We provide a porosity based approach to the differentiability and continuity of real valued functions on separable Banach spaces, when the function is monotone with respect to an ordering induced by a convex cone K with non-empty interior. We also show that the set of nowhere K-monotone functions has a σ-porous complement in the space of the continuous functions.

The paper is devoted to the investigation of directional derivatives and the cone of decrease directions for convex operators on Banach spaces. We prove a condition for the existence of directional derivatives which does not assume regularity of the ordering cone K. This result is then used to prove that for continuous convex operators the cone of decrease directions can be represented in terms...

the objective of this paper is to deal with the fuzzy conic program- ming problems. the aim here is to derive weak and strong duality theorems for a general fuzzy conic programming. toward this end, the convexity-like concept of fuzzy mappings is introduced and then a speci c ordering cone is established based on the parameterized representation of fuzzy numbers. un- der this setting, duality t...

The objective of this paper is to deal with the fuzzy conic program- ming problems. The aim here is to derive weak and strong duality theorems for a general fuzzy conic programming. Toward this end, The convexity-like concept of fuzzy mappings is introduced and then a speci c ordering cone is established based on the parameterized representation of fuzzy numbers. Un- der this setting, duality t...

In this paper we introduce the cone bounded linear mapping and demonstrate a proof to show that the cone norm is continuous. Among other things, we prove the open mapping theorem and the closed graph theorem in TVS-cone normed spaces. We also show that under some restrictions on the cone, two cone norms are equivalent if and only if the topologies induced by them are the same. In the sequel, we...

The aim of this paper is to investigate partially ordered real linear topological spaces in which directed sets admit a supremum in their closure. In particular, we point out that this property is intimately related to the normality of the ordering cone and also to the Scott continuity of functionals belonging to the nonnegative polar of the ordering cone. Mathematics Subject Classification (20...

*Correspondence: [email protected] Faculty of Mathematics and Informatics, Plovdiv University, Plovdiv, 4000, Bulgaria Abstract In this paper, we develop a unified theory for cone metric spaces over a solid vector space. As an application of the new theory, we present full statements of the iterated contraction principle and the Banach contraction principle in cone metric spaces over a sol...

A comparison theorem is stated for Markov processes in polish state spaces. We consider a general class of stochastic orderings induced by a cone of real functions. The main result states that stochastic monotonicity of one process and comparability of the infinitesimal generators imply ordering of the processes. Several applications to convex type and to dependence orderings are given. In part...

Motivated by applications to (directionally) Lipschitz functions, we provide a general result on the almost everywhere Gâteaux differentiability of real-valued functions on separable Banach spaces, when the function is monotone with respect to an ordering induced by a convex cone with nonempty interior. This seemingly arduous restriction is useful, since it covers the case of directionally Lips...