Proposition 1.2. Let (X, d) be a metric space. Let (x)j=k be a sequence of elements of X. Let x, x′ be elements of X. Assume that the sequence (x)j=k converges to x with respect to d. Assume also that the sequence (x)j=k converges to x ′ with respect to d. Then x = x′. Proposition 1.3. Let a < b be real numbers, and let f : [a, b] → R be a function which is both continuous and strictly monotone...

In this paper we consider a global optimization approach for solving fuzzy fractional posynomial geometric programming problems. The problem of concern involves positive trapezoidal fuzzy numbers in the objective function. For obtaining an optimal solution, Dinkelbach&rsquo;s algorithm which achieves the optimal solution of the optimization problem by means of solving a sequence of subproblems ...

Proof of Lemmas A.2 and A.1. {Λi}i is an equilibrium if and only if {Λi}i = F ({Λi}i). By direct calculation, defining Xi = (Λi + αiVN(i)), we get {Λi}i = F ({Λi}i) if, and only if, {Xi}i = G({Xi}i). That F and G are monotone increasing follows because matrix inversion Y → Y −1 is monotone decreasing (e.g., Horn and Johnson (2013)), and projection onto N(i) Y → YN(i) is monotone increasing in t...

Misrepresenting private information is often costly, for technological, legal, or psychological reasons. I develop a model of strategic information transmission based on Crawford and Sobel (1982) (CS), but with a convex cost of lying or misreporting. There are three main results. First, I prove that a sequence of monotone equilibria converges to a CS equilibrium as the cost of misreporting shri...

Labeled infinite trees provide combinatorial interpretations for many integer sequences generated by nested recurrence relations. Typically, such are monotone increasing. Several of these also have straightforward descriptions in terms how often each value the sequence occurs. In this paper, we generalize most classical examples to a larger family parametrized linear Each our can be constructed...

As a continuation of previous work of the first author with S. Ranjbar [26] on a special form of variational inequalities in Hadamard spaces, in this paper we study equilibrium problems in Hadamard spaces, which extend variational inequalities and many other problems in nonlinear analysis. In this paper, first we study the existence of solutions of equilibrium problems associated with pseudomon...

We develop a generalized quasilinearization method for nonlinear initial value problems involving functional differential equations and obtain a sequence of approximate solutions converging monotonically and quadratically to the solution of the problem. In addition, we obtain a monotone sequence of approximate solutions converging uniformly to the solution of the problem, possessing the rate of...

Let H be a real Hilbert space. Let K, F : H → H be bounded, continuous and monotone mappings. Suppose that u∗ ∈ H is a solution to Hammerstein equation u + KFu = 0. We introduce a new explicit iterative sequence and prove strong convergence of the sequence to a solution of the Hammerstein equation.