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On rough weighted ideal convergence of triple sequence of Bernstein polynomials
Bipan Hazarika,N. Subramanian,Ayhan Esi 장전수학회 2018 Proceedings of the Jangjeon mathematical society Vol.21 No.3
We introduce and study some basic properties of rough Iλ-convergent of weight g, where g : N³ → [0,∞) is a function satisfying g (m, n, k) → ∞ and |(m,n,k)|/g(m,nk) ↛ 0 as m, n, k → ∞, of triple sequence of Bernstein polynomials and also investigate certain properties of rough Iλ-convergence of weight g.
ON ASYMPTOTICALLY f-ROUGH STATISTICAL EQUIVALENT OF TRIPLE SEQUENCES
N. Subramanian,A. Esi 한국전산응용수학회 2019 Journal of applied mathematics & informatics Vol.37 No.5
In this work, via Orlicz functions, we have obtained a generalization of rough statistical convergence of asymptotically equivalent triple sequences a new non-matrix convergence method, which is intermediate between the ordinary convergence and the rough statistical convergence. We also have examined some inclusion relations related to this concept. We obtain the results are non negative real numbers with respect to the partial order on the set of real numbers.
ON EXTREMAL ROUGH I-CONVERGENCE LIMIT POINT OF TRIPLE SEQUENCE SPACES DEFINED BY A METRIC FUNCTION
SUBRAMANIAN, N.,ESI, A.,DEBNATH, S. The Korean Society for Computational and Applied M 2020 Journal of applied mathematics & informatics Vol.38 No.3
We introduce and study some basic properties of rough I-convergent of triple sequence spaces and also study the set of all rough I-limits of a triple sequence spaces.
INTEGRATED RATE SPACE ∫ ℓ<sub>π</sub>
Subramanian, N.,Rao, K. Chandrasekhara,Gurumoorthy, N. Korean Mathematical Society 2007 대한수학회논문집 Vol.22 No.4
This paper deals with the BK-AK property of the integrated rate space ${\int}{\ell}_{\pi}$. Importance of ${\delta}^{(k)}$ in this content is pointed out. We investigate a determining set for the integrated rate space ${\int}{\ell}_{\pi}$. The set of all infinite matrices transforming ${\int}{\ell}_{\pi}$, into BK-AK space Y is denoted $({\int}{\ell}_{\pi}:\;Y)$. We characterize the classes $({\int}{\ell}_{\pi}:\;Y)$. When $Y={\ell}_{\infty},\;c_0,\;c,\;{\ell}^p,\;bv,\;bv_0,\;bs,\;cs,\;{\ell}_p,\;{\ell}_{\pi}$. In summary we have the following table:
RIESZ TRIPLE ALMOST LACUNARY χ3 SEQUENCE SPACES DEFINED BY A ORLICZ FUNCTION-I
N. Subramanian,Ayhan Esi,M. Aiyub 한국전산응용수학회 2019 Journal of applied mathematics & informatics Vol.37 No.1
In this paper we introduce a new concept for Riesz almost lacunary χ3 sequence spaces strong P convergent to zero with respect to an Orlicz function and examine some properties of the resulting sequence spaces. We introduce and study statistical convergence of Riesz almost lacunary χ3 sequence spaces and some inclusion theorems are discussed.
Bernstein Stancu operator of rough $I$-core of triple sequences
N. Subramanian,A. Esi,M. K. Ozdemir 원광대학교 기초자연과학연구소 2019 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.18 No.3
We introduce and study some basic properties of Bernstein-Stancu polynomials of rough $I$-convergent of triple sequences and also study the set of all Bernstein-Stancu polynomials of rough $I$-limits of a triple sequence and relation between analyticness and Bernstein-Stancu polynomials of rough $I$-core of a triple sequence.
RIESZ TRIPLE ALMOST LACUNARY χ<sup>3</sup> SEQUENCE SPACES DEFINED BY A ORLICZ FUNCTION-I
SUBRAMANIAN, N.,Esi, Ayhan,AIYUB, M. The Korean Society for Computational and Applied M 2019 Journal of applied mathematics & informatics Vol.37 No.1
In this paper we introduce a new concept for Riesz almost lacunary ${\chi}^3$ sequence spaces strong P - convergent to zero with respect to an Orlicz function and examine some properties of the resulting sequence spaces. We introduce and study statistical convergence of Riesz almost lacunary ${\chi}^3$ sequence spaces and some inclusion theorems are discussed.
ON ASYMPTOTICALLY f-ROUGH STATISTICAL EQUIVALENT OF TRIPLE SEQUENCES
SUBRAMANIAN, N.,ESI, A. The Korean Society for Computational and Applied M 2019 Journal of applied mathematics & informatics Vol.37 No.5
In this work, via Orlicz functions, we have obtained a generalization of rough statistical convergence of asymptotically equivalent triple sequences a new non-matrix convergence method, which is intermediate between the ordinary convergence and the rough statistical convergence. We also have examined some inclusion relations related to this concept. We obtain the results are non negative real numbers with respect to the partial order on the set of real numbers.
On extremal rough I-convergence limit point of triple sequence spaces defined by a metric function
N. Subramanian,A. Esi,S. Debnath 한국전산응용수학회 2020 Journal of applied mathematics & informatics Vol.38 No.3
We introduce and study some basic properties of rough I-convergent of triple sequence spaces and also study the set of all rough I-limits of a triple sequence spaces.
A. Esi,N. Subramanian,Ayten Esi 원광대학교 기초자연과학연구소 2018 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.16 No.3
We introduce and study some basic properties of rough $I_{\lambda}% -$statistical convergent of weight $g\left( A\right) $, where $g:\mathbb{N}% ^{3}\rightarrow\left[ 0,\infty\right) $ is a function statisying $g\left( m,n,k\right) \rightarrow\infty$ and $g\left( m,n,k\right) \not \rightarrow 0$ as $m,n,k\rightarrow\infty$ and $A$ represent the RH-regular matrix and also prove the Korovkin approximation theorem by using the notion of weighted A-statistical convergence of weight $g\left( A\right) $ limits of a triple sequence of Bernstein-Stancu polynomials.