This insightful article examines the $\lambda$-statistical convergence of function sequences within neutrosophic norm spaces. It introduces novel concepts such as $\lambda$-statistical pointwise convergence and $\lambda$-statistical uniform convergence specifically tailored for neutrosophic norm spaces, representing a notable advancement in the field. The article elucidates the foundational properties of these innovative concepts, offering valuable insights into their theoretical foundations and practical applications.

We study the space of all continuous fuzzy-valued functions from a space X into the space of fuzzy numbers (e1, d¥) endowed with the pointwise convergence topology. Our results generalize the classical ones for continuous real-valued functions. The field of applications of this approach seems to be large, since the classical case allows many known devices to be fitted to general topology, functional analysis, coding theory, Boolean rings, etc.

We show, for a commutative and integral quantale, that the recently introduced  category of $\top$-uniform convergence spaces is a topological category which possesses natural function spaces, making it Cartesian closed. Furthermore, as two important examples for $\top$-uniform convergence spaces, we study probabilistic uniform spaces and quantale-valued metric spaces. The underlying $\top$-convergence spaces are also described and it is shown that in the case of a probabilistic uniform space this $\top$-convergence is the convergence of a fuzzy topology with conical neighbourhood filters. Finally it is shown that the category of $\top$-uniform convergence spaces can be embedded into the category of stratified lattice-valued uniform convergence spaces as a reflective subcategory.

We apply Preuss' concept of E-connectedness to the categories of lattice-valued uniform convergence spaces and of lattice-valued uniform spaces. A space is uniformly E-connected if the only uniformly continuous mappings from the space to a space in the class E are the constant mappings. We develop the basic theory for E-connected sets, including the product theorem. Furthermore, we define and study uniform local E-connectedness, generalizing a classical definition from the theory of uniform convergence spaces to the lattice-valued case. In particular it is shown that if the underlying lattice is completely distributive, the quotient space of a uniformly locally E-connected space and products of locally uniformly E-connected spaces are locally uniformly E-connected.

The aim of this paper is to study the completeness of L-quasi-uniform convergence spaces and L-quasi-uniform spaces. Firstly, we describe L-quasi-uniform convergence spaces as enriched categories. Then we give two kinds of completeness of L-quasi-uniform convergence spaces and show that Lawvere completeness implies Cauchy completeness. Finally, we use the Cauchy completeness of L-quasi-uniform convergence spaces to define the Cauchy completeness of L-quasi-uniform spaces, and show that Cauchy completeness is equivalent to Lawvere completeness in L-quasi-uniform spaces.

The concept of Fst -fundamentality is introduced in uniform spaces, generated by some filter F. Its equivalence to the concept of F-convergence in uniform spaces is proved. This convergence generalizes many kinds of convergence, including the well-known statistical convergence.

Let  $\left\{a_\alpha\right\}_{\alpha\in I}$ be a bounded net in a Banach algebra $A$ and $\varphi$ a nonzero multiplicative linear functional on $A$. In this paper, we deal with the problem of when $\|aa_\alpha-\varphi(a)a_\alpha\|\to0$ uniformly for all $a$ in weakly compact subsets of $A$. We show that Banach algebras associated to locally compact groups such  as Segal algebras and $L^1$-algebras are responsive to this concept. It is also shown that $Wap(A)$ has a left invariant $\varphi$-mean if and only if there exists a bounded net $\left\{a_\alpha\right\}_{\alpha\in I}$ in $\left\{a\in A;\ \varphi(a)=1\right\}$ such that $\|aa_\alpha-\varphi(a)a_\alpha\|_{Wap(A)}\to0$ uniformly for all $a$ in weakly compact subsets of $A$. Other results in this direction are also obtained.

We develop a general framework for various lattice-valued, probabilistic and approach uniform convergence spaces. To this end, we use the concept of s-stratified LM- filter, where L and M are suitable frames. A stratified LMN-uniform convergence tower is then a family of structures indexed by a quantale N. For different choices of L; M and N we obtain the lattice valued, probabilistic and approach uniform convergence spaces as examples. We show that the resulting category sLMN-UCTS is topological, well- bred and Cartesian closed. We furthermore de ne stratified LMN-uniform tower spaces and show that the category of these spaces is isomorphic to the subcategory of stratified LMN-principal uniform convergence tower spaces. Finally we study the underlying stratified LMN-convergence tower spaces.

Non-uniform grids inevitably arise in multiphase flow simulation scenarios due to the need to resolve near-wall phenomena and/or large L/D ratios associated with the reactor configuration. This in conjunction with large density ratios of the constituent phases can retard the convergence of the pressure-correction equation that results from applying operator-splitting methods to the incompressible Navier-Stokes equations. Various pre-conditioning strategies to this ill-conditioned pressurecorrection matrix are explored in this study for a class of bubbling bed simulations encompassing: different particle densities, bedheights and dimensions (2D/3D). The right-side Block Jacobi preconditioning option resulted in a 20-35% decrease in CPU time that correlated well with a decrease in the number of iterations to reach a specified tolerance.

In this paper we give some fixed point theorems in cone metric spaces and the purpose of this paper is the investigation of some manners for finding the fixed point of pointwise contraction and asymptotic pointwise contraction mappings.