Abstract
In this paper we introduce rough weighted statistical limit set and weighted statistical cluster points set which are natural generalizations of rough statistical limit set and statistical cluster points set of double sequences respectively. Some new examples are constructed to ensure the deviation of basic results. Both the sets don’t follow the usual extension properties which will be discussed here.
Two classes of sets are introduced: rough weighted I-lacunary statistical
limit set and weighted I-lacunary statistical cluster points set which are
natural generalizations of rough I-limit set and I-cluster points set
respectively. To highlight the variation from basic results we place into
some new examples. So our aim is to analyze the different behaviors of the
new convergences and characterize both the sets with topological approach
like closedness, boundedness, compactness etc.
In this paper, some existing theories on convergence of fuzzy number sequences are extended to
I
2
-statistical convergence of fuzzy number sequence. Also, we broaden the notions of
I
-statistical limit points and
I
-statistical cluster points of a sequence of fuzzy numbers to
I
2
-statistical limit points and
I
2
-statistical cluster points of a double sequence of fuzzy numbers. Also, the researchers focus on important fundamental features of the set of all
I
2
-statistical cluster points and the set of all
I
2
-statistical limit points of a double sequence of fuzzy numbers and examine the relationship between them.
The aim of present work is to introduce and study lacunary statistical limit and lacunary statistical cluster points for generalized difference sequences of fuzzy numbers. Some inclusion relations among the sets of ordinary limit points, statistical limit points, statistical cluster points, lacunary statistical limit points, and lacunary statistical cluster points for these type of sequences are obtained.
In this paper, we define the concepts of rough statistical cluster point and
rough statistical limit point of a sequence in a finite dimensional normed
space. Then we obtain an ordinary statistical convergence criteria
associated with rough statistical cluster point of a sequence. Applying
these definitions to the sequences of functions, we come across a new
concept called statistical condensation point. Finally, we observe the
relations between the sets of statistical condensation points, rough
statistical cluster points and rough statistical limit points of a sequence
of functions.
In this paper we introduce f-rough weighted statistical limit set and f-weighted statistical cluster points set which are natural generalizations
of rough statistical limit set and f-statistical cluster points set of
sequence respectively. Some new examples are constructed to ensure the
deviation of basic results. So both the sets don?t follow the nature of
usual extension properties which will be discussed here.