Zaman Skalası Üzerinde Δ-Düzgün ve Δ-Noktasal Yakınsaklık

Bu makalede j bir zaman skalası olmak üzere, {fj}j∈j fonksiyon ailesi için Δ-Cauchy, Δdüzgün yakınsaklık ve Δ-noktasal yakınsaklık kavramları verilerek bu kavramlar arasındaki ilişkiler incelenmiştir. Δ-limit ile Riemann Δ-integrali ve Δ-türevin yer değişme problemi araştırılarak Dini Teoreminin farklı bir versiyonu elde edilmiştir. Anahtar Kelimeler: Δ-Yakınsaklık; Δ-Cauchy; İstatistiksel yakınsaklık.

On Δ-Uniform and Δ-Pointwise Convergence on Time Scale

In this article, we define the concept of Δ-Cauchy, Δ-uniform convergence and Δpointwise convergence of a family of functions {f}f∈j, where j is a time scale. We study the relationships between these notions. Moreover, we introduced sufficient conditions for interchangeability Δ-limitation with Riemann Δ-integration or Δ-differentiation. Also, we obtain the analogue of the well-known Dini's Theorem. Keywords: Δ-Convergence; Δ-Cauchy; Statistical convergence.

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