Kuvvetli Boşluklu quasi-Cauchy Dizileri Üzerine Yeni Bir Çalışma

Abstract

Bu çalışmada  N theta 2-quasi-Cauchy dizisi kavramı tanıtılmış ve bu dizilerle ilgili ilginç teoremler  ispatlanmıştır. (a_k) R nin bir A altkümesi üzerinde tanımlı bir dizi olmak üzere,   (Delta²a_k )dizisi N theta- quasi-Cauchy oluyorsa (a_k) dizisine  N theta delta 2-quasi-Cauchy dizisidir denir. Burada Delta²a_k=a_k+2-2a_k+1+ a_k dır. f fonksiyonu R nin bir A altkümesinde tanımlı reel değerli bir fonksiyon olsun. Eğer f fonksiyonu A daki  N theta delta 2-quasi-Cauchy dizilerini koruyorsa, yani,  (a_k) dizisi A da  N theta delta 2-quasi-Cauchy dizisi iken   (f(a_k)) dizisi de N theta delta 2-quasi-Cauchy oluyorsa f e  A da N theta delta 2-ward süreklidir denir. 

Keywords

• toplanabilme,kuvvetli boşluklu yakınsaklık,quasi Cauchy dizisi,süreklilik

A new study on the strongly lacunary quasi Cauchy sequences

Abstract

In this paper, the concept of an  -quasi-Cauchy sequence is introduced. We proved interesting theorems related to  -quasi-Cauchy sequences. A real valued function defined on a subset  of , the set of real numbers, is -ward continuous on  if it preserves  -quasi-Cauchy sequences of points in , i.e. is an  -quasi-Cauchy sequences whenever  is an  -quasi-Cauchy sequences of points in , where a sequence  is called  -quasi-Cauchy if is an - quasi-Cauchy sequence where  for each positive integer k.

Keywords

• summabilty,strongly lacunary convergence,quasi-Cauchy sequences,boundedness,continuity

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