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Applications of infinite matrices and λ-convergence for fuzzy sequence spaces
Kuldip Raj,Ayhan Esi,Sonali Sharma 원광대학교 기초자연과학연구소 2021 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.21 No.3
In the present paper we study some applications of infinite matrices and $\lambda$-convergence of order $\alpha$ to introduce some Ideal convergent sequence spaces of fuzzy numbers by means of Orlicz function. We make an effort to study some algebraic and topological properties of these spaces. We also study some interesting inclusions relation between these spaces. Finally, we have prove that these spaces are normal as well as monotone and convergence free. We shall prove these results with the help of examples.
Orlicz sequence spaces of four dimensional regular matrix and their closed ideal
Kuldip Raj,Suruchi Pandoh,Anu Choudhary 호남수학회 2019 호남수학학술지 Vol.41 No.4
In this paper we introduce some new types of double difference sequence spaces defined by a new definition of convergence of double sequences and a double series with the help of sequence of Orlicz functions and a four dimensional bounded regular matrices $A=(a_{rtkl})$. We also make an effort to study some topological properties and inclusion relations between these sequence spaces. Finally, we compute the closed ideals in the space $l_{\infty}^{2}.$
ORLICZ SEQUENCE SPACES OF FOUR DIMENSIONAL REGULAR MATRIX AND THEIR CLOSED IDEAL
Raj, Kuldip,Pandoh, Suruchi,Choudhary, Anu The Honam Mathematical Society 2019 호남수학학술지 Vol.41 No.4
In this paper we introduce some new types of double difference sequence spaces defined by a new definition of convergence of double sequences and a double series with the help of sequence of Orlicz functions and a four dimensional bounded regular matrices A = (a<sub>rtkl</sub>). We also make an effort to study some topological properties and inclusion relations between these sequence spaces. Finally, we compute the closed ideals in the space 𝑙<sup>2</sup><sub>∞</sub>.
SOME DIFFERENCE SEQUENCE SPACES OF INFINITE MATRIX AND ORLICZ FUNCTION
Kuldip Raj,CHARU SHARMA 장전수학회 2018 Advanced Studies in Contemporary Mathematics Vol.28 No.3
In this paper we introduce some generalized difference sequence spaces of ideal convergence, infinite matrix and sequence of Orlicz functions of order α over n-normed spaces. We study some basic topological and algebraic properties of these spaces. We also investigate some inclusion relations related to these spaces.
Linear isomorphic Euler fractional difference sequence spaces and their Toeplitz duals
Kuldip Raj,Mohammad Aiyub,Kavita Saini 한국전산응용수학회 2022 Journal of applied mathematics & informatics Vol.40 No.3
In the present paper we introduce and study Euler sequence spaces of fractional difference and backward difference operators. We make an effort to prove that these spaces are BK-spaces and linearly isomorphic. Further, Schauder basis for Euler fractional difference sequence spaces e_{0,p}^{\varsigma}(\Delta^{(\tilde{\beta})},\nabla^{m}) and e_{c,p}^{\varsigma}(\Delta^{(\tilde{\beta})},\nabla^{m}) are also elaborate. In addition to this, we determine the \alpha-, \beta- and \gamma- duals of these spaces.
Raj, Kuldip,Sharma, Sunil K.,Gupta, Amit Department of Mathematics 2014 Kyungpook mathematical journal Vol.54 No.1
In the present paper we introduce difference paranormed sequence spaces $c_0(\mathcal{M},{\Delta}^n_m,p,u,{\parallel}{\cdot},{\cdots},{\cdot}{\parallel})$, $c(\mathcal{M},{\Delta}^n_m,p,u,{\parallel}{\cdot},{\cdots},{\cdot}{\parallel})$ and $l_{\infty}(\mathcal{M},{\Delta}^n_m,p,u,{\parallel}{\cdot},{\cdots},{\cdot}{\parallel})$ defined by a Musielak-Orlicz function $\mathcal{M}$ = $(M_k)$ over n-normed spaces. We also study some topological properties and some inclusion relations between these spaces.
On almost deferred weighted convergence
M. Aiyub,Sonali Sharma,Kuldip Raj 한국전산응용수학회 2024 Journal of applied mathematics & informatics Vol.42 No.2
This article introduces the notion of almost deferred weighted convergence, statistical deferred weighted almost convergence and almost deferred weighted statistical convergence for real valued sequences. Further, with the aid of interesting examples, we investigated some relationships among our proposed methods. Moreover, we prove a new type of approximation theorem and demonstrated that our theorem effectively extends and improves most of the earlier existing results. Finally, we have presented an example which proves that our theorem is a stronger than its classical versions.