On relative uniform convergence of triple sequence of functions. (English) Zbl 07905413
Summary: This paper discusses relative uniform convergence of triple sequence of functions that are defined on a compact domain. Another central idea that is discussed is the regular relative uniform convergence and the Cauchy relative uniform convergence of triple sequence of functions. The idea that a continuous triple sequence defined on a compact domain is relative uniform convergent if and only if it is relative uniform Cauchy has been discussed and established. Then we have introduced the Cesaŕo summability of triple sequences and a theorem regarding triple Cesaŕo summability of bounded relative uniform triple sequence of functions.
MSC:
| 40A05 | Convergence and divergence of series and sequences |
| 40B05 | Multiple sequences and series |
| 46A45 | Sequence spaces (including Köthe sequence spaces) |
| 46B45 | Banach sequence spaces |
| 46E30 | Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) |
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