A pointwise selection principle for metric semigroup valued functions

Ekeland's Variational Principle for Set-Valued Functions

We establish several set-valued function versions of Ekeland’s variational principle and hence provide some sufficient conditions ensuring the existence of error bounds for inequality systems defined by finitely many lower semicontinuous functions.

A characterization of triple semigroup of ternary functions and Demorgan triple semigroup of ternary functions

Group-valued Continuous Functions with the Topology of Pointwise Convergence

Let G be a topological group with the identity element e. Given a space X, we denote by Cp(X,G) the group of all continuous functions from X to G endowed with the topology of pointwise convergence, and we say that X is: (a) G-regular if, for each closed set F ⊆ X and every point x ∈ X \ F , there exist f ∈ Cp(X,G) and g ∈ G \ {e} such that f(x) = g and f(F ) ⊆ {e}; (b) G-regular provided that t...

Contraction Principle in Complex Valued G-Metric Spaces

In this paper, we introduce the notion of complex valued G-metric spaces and prove contraction principle in the newly spaces. Mathematics Subject Classification: 47H10, 54H25

Error Bounds for Vector-valued Functions on Metric Spaces

In this paper, we attempt to extend the definition and existing local error bound criteria to vector-valued functions, or more generally, to functions taking values in a normed linear space. Some new primal space derivative-like objects – slopes – are introduced and a classification scheme of error bound criteria is presented.