What question did this study set out to answer?

The aim is to explore statistical convergence of double sequences using deferred Cesàro summability.

April 10, 2026AxiomsOpen Access

Deferred Cesàro Summability and Korovkin-Type Approximation Theorems for Double Sequences on Time Scales

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This investigation reveals new convergence conditions for double sequences, suggesting practical applications in approximation theory.

The aim is to explore statistical convergence of double sequences using deferred Cesàro summability.
Introduced new convergence notions for double sequences of time-scale functions.
Established limit properties and inclusion relations.
Proved Korovkin-type approximation theorems for functions of two variables.
Analyzed the rate of statistical convergence with deferred Cesàro summability.
New convergence criteria were established for double sequences.
Several Korovkin-type theorems were successfully demonstrated.
Illustrative examples showed the practical applicability of the theoretical findings.
The rate of convergence was estimated effectively using the deferred Cesàro method.

Srivastava et al. (2026) studied this question.

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