in this paper we introduce the concept of topological number for locally convex topological spaces and prove some of its properties. it gives some criterions to study locally convex topological spaces in a discrete approach.

In this paper, firstly, we obtain some new results about bornological convergence in locally convex cones (which was studied in [1]) and then we introduce the concept of bornological completion for locally convex cones. Also, we prove that the completion of a bornological locally convex cone is bornological. We illustrate the main result by an example.

In this paper, we have focused to study convex $L$-subgroups of an $L$-ordered group. First, we introduce the concept of a convex $L$-subgroup and a convex $L$-lattice subgroup of an $L$-ordered group and give some examples. Then we find some properties and use them to construct convex $L$-subgroup generated by a subset $S$ of an $L$-ordered group $G$ . Also, we generalize a well known result a...

In this paper we analyze the randomized block-coordinate descent (RBCD) methods proposed in [11, 15] for minimizing the sum of a smooth convex function and a blockseparable convex function, and derive improved bounds on their convergence rates. In particular, we extend Nesterov’s technique developed in [11] for analyzing the RBCD method for minimizing a smooth convex function over a block-separ...

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...

the analysis of flow in water-distribution networks with several pumps by the content model may be turned into a non-convex optimization uncertain problem with multiple solutions. newton-based methods such as gga are not able to capture a global optimum in these situations. on the other hand, evolutionary methods designed to use the population of individuals may find a global solution even for ...

In this manuscript, we introduce concepts of (m1,m2)-logarithmically convex (AG-convex) functions and establish some Hermite-Hadamard type inequalities of these classes of functions.