a concept of weak $f$-property for a set-valued mapping is introduced‎, ‎and then under some suitable assumptions‎, ‎which do not involve any information‎ ‎about the solution set‎, ‎the lower semicontinuity of the solution mapping to‎ ‎the parametric‎ ‎set-valued vector equilibrium-like problems are derived by using a density result and scalarization method‎, ‎where the‎ ‎constraint set $k$...

We show that rough isometries between metric spacesX,Y can be lifted to the spaces of real valued 1-Lipschitz functions over X and Y with supremum metric and apply this to their scaling limits. For the inverse, we show how rough isometries between X and Y can be reconstructed from structurally enriched rough isometries between their Lipschitz function spaces.

We prove that every Lipschitz function from a subset of a locally compact length space to a metric tree has a unique absolutely minimal Lipschitz extension (AMLE). We relate these extensions to a stochastic game called Politics — a generalization of a game called Tug of War that has been used in [42] to study real-valued AMLEs.

We proved that a finite commuting Boyd-Wong type contractive family with equicontinuous words have the approximate common fixed point property. We also proved that given X Ă R, compact and convex subset, F : X Ñ X a compact-and-convex valued Lipschitz correspondence and g an isometry on X, then gF “ F g implies F admits a Lipschitz selection commuting with g.

We introduce the Fourier-Stieltjes algebra in Rn which we denote by FS(Rn). It is a subalgebra of the algebra of bounded uniformly continuous functions in Rn, BUC(Rn), strictly containing the almost periodic functions, whose elements are invariant by translations and possess a mean-value. Thus, it is a so called algebra with mean value, a concept introduced by Zhikov and Krivenko (1986). Namely...

We study Lipschitz continuity with respect to the parameter of the set of solutions of a parameterized minimax problem on a product Banach space. We present a sufficient condition ensuring that the map which to any value of the parameter assigns the set of solutions of the problem (possibly multi-valued, and unbounded) possesses Lipschitz-like property, introduced by J.-P. Aubin.

Let E be a nonempty finite set, and let V be a real or complex vector space. In these notes we write F(E, V ) for the vector space of V -valued functions on E. Suppose that E1, E2 are nonempty finite sets, and that V is the vector space of real or complex-valued functions on E2. In this case we can identify F(E1, V ) with the vector space of real or complex-valued functions on the Cartesian pro...

A multiple-valued function f : X → QQ(Y ) is essentially a rule assigning Q unordered and non necessarily distinct elements of Y to each element of X. We study the Lipschitz extension problem in this context by using two general Lipschitz extension theorems recently proved by U. Lang and T. Schlichenmaier. We prove that the pair ` X,QQ(Y ) ́ has the Lipschitz extension property if Y is a Banach ...