By applying (a) of Theorem 2.2, there exists v ∈ A such that d ( v, T v ) = dist ( A, B ). □.
Also along Bayesian lines, Goldman (1999) applies a related theorem of his and Shaked (Goldman and Shaked 1991) to testimony.
We apply an existence theorem of variational inclusion problem on metric spaces to study optimization problems, set-valued vector saddle point problems, bilevel problems, and mathematical programs with equilibrium constraint on metric spaces.
We firstly convert the problem to an equivalent integral equation, and then by applying a fixed point theorem of a sum operator, the existence and uniqueness of positive solutions is established.
By applying a fixed point theorem of strict-set contractions, some sufficient conditions have been established to guarantee the existence of periodic solutions.
(3.6) By applying a similar proof of Theorem 3.1, one can prove next result.
Several new results are obtained by applying a variety of fixed point theorems.
Later, Sine [3] gave a simple proof of Theorem 1.2 by applying a version of the uniform boundedness principle and the convex combination of a sequence of metric projections onto closed and convex sets.
Further, the authors in [9], applying a recent critical point theorem of Ricceri [7], established the existence of at least one nontrivial solution for the problem left { begin{array}l} -u"= [lambda f x,u +g u) ]h x,u') quadmbox{in } (0,1), u(0)=u(1)=0, end{array} right.
