In this paper, on the basis of some recent works of Fan, Jiang and Jia, we establish a representation theorem in the space of processes for generators of BSDEs with monotonic and polynomialgrowth generators, which generalizes the corresponding results in Fan (2006, 2007), and Fan and Hu (2008).

The uniform continuity theorem ( UCT ) states that every pointwise continuous real-valued function on the unit interval is uniformly continuous. In constructive mathematics, strictly stronger than decidable fan DFT , but Loeb [17] has shown two principles become equivalent by encoding functions as type-one functions. However, precise relation between such and (usually described type-two objects...

In recent years there has been interest in a theorem on positive definite matrices known as Lyapunov's theorem. Several authors have proved generalizations of this theorem, (WIELANDT [29J, TAUSSKY [24J, [25J, [26J , OSTROWSKISCHNEIDER [20J, GIVENS [10J, CARLSON-SCHNEIDER [3J, CARLSON [4J) . Lyapunov's theorem and its generalizations have become known as inertia theorems. In this note we shall u...

This paper provides necessary and sufficient conditions for fixed-point theorems, minimax inequalities and some related theorems defined on arbitrary topological spaces that may be discrete, continuum, non-compact or non-convex. We establish a single condition, γ-recursive transfer lower semicontinuity, which fully characterizes the existence of equilibrium of minimax inequality without imposin...

We introduce the new generalized mixed equilibrium problem with respect to relaxed semimonotone mappings. Using the KKM technique, we obtain the existence of solutions for the generalizedmixed equilibriumproblem in Banach spaces. Furthermore, we also introduce a hybrid projection algorithm for finding a common element in the solution set of a generalized mixed equilibrium problem and the fixed ...

Veldman proved that the contrapositive of countable binary choice is a theorem of full-fledged intuitionism, to which end he used a principle of continuous choice and the fan theorem. It has turned out that continuous choice is unnecessary in this context, and that a weak form of the fan theorem suffices which holds in the presence of countable choice. In particular, the contrapositive of count...

Combinatorics of complexes plays an important role in topology, nonlinear analysis, game theory, and mathematical economics. In 1967, Ky Fan used door-to-door principle to prove a combinatorial Stokes’ theorem on pseudomanifolds. In 1993, Shih and Lee developed the geometric context of general position maps, π-balanced and π-subbalanced sets and used them to prove a combinatorial formula for mu...

In the present paper, we extend known KKM theorems and matching theorems for generalized KKM maps to G-convex spaces. From these results, we deduce generalized versions of main results of Kassay and Kolumbán [KK] and some others.