We prove a Desch-Schappacher type perturbation theorem for strongly continuous and locally equicontinuous one-parameter semigroups which are defined on a sequentially complete locally convex space.

The main purpose of this paper is to introduce the compatibility of $M$-fuzzifying topologies and $M$-fuzzifying convexities, define an $M$-fuzzifying topological convex space, and give a method to generate an $M$-fuzzifying topological convex space. Some characterizations of $M$-fuzzifying topological convex spaces are presented. Finally, the notion of $M$-fuzzifying weak topologies is obtaine...

We present a constructive proof of Tychonoff’s fixed point theorem in a locally convex space for uniformly continuous and sequentially locally non-constant functions. Keywords—sequentially locally non-constant functions, Tychonoff’s fixed point theorem, constructive mathematics.

In this paper the existence of a common fixed point for an arbitrary family of nonexpansive mappings is proved in a locally convex topological vector space. Our theorem is a (partial) generalization of the theorem of Lim [8] to this more general setting. Our main tool is the gauge function in locally convex spaces.

The notion of a bead metric space is defined as a nice generalization of the uniformly convex normed space such as $CAT(0)$ space, where the curvature is bounded from above by zero. In fact, the bead spaces themselves can be considered in particular as natural extensions of convex sets in uniformly convex spaces and normed bead spaces are identical with uniformly convex spaces. In this paper, w...

Abstract. In this paper we derive by means of the duality theory necessary and sufficient optimality conditions for convex optimization problems having as objective function the composition of a convex function and a linear continuous mapping defined on a separated locally convex space with values in an finitedimensional space. We use the general results for deriving optimality conditions for t...

We present a generalization of the Phelps lemma to locally convex topological vector spaces and show the equivalence of this theorem, Ekeland's principle and Dane s' drop theorem in locally convex spaces to their Banach space counterparts and to a Pareto eeciency theorem due to Isac. Concerning the drop theorem this solves a problem proposed by G. Isac in 1997. We show that another formulation ...

The present paper is concerned with some representatons of linear mappings of continuous functions into locally convex vector spaces, namely Theorem. If X is a complete Hausdorff locally convex vector space, then a general form of weakly compact mapping T : C[a, b] → X is of the form Tg = ∫ b a g(t)dx(t), where the function x(·) : [a, b] → X has a weakly compact semivariation on [a, b]. This th...

‎We prove that a remainder $Y$ of a non-locally compact‎ ‎rectifiable space $X$ is locally a $p$-space if and only if‎ ‎either $X$ is a Lindel"{o}f $p$-space or $X$ is $sigma$-compact‎, ‎which improves two results by Arhangel'skii‎. ‎We also show that if a non-locally compact‎ ‎rectifiable space $X$ that is locally paracompact has a remainder $Y$ which has locally a $G_{delta}$-diagonal‎, ‎then...