scholarly journals GATEAUX and FRÉCHET DERIVATIVE IN INTUITIONISTIC FUZZY NORMED LINEAR SPACES

2012 ◽  
Vol 08 (03) ◽  
pp. 311-322 ◽  
Author(s):  
BIVAS DINDA ◽  
T. K. SAMANTA ◽  
U. K. BERA
Keyword(s):  
Fréchet Derivative ◽  
Linear Spaces ◽  
Gâteaux Derivative ◽  
Frechet Derivative ◽  
Normed Linear Spaces ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Derivative ◽  
Gateaux Derivative

In this paper, we introduce intuitionistic fuzzy derivative, intuitionistic fuzzy Gateaux derivative and intuitionistic fuzzy Fréchet derivative and some of their properties are studied. The relations between intuitionistic fuzzy Gateaux derivative and intuitionistic fuzzy Fréchet derivative are studied.

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.

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).

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.

Sign in / Sign up

Export Citation Format

Share Document