A lower bound for 1-median selection in metric spaces

Generalized multivalued $F$-contractions on non-complete metric spaces

In this paper, we explain a new generalized contractive condition for multivalued mappings and prove a fixed point theorem in metric spaces (not necessary complete) which extends some well-known results in the literature. Finally, as an application, we prove that a multivalued function satisfying a general linear functional inclusion admits a unique selection fulfilling the corresp...

A lower bound for metric 1-median selection

Consider the problem of finding a point in an n-point metric space with the minimum average distance to all points. We show that this problem has no deterministic o(n 2)-query (4 − Ω(1))-approximation algorithms.

A deterministic sublinear-time nonadaptive algorithm for metric 1-median selection

We give a deterministic O(hn1+1/h)-time (2h)-approximation nonadaptive algorithm for 1-median selection in n-point metric spaces, where h ∈ Z+ \ {1} is arbitrary. Our proof generalizes that of Chang [2].

Lower bounds of Copson type for the transpose of matrices on weighted sequence spaces

Definition of General Operator Space and The s-gap Metric for Measuring Robust Stability of Control Systems with Nonlinear Dynamics

In the recent decades, metrics have been introduced as mathematical tools to determine the robust stability of the closed loop control systems. However, the metrics drawback is their limited applications in the closed loop control systems with nonlinear dynamics. As a solution in the literature, applying the metric theories to the linearized models is suggested. In this paper, we show that usin...