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Papers by amar dutta

Research paper thumbnail of LACUNARY p-ABSOLUTELY SUMMABLE SEQUENCES

Abstract. In this paper we have introduced the sequence space (ℓp) F θ. We have established a rel... more Abstract. In this paper we have introduced the sequence space (ℓp) F θ. We have established a relation between (ℓp) F θ and Ces(p). We have studied some algebraic properties like solidness, symmetricness, convergence free and provided some inclusion results.

Research paper thumbnail of Statistically Convergent and Cesàro Summable Double Sequences of Fuzzy Real Numbers by Binod

In this article we introduce the notion of different types of statistically convergent and statis... more In this article we introduce the notion of different types of statistically convergent and statistically null fuzzy real-valued double sequence spaces. We study their different properties like solidness, symmetric, convergence free, sequence algebra etc. The fuzzy real-valued Cesàro summable double sequence space is introduced. A relation between strongly p-Cesàro summability and bounded statistically convergent double sequences has been established.

Research paper thumbnail of Fine Spectrum of the Generalized Difference Operator <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>B</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>r</mml:mi><mml:mo>,</mml:mo><mml:mi>s</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> over the Class of Converg...

International Journal of Analysis, Jan 17, 2013

Research paper thumbnail of On fuzzy real-valued double sequence space <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:msubsup><mml:mrow><mml:mi>ℓ</mml:mi></mml:mrow><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:...

Mathematical and Computer Modelling, Nov 1, 2007

In this article we introduce the fuzzy real-valued double sequence space ℓFp2. We study different... more In this article we introduce the fuzzy real-valued double sequence space ℓFp2. We study different properties of the space like completeness, solidity, symmetry, convergence free, sequence algebra, etc. We prove some inclusion results too.

Research paper thumbnail of Class of p-Absolutely Summable Sequence of Interval Number

Trends in Mathematics, 2017

In this article we have introduced the class of sequence l i ( p) of interval numbers. We establi... more In this article we have introduced the class of sequence l i ( p) of interval numbers. We established some properties like completeness, linearity, symmetric and some inclusion relation.

Research paper thumbnail of Regular matrix of interval numbers based on Fibonacci numbers

Afrika Matematika, 2014

The main purpose of this paper is to introduce the criterion for the regularity of a matrix whose... more The main purpose of this paper is to introduce the criterion for the regularity of a matrix whose elements are interval numbers and define a regular matrixF of interval numbers using fibonacci numbers and to introduce some new sequence spaces c i 0 (F), c i (F), l i ∞ (F) based on the newly defined regular matrix of interval numbersF and investigate some relations related to these spaces.

Research paper thumbnail of Class of p-Absolutely Summable Sequence of Interval Number

Trends in mathematics, 2017

In this article we have introduced the class of sequence l i ( p) of interval numbers. We establi... more In this article we have introduced the class of sequence l i ( p) of interval numbers. We established some properties like completeness, linearity, symmetric and some inclusion relation.

Research paper thumbnail of On the class of p-absolutely summable sequence i p of interval numbers

Research paper thumbnail of Studies on some fuzzy realvalued double sequence spaces

Research paper thumbnail of Asymptotically Equivalent Generalized Difference Sequences of Fuzzy Real Numbers Defined by Orlicz Function

Thai Journal of Mathematics, 2017

The aim of this article is to introduce the classes of strong Deltam\Delta^mDeltam-lacunary asymptotically ... more The aim of this article is to introduce the classes of strong Deltam\Delta^mDeltam-lacunary asymptotically equivalent, Deltam\Delta^mDeltam-lacunary asymptotically statistically equivalent, strong Deltam\Delta^mDeltam-almost asymptotically equivalent sequences of fuzzy real numbers in terms of Orlicz function. We have established some relations between the classes of the sequences.

Research paper thumbnail of A new class of fuzzy sequences related to the ℓp space defined by Orlicz function

Journal of Intelligent & Fuzzy Systems

Research paper thumbnail of Lacunary bounded variation sequence of fuzzy real numbers

Journal of Intelligent & Fuzzy Systems

ABSTRACT In this article we have introduced the concept of lacunary bounded variation sequence of... more ABSTRACT In this article we have introduced the concept of lacunary bounded variation sequence of fuzzy real numbers. We have verified some properties like solid, symmetric, convergence free etc. and also proved some inclusion results.

Research paper thumbnail of A new type of difference class of interval numbers

Proyecciones (Antofagasta)

In this article we introduce the notation difference operator ∆ m (m ≥ 0 be an integer) for study... more In this article we introduce the notation difference operator ∆ m (m ≥ 0 be an integer) for studying some properties defined with interval numbers. We introduced the classes of sequence¯ (p)(∆ m),c(p)(∆ m) andc 0 (p)(∆ m) and investigate different algebraic properties like completeness, solidness, convergence free etc.

Research paper thumbnail of On fuzzy real-valued double sequence space 2lpF

Mathematical and Computer Modelling, 2007

Research paper thumbnail of On pointwise statistical convergence of order α of sequences of fuzzy mappings

Kuwait Journal of Science, Sep 29, 2014

Research paper thumbnail of Lacunary I-convergent sequences of fuzzy real numbers

Proyecciones (Antofagasta), 2015

In this article we introduce the concept of lacunary I-convergent sequence of fuzzy real numbers ... more In this article we introduce the concept of lacunary I-convergent sequence of fuzzy real numbers and the spaces and. We also obtain some inclusion relations between these spaces.

Research paper thumbnail of Statistically convergent and Cesàrio summable double sequences of fuzzy real numbers

Research paper thumbnail of On Lacunary p-Absolutely Summable Fuzzy Real-Valued Double Sequence Space

Demonstratio Mathematica, 2014

In this article, we introduce the class of p-absolutely summable fuzzy real valued double sequence (

Research paper thumbnail of Statistically pre-Cauchy Fuzzy real-valued sequences defined by Orlicz function

Proyecciones (Antofagasta), 2014

In this article we have defined statistically pre-Cauchy sequence of fuzzy real numbers defined b... more In this article we have defined statistically pre-Cauchy sequence of fuzzy real numbers defined by Orlicz function. We have proved a necessary and sufficient condition for a sequence X = (X k) of fuzzy real numbers to be statistically pre-Cauchy. We have also established some other results.

Research paper thumbnail of p-Bounded variation fuzzy real-valued double sequence space

Acta Scientiarum. Technology, 2013

In this paper we have introduced the notion of fuzzy real-valued p-bounded variation double seque... more In this paper we have introduced the notion of fuzzy real-valued p-bounded variation double sequence space p F bv 2 (1 ≤ p < ∞). We have studied some important properties like completeness, convergence free, solid, symmetric. Some inclusion results are also established.

Research paper thumbnail of LACUNARY p-ABSOLUTELY SUMMABLE SEQUENCES

Abstract. In this paper we have introduced the sequence space (ℓp) F θ. We have established a rel... more Abstract. In this paper we have introduced the sequence space (ℓp) F θ. We have established a relation between (ℓp) F θ and Ces(p). We have studied some algebraic properties like solidness, symmetricness, convergence free and provided some inclusion results.

Research paper thumbnail of Statistically Convergent and Cesàro Summable Double Sequences of Fuzzy Real Numbers by Binod

In this article we introduce the notion of different types of statistically convergent and statis... more In this article we introduce the notion of different types of statistically convergent and statistically null fuzzy real-valued double sequence spaces. We study their different properties like solidness, symmetric, convergence free, sequence algebra etc. The fuzzy real-valued Cesàro summable double sequence space is introduced. A relation between strongly p-Cesàro summability and bounded statistically convergent double sequences has been established.

Research paper thumbnail of Fine Spectrum of the Generalized Difference Operator <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>B</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>r</mml:mi><mml:mo>,</mml:mo><mml:mi>s</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> over the Class of Converg...

International Journal of Analysis, Jan 17, 2013

Research paper thumbnail of On fuzzy real-valued double sequence space <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:msubsup><mml:mrow><mml:mi>ℓ</mml:mi></mml:mrow><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:...

Mathematical and Computer Modelling, Nov 1, 2007

In this article we introduce the fuzzy real-valued double sequence space ℓFp2. We study different... more In this article we introduce the fuzzy real-valued double sequence space ℓFp2. We study different properties of the space like completeness, solidity, symmetry, convergence free, sequence algebra, etc. We prove some inclusion results too.

Research paper thumbnail of Class of p-Absolutely Summable Sequence of Interval Number

Trends in Mathematics, 2017

In this article we have introduced the class of sequence l i ( p) of interval numbers. We establi... more In this article we have introduced the class of sequence l i ( p) of interval numbers. We established some properties like completeness, linearity, symmetric and some inclusion relation.

Research paper thumbnail of Regular matrix of interval numbers based on Fibonacci numbers

Afrika Matematika, 2014

The main purpose of this paper is to introduce the criterion for the regularity of a matrix whose... more The main purpose of this paper is to introduce the criterion for the regularity of a matrix whose elements are interval numbers and define a regular matrixF of interval numbers using fibonacci numbers and to introduce some new sequence spaces c i 0 (F), c i (F), l i ∞ (F) based on the newly defined regular matrix of interval numbersF and investigate some relations related to these spaces.

Research paper thumbnail of Class of p-Absolutely Summable Sequence of Interval Number

Trends in mathematics, 2017

In this article we have introduced the class of sequence l i ( p) of interval numbers. We establi... more In this article we have introduced the class of sequence l i ( p) of interval numbers. We established some properties like completeness, linearity, symmetric and some inclusion relation.

Research paper thumbnail of On the class of p-absolutely summable sequence i p of interval numbers

Research paper thumbnail of Studies on some fuzzy realvalued double sequence spaces

Research paper thumbnail of Asymptotically Equivalent Generalized Difference Sequences of Fuzzy Real Numbers Defined by Orlicz Function

Thai Journal of Mathematics, 2017

The aim of this article is to introduce the classes of strong Deltam\Delta^mDeltam-lacunary asymptotically ... more The aim of this article is to introduce the classes of strong Deltam\Delta^mDeltam-lacunary asymptotically equivalent, Deltam\Delta^mDeltam-lacunary asymptotically statistically equivalent, strong Deltam\Delta^mDeltam-almost asymptotically equivalent sequences of fuzzy real numbers in terms of Orlicz function. We have established some relations between the classes of the sequences.

Research paper thumbnail of A new class of fuzzy sequences related to the ℓp space defined by Orlicz function

Journal of Intelligent & Fuzzy Systems

Research paper thumbnail of Lacunary bounded variation sequence of fuzzy real numbers

Journal of Intelligent & Fuzzy Systems

ABSTRACT In this article we have introduced the concept of lacunary bounded variation sequence of... more ABSTRACT In this article we have introduced the concept of lacunary bounded variation sequence of fuzzy real numbers. We have verified some properties like solid, symmetric, convergence free etc. and also proved some inclusion results.

Research paper thumbnail of A new type of difference class of interval numbers

Proyecciones (Antofagasta)

In this article we introduce the notation difference operator ∆ m (m ≥ 0 be an integer) for study... more In this article we introduce the notation difference operator ∆ m (m ≥ 0 be an integer) for studying some properties defined with interval numbers. We introduced the classes of sequence¯ (p)(∆ m),c(p)(∆ m) andc 0 (p)(∆ m) and investigate different algebraic properties like completeness, solidness, convergence free etc.

Research paper thumbnail of On fuzzy real-valued double sequence space 2lpF

Mathematical and Computer Modelling, 2007

Research paper thumbnail of On pointwise statistical convergence of order α of sequences of fuzzy mappings

Kuwait Journal of Science, Sep 29, 2014

Research paper thumbnail of Lacunary I-convergent sequences of fuzzy real numbers

Proyecciones (Antofagasta), 2015

In this article we introduce the concept of lacunary I-convergent sequence of fuzzy real numbers ... more In this article we introduce the concept of lacunary I-convergent sequence of fuzzy real numbers and the spaces and. We also obtain some inclusion relations between these spaces.

Research paper thumbnail of Statistically convergent and Cesàrio summable double sequences of fuzzy real numbers

Research paper thumbnail of On Lacunary p-Absolutely Summable Fuzzy Real-Valued Double Sequence Space

Demonstratio Mathematica, 2014

In this article, we introduce the class of p-absolutely summable fuzzy real valued double sequence (

Research paper thumbnail of Statistically pre-Cauchy Fuzzy real-valued sequences defined by Orlicz function

Proyecciones (Antofagasta), 2014

In this article we have defined statistically pre-Cauchy sequence of fuzzy real numbers defined b... more In this article we have defined statistically pre-Cauchy sequence of fuzzy real numbers defined by Orlicz function. We have proved a necessary and sufficient condition for a sequence X = (X k) of fuzzy real numbers to be statistically pre-Cauchy. We have also established some other results.

Research paper thumbnail of p-Bounded variation fuzzy real-valued double sequence space

Acta Scientiarum. Technology, 2013

In this paper we have introduced the notion of fuzzy real-valued p-bounded variation double seque... more In this paper we have introduced the notion of fuzzy real-valued p-bounded variation double sequence space p F bv 2 (1 ≤ p < ∞). We have studied some important properties like completeness, convergence free, solid, symmetric. Some inclusion results are also established.