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On vector valued difference sequence spaces

Sandeep Gupta|Manoj Kumar|Ritu
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2024.09|한국수학논문집 (Korean Journal of Mathematics)|제32권 제3호|pp. 439-451

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키워드

Difference sequence spacesModulus functionParanormStatistical convergence.
주제분류수학

초록

In the present paper, using the notion of difference sequence spaces, we introduce new kind of Cesàro summable difference sequence spaces of vector valued sequences with the aid of paranorm and modulus function. In addition, we extend the notion of statistical convergence to introduce a new sequence space $SC_1(\Delta,q)$ which coincides with $C_1^1(X,\Delta,\phi,\lambda,q)$ (one of the above defined Cesàro summable difference sequence spaces) under the restriction of bounded modulus function.

Abstract

In the present paper, using the notion of difference sequence spaces, we introduce new kind of Cesàro summable difference sequence spaces of vector valued sequences with the aid of paranorm and modulus function. In addition, we extend the notion of statistical convergence to introduce a new sequence space $SC_1(\Delta,q)$ which coincides with $C_1^1(X,\Delta,\phi,\lambda,q)$ (one of the above defined Cesàro summable difference sequence spaces) under the restriction of bounded modulus function.

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