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, we prove that every metric line in the poincare ball model of hyperbolic geometry is exactly a classical line of itself. we also proved nonexistence of periodic lines in the poincare ball model of hyperbolic geometry.

In this paper, a new mixed type iteration process for approximating common fixed point of two asymptotically nonexpansive self-mappings and nonself-mappings is constructed. We then establish strong convergence theorem under mild conditions in uniformly convex hyperbolic space. The results presented here extend improve some related the literature.

In this paper, weak and strong convergence of two-step iteration sequences to a common fixed point for a pair of a finite family of asymptotically nonexpansive mappings and a finite family of generalized nonexpansive multivalued mappings in a nonempty closed convex subset of uniformly convex Banach spaces are presented. The results obtained in this paper extend and improve some recent known res...

We study the strong convergence of two kinds of viscosity iteration processes for approximating common fixed points of the pseudocontractive semigroup in uniformly convex Banach spaces with uniformly Gâteaux differential norms. As special cases, we get the strong convergence of the implicit viscosity iteration process for approximating common fixed points of the nonexpansive semigroup in Banach...

We prove some existence theorems for solutions of a certain system of multivariate nonexpansive operator equations and calculate the solutions by using the generalized Mann and Halpern iterative algorithms in uniformly convex and uniformly smooth Banach spaces. The results of this paper improve and extend the previously known ones in the literature.

The viscosity approximation methods are employed to establish strong convergence theorems of the modified Mann iteration scheme to λ-strict pseudocontractions in p-uniformly convex Banach spaces with a uniformly Gâteaux differentiable norm. The main result improves and extends many nice results existing in the current literature.

The concepts of $L$-convex systems and Scott-hull spaces are proposed on frame-valued setting. Also, we establish the categorical isomorphism between  $L$-convex systems and Scott-hull spaces. Moreover, it is proved that the category of $L$-convex structures is  bireflective in the category of $L$-convex systems. Furthermore, the quotient systems of $L$-convex systems are studied.

It is shown that a Banach space with locally uniformly convex dual admits an equivalent norm that is itself locally uniformly convex.

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...