A condition under which slow oscillation of a sequence follows from Cesàro summability of its generator sequence

In this paper we retrieve slow oscillation of a real sequence fromCesàro summability of its generator sequence under some one-sided condition. References[1] F. Dik, Tauberian theorems for convergence and subsequential convergence with moderatelyoscillatory behavior, Math. Morav. 5: 19–56 (2001).[2] M. Dik, Tauberian theorems for sequences with moderately oscillatory control moduli. Math.Morav. 5: 57–94 (2001).[3] R. P. Agnew, On deferred Cesàro means. Ann. Math., 33 (2): 413–421 (1932).[4] E. Landau, Über die Bedeutung einiger neuen Grenzwertsätze der Herren Hardy und Axer.Prace Mat. Fiz., 21: 97–177 (1910).[5] İ. Çanak and Ü. Totur, A Tauberian theorem with a generalized one-sided condition. Abstr.Appl. Anal., 2007 (Article ID 60360) (2007).[6] Č. V. Stanojević, Analysis of Divergence: Control and Management of Divergent Process,Graduate Research Seminar Lecture Notes, edited by İ. Çanak. University of MissouriRolla,Fall 1998, p. 56.[7] Č. V. Stanojević and V. B. Stanojević, Tauberian retrieval theory. Publ. Inst. Math.,Nouv.Ser. 71 (85): 105–111 (2002).[8] İ. Çanak, An extended Tauberian theorem for the (C,1) summability method. Appl. Math.Lett., 21 (1): 74–80 (2008). Adnan Menderes University Department of Mathematics 09010 Aydın TURKEYE-mail address: [email protected] Adnan Menderes University Department of Mathematics 09010 Aydın TURKEYE-mail address: [email protected] 2000 Mathematics Subject Classification. 40E05.