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

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.