scholarly journals Lacunary statistical and lacunary strongly convergence of generalized difference sequences in intuitionistic fuzzy normed linear spaces

2018 ◽  
Vol 38 (1) ◽  
pp. 117-129
Author(s):  
Mausumi Sen ◽  
Mikail Et
Keyword(s):  
Cauchy Sequence ◽  
Statistical Convergence ◽  
Sufficient Conditions ◽  
Inclusion Relation ◽  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Intuitionistic Fuzzy ◽  
Difference Sequences ◽  
Lacunary Statistical Convergence ◽  
Necessary And Sufficient

In this article we introduce the concepts of lacunary statistical convergence and lacunary strongly convergence of generalized difference sequences in intuitionistic fuzzy normed linear spaces and give their characterization. We obtain some inclusion relation relating to these concepts. Further some necessary and sufficient conditions for equality of the sets of statistical convergence and lacunary statistical convergence of generalized difference sequences have been established. The notion of strong Cesaro summability in intuitionistic fuzzy normed linear spaces has been introduced and studied. Also the concept of lacunary generalized difference statistically Cauchy sequence has been introduced and some results are established.

Generalized weighted statistical convergence in intuitionistic fuzzy normed linear spaces

2018 ◽  
Vol 27 (2) ◽  
pp. 101-110
Author(s):  
SELMA ALTUNDAG ◽  
◽  
ESRA KAMBER ◽  
Keyword(s):  
Statistical Convergence ◽  
Summability Method ◽  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Intuitionistic Fuzzy ◽  
Convergence Type

In this paper, we introduce a new statistical convergence type, named weighted λ-statistical convergence to generalize the concept of weighted statistical convergence with respect to the intuitionistic fuzzy norm (µ, υ). Moreover, we establish its relation to weighted statistical convergence and a new summability method, named as Nλ, p -summability with respect to the intuitionistic fuzzy norm (µ, υ).

Fundamental properties of statistical convergence and lacunary statistical convergence on time scales

Filomat ◽  
2017 ◽  
Vol 31 (14) ◽  
pp. 4455-4467 ◽  
Author(s):  
Ceylan Turan ◽  
Oktay Duman
Keyword(s):  
Time Scales ◽  
Statistical Convergence ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Tauberian Condition ◽  
Fundamental Properties ◽  
Lacunary Statistical Convergence ◽  
Necessary And Sufficient

In this paper, we first obtain a Tauberian condition for statistical convergence on time scales. We also find necessary and sufficient conditions for the equivalence of statistical convergence and lacunary statistical convergence on time scales. Some significant applications are also presented.

scholarly journals Rough I2-Lacunary Statistical Convergence of Double Sequences

2018 ◽  
Author(s):  
Ömer Kişi ◽  
Erdinç Dündar
Keyword(s):  
Statistical Convergence ◽  
Double Sequence ◽  
Limit Set ◽  
Double Sequences ◽  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Statistical Limit ◽  
Lacunary Statistical Convergence

In this paper, we introduce and study the notion of rough I2-lacunary statistical convergence of double sequences in normed linear spaces. We also introduce the notion of rough I2-lacunary statistical limit set of a double sequence and discuss about some properties of this set.

New Fixed Point Theorems via Contraction Mappings in Complete Intuitionistic Fuzzy Normed Linear Space

2018 ◽  
Vol 15 (01) ◽  
pp. 65-83
Author(s):  
Nabanita Konwar ◽  
Ayhan Esi ◽  
Pradip Debnath
Keyword(s):  
Fixed Point ◽  
Mathematical Models ◽  
Linear Space ◽  
Fixed Point Theorems ◽  
Normed Linear Space ◽  
Existence Of A Solution ◽  
Linear Spaces ◽  
Contraction Mappings ◽  
Normed Linear Spaces ◽  
Intuitionistic Fuzzy

Contraction mappings provide us with one of the major sources of fixed point theorems. In many mathematical models, the existence of a solution may often be described by the existence of a fixed point for a suitable map. Therefore, study of such mappings and fixed point results becomes well motivated in the setting of intuitionistic fuzzy normed linear spaces (IFNLSs) as well. In this paper, we define some new contraction mappings and establish fixed point theorems in a complete IFNLS. Our results unify and generalize several classical results existing in the literature.

Intuitionistic Fuzzy Pseudo-Normed Linear Spaces

2018 ◽  
Vol 15 (01) ◽  
pp. 113-127
Author(s):  
Bivas Dinda ◽  
Santanu Kumar Ghosh ◽  
T. K. Samanta
Keyword(s):  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Intuitionistic Fuzzy ◽  
Definition Of

We introduce the definition of intuitionistic fuzzy pseudo-norm and study some properties of convergence and [Formula: see text]-convergence in intuitionistic fuzzy pseudo-normed linear spaces.

Statistical convergence in fuzzy normed linear spaces

2008 ◽  
Vol 159 (3) ◽  
pp. 361-370 ◽  
Author(s):  
C. Şençı˙men ◽  
S. Pehlı˙van
Keyword(s):  
Statistical Convergence ◽  
Linear Spaces ◽  
Normed Linear Spaces
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