In this work, we introduce new approximation operators for univariate setvalued functions with general compact images. We adapt linear approximation methods for real-valued functions by replacing linear combinations of numbers with new metric linear combinations of finite sequences of compact sets, thus obtaining ”metric analogues” operators for set-valued functions. The new metric linear combi...

To begin with, let us agree to some basic conventions. We employ the symbols ∆ and ∇ to denote the Laplace operator ∑nk=1 ∂/∂xk and the gradient vector (∂/∂x1, ..., ∂/∂xn) over the Euclidean space R , n ≥ 2. For notational convenience we use X . Y as X ≤ CY for a constant C > 0. We always assume that u is a smooth real-valued function on R, written u ∈ C∞(Rn), and then it generates a conformal ...

The Hölder setting of the metric subregularity property of set-valued mappings between general metric or Banach/Asplund spaces is investigated in the framework of the theory of error bounds for extended real-valued functions of two variables. A classification scheme for the general Hölder metric subregularity criteria is presented. The criteria are formulated in terms of several kinds of primal...

This paper shows the usefulness of Perov's contraction principle, which generalizes Banach's principle to a vector-valued metric, for studying dynamic programming problems in discount factor can be stochastic. The discounting condition β<1 is replaced by ρ(B)<1, where B an appropriate nonnegative matrix and ρ denotes spectral radius. Blackwell's sufficient also generalized this setting. Applica...

Very recently, Ma et al. (Fixed Point Theory Appl. 2014:206, 2014) introduced C∗-algebra-valued metric spaces as a new concept. Also, Ma and Jiang (Fixed Point Theory Appl. 2015:222, 2015), generalizing this concept, introduced C∗-algebra-valued b-metric spaces. In both frameworks, these and other authors proved some fixed point results. We show in this paper that all these results (as well as ...