Abel statistical quasi Cauchy sequences

Statistical quasi-Cauchy sequences

A subset E of a metric space (X, d) is totally bounded if and only if any sequence of points in E has a Cauchy subsequence. We call a sequence (xn) statistically quasiCauchy if st − limn→∞ d(xn+1, xn) = 0, and lacunary statistically quasi-Cauchy if Sθ − limn→∞ d(xn+1, xn) = 0.Weprove that a subset E of ametric space is totally bounded if and only if any sequence of points in E has a subsequence...

Ideal quasi-Cauchy sequences

*Correspondence: [email protected]; [email protected] 1Department of Mathematics, Maltepe University, Marmara Eğİtİm Köyü, TR 34857, Maltepe, İstanbul, Turkey Full list of author information is available at the end of the article Abstract An ideal I is a family of subsets of positive integersN which is closed under taking finite unions and subsets of its elements. A sequence (xn) of real...

The Quasi-Cauchy Relation and Diagonal Updating

The quasi-Cauchy (QC) relation is the weak quasi-Newton relation of Dennis and Wolkowicz [SIAM J. Numer. Anal., 30 (1993), pp. 1291–1314] with the added restriction that full matrices are replaced by diagonal matrices. This relation is justified and explored and, in particular, two basic variational techniques for updating diagonal matrices that satisfy it are formulated. For purposes of illust...

Generalized Fuzzy Quasi-Ideals of an Intraregular Abel-Grassmann's Groupoid

Moment sequences and abstract Cauchy problems

We give a new characterization of the solvability of an abstract Cauchy problems in terms of moment sequences, using the resolvent operator at only one point.