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Space of Wijsman \(\mu \)-Deferred Cesàro I-Statistically Convergent of Order (a, b) Set Sequence

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Abstract

In this paper, we present the notions of Wijsman strongly ideal \(r-\)deferred Cesàro summability and Wijsman \(\mu \)-deferred Cesàro I-statistical convergence of order (a, b) allied with modulus function f for a sequence of closed sets of a separable metric space \((\mathcal {X},\rho )\). We also define their respective sequence spaces \( \left[ {{\text{DC}}\left[ {p,q} \right]_{W}^{{(a,b)}} (r,f)} \right]^{I} \) and \( \left[ {_{\mu } {\text{DS}}\left[ {p,q} \right]_{W}^{{(a,b)}} \left( f \right)} \right]^{I} \), respectively. We also prove that for \(a\le b\), the newly formed sequence space is well defined but for \( a>b \), foresaid space is not well defined in general. Some inclusion relation-based results are also established with some counterexamples to support our results. At last, it is shown that if a bounded sequence of closed sets is Wijsman \(\mu \)-deferred Cesàro I-statistical convergence of order (a, b), then it need not be Wijsman strongly ideal \(r-\)deferred Cesàro summable.

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Authors and Affiliations

  1. Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India

    Vakeel A Khan & Izhar Ali Khan

  2. Department of Mathematics, Gauhati University, Guwahati, Assam, 781014, India

    Bipan Hazarika

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  1. Vakeel A Khan
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  2. Izhar Ali Khan
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  3. Bipan Hazarika
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Khan, V.A., Khan, I.A. & Hazarika, B. Space of Wijsman \(\mu \)-Deferred Cesàro I-Statistically Convergent of Order (a, b) Set Sequence. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 93, 321–329 (2023). https://doi.org/10.1007/s40010-023-00816-0

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