In 1937, Von Neumann [1] established the famous coincidence theorem. Since then, the coincidence theorem was generalized in many directions. Browder [2] first proved some basic coincidence theorems for a pair of set-valued mappings in compact setting of topological vector spaces and gave some applications to minimax inequalities and variational inequalities. Recently, Ding [3] established some ...

Convergence Theorems for Generalized Projections and Maximal Monotone Operators in Banach Spaces

Riesz Theorems in 2-inner Product Spaces

In this paper we describe the proof of ’Riesz Theorems’ in 2inner product spaces. The main result holds only for a b-linear functional but not for a bilinear functional. AMS Mathematics Subject Classification (2010): 41A65, 41A15

Maximal elements of $mathscr{F}_{C,theta}$-majorized mappings and applications to‎ ‎generalized games

In the paper‎, ‎some new existence theorems of maximal elements for‎ ‎$mathscr{F}_{C,theta}$-mappings and $mathscr{F}_{C,theta}$-majorized mappings are established‎. ‎As applications, ‎some new existence theorems of equilibrium points for‎ ‎one-person games‎, ‎qualitative games and generalized games are obtained‎. ‎Our results unify and generalize most known results‎ ‎in recent literature‎.