In this paper, we introduce and study a generalized Yosida approximation operator associated to H(·, ·)-co-accretive operator and discuss some of its properties. Using the concept of graph convergence and resolvent operator, we establish the convergence for generalized Yosida approximation operator. Also, we show an equivalence between graph convergence for H(·, ·)-co-accretive operator and gen...

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, probabili...

In this paper, we discuss the equivalent conditions of pretopological and topological $L$-fuzzy Q-convergence structures and define $T_{0},~T_{1},~T_{2}$-separation axioms in $L$-fuzzy Q-convergence space. {Furthermore, $L$-ordered Q-convergence structure is introduced and its relation with $L$-fuzzy Q-convergence structure is studied in a categorical sense}.

in this paper, we discuss the equivalent conditions of pretopological and topological $l$-fuzzy q-convergence structures and define $t_{0},~t_{1},~t_{2}$-separation axioms in $l$-fuzzy q-convergence space. {furthermore, $l$-ordered q-convergence structure is introduced and its relation with $l$-fuzzy q-convergence structure is studied in a categorical sense}.

We develop a theory of stratified $LM$-filters which generalizes the theory of stratified $L$-filters. Our stratification condition explicitly depends on a suitable mapping between the lattices $L$ and $M$. If $L$ and $M$ are identical and the mapping is the identity mapping, then we obtain the theory of stratified $L$-filters. Based on the stratified $LM$-filters, a general theory of lattice-v...

in this paper, we shall define and study the concept of  -statistical convergence and  -statistical cauchy inrandom 2-normed space. we also introduce the concept of  -statistical completeness which would provide amore general frame work to study the completeness in random 2-normed space. furthermore, we also prove some new results.

$top$-filters can be used to define $top$-convergence spaces in the lattice-valued context. Connections between $top$-convergence spaces and lattice-valued convergence spaces are given. Regularity of a $top$-convergence space has recently been defined and studied by Fang and Yue. An equivalent characterization is given in the present work in terms of convergence of closures of $top$-filters.  M...

L-sets over a base set X are generalizations of classical sets where subsets are not specified by characteristic functions from X to {0, 1} but rather by functions from X to a lattice L. For an L-set a ∈ L and an element x ∈ X, a(x) is interpreted as the grade of membership of x in a. Stratified L-topological spaces are generalizations of topological spaces to the L-set case [1]. In [2], strati...

In this paper, the concepts of derived sets and derived operators are generalized to $(L, M)$-fuzzy topological spaces and their characterizations are given.What is more, it is shown that the category of stratified $(L, M)$-fuzzy topological spaces,the category of stratified $(L, M)$-fuzzy closure spaces and the category of stratified $(L, M)$-fuzzy quasi-neighborhood spaces are all isomorphic ...