Some minimax theorems with strictly monotone transformation

Some two-function minimax theorems are proved. In these results, the staircase and quantitative-topological conditions of both functions involve strictly monotone transformation and mixing of functional values. Consequently, Lin Quan and Kindler＇s minimax theorems are generalized.

MINIMAX THEOREMS FOR SUBCONVEXLIKEFUNCTIONS WITH APPLICATIONS TO SADDLEPOINT PROBLEMS

In this paper some minimax theorems are presented for subconvexlike functions. These are then applied to obtain saddle point theorems.

Topologically Finite Intersection Property and Minimax Theorems

A more general lopologically finite intersection property is obtained. As anapplication,we utilize this result to obtain some more general minimax theorems. Theresults presented in this paper unify and extend the main results of [5, 6, 9].

Minimax Theorems Involving Two Functions and Strictly Monotone Transformations of Their Values

Two two-function minimax theorems are proved. The concavity-convexity conditions of the two functions involve strictly monotone transformations and mixing of the values of the two functions, and are described by the inequalities as upward and weakly downward conditions.

Minimax principle on energy dissipation of incompressible shear flow

The energy dissipation rate is an important concept in the theory of turbulence. Doering-Constantin＇s variational principle characterizes the upper bounds （maxi- mum） of the time-averaged rate of viscous energy dissipation. In the present study, an optimization theoretical point of view was adopted to recast Doering-Constantin＇s formu- lation into a minimax principle for the energy dissipation of an incompressible shear flow. Then, the Kakutani minimax theorem in the game theory is applied to obtain a set of conditions, under which the maximization and the minimization in the minimax principle are commutative. The results explain the spectral constraint of Doering-Constantin, and confirm the equivalence between Doering-Constantin＇s variational principle and Howard- Busse＇s statistical turbulence theory.

MINIMAX THEOREM AND SADDLE POINT THEOREM WITHOUT LINEAR STRUCTURE

In this paper, a new kind of concavity of a function defined on a set without linear structure is introduced and a generalization of Fam Ky inequality is given. Minimax theorem in a general topological space is obtained. Moreover, a saddle point theorem on a topological space without any linear structure is established.

A General Topological Version of Minimax Theorem

A more general topological version of minimax theorem inchuding the main resultsin Konig[3]as its special cases are given,and an open question suggested in Konig[3]is answered.

Some Vector Ky Fan Minimax Inequalities with Nonconvex Domain

In this paper, by virtue of separation theorems of convex sets and scalarization functions, some minimax inequalities are first considered. As applications, some existence theorems of vector equilibrium problems with different order structures were also obtained.

A New Section Theorem in L-convex Spaces and Its Applications

In this paper, the author gives a new section theorem in L-convex spaces. And as its applications, the author proves a coincident theorem and a two-functional minimax theorem established in L-convex spaces.

Statistical Learning in Game Theory

In economics, buyers and sellers are usually the main sides in a market. Game theory can perfectly model decisions behind each “player” and calculate an outcome that benefits both sides. However, the use of game theory is not lim-ited to economics. In this paper, I will introduce the mathematical model of general sum game, solutions and theorems surrounding game theory, and its real life applications in many different scenarios.

Error Bounds for Generalized Mixed Vector Equilibrium Problems via a Minimax Strategy

In this paper,by using scalarization techniques and a minimax strategy,error bound results in terms of gap functions for a generalized mixed vector equilibrium problem are established,where the solutions for vector problems may be general sets under natural assumptions,but are not limited to singletons.The other essentially equivalent approach via a separation principle is analyzed.Special cases to the classical vector equilibrium problem and vector variational inequality are also discussed.

A General Two-function Minimax Theorem

A two-function minimax theorem is proved. In this result, the concavity-convexity conditions of both functions involve monotone transforms and mixing of functional values, and the ＂w- upwardness/w-downwardness＂ conditions; both spaces are required to be compact topological spaces but without linear structure. By this result, an open question proposed by Forgo and Joo in 1998 is answered.

Some Minimax Problems in Lexicographic Order

In this paper, minimax theorems and saddle points for a class of vector-valued mappings f（x, y） = u（x） ＋ β（x）v（y） are first investigated in the sense of lexicographic order, where u, v are two general vector-valued mappings and β is a non-negative real-valued function. Then, by applying the existence theorem of lexicographic saddle point, we investigate a lexicographic equilibrium problem and establish an equivalent relationship between the lexicographic saddle point theorem and existence theorem of a lexicographic equilibrium problem for vector-valued mappings.

A Topological Minimax Theorem Involving Two Functions

A topological minimax theorem involving two functions is derived. It generalizes Greco and Horvath’minimax theorem given by them in 2002.

Singular Value Inequalities of Matrix Sum in Log-ma jorizations

We show some upper bounds for the product of arbitrarily selected singular values of the sum of two matrices.The results are additional to our previous work on the lower bound eigenvalue inequalities of the sum of two positive semidefinite matrices.Besides,we state explicitly Hoffman’s minimax theorem with a proof,and as applications of our main results,we revisit and give estimates for related determinant inequalities of Hua type.