Comparison of speeds of convergence in some families of summability methods for functions

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dc.contributor.authorSheletski, Anna
dc.date.accessioned2024-07-12T20:51:35Z
dc.date.available2024-07-12T20:51:35Z
dc.date.issued2009en_US
dc.departmentFakülteler, İnsan ve Toplum Bilimleri Fakültesi, Matematik Bölümüen_US
dc.description.abstractSpeeds of convergence in certain family of summability methods for functions are compared in the talk. The results introduced here extend the results proved in [1] for ”matrix case” to ”integral case” and are partly published in [2]. 1. Let us denote by X the set of all functions x = x(u) defined for u ? 0, bounded and measurable by Lebesgue on every finite interval [0, u0]. Suppose that A is a transformation of functions x = x(u) (or, in particular, of sequences x = (xn)) into functions Ax = y = y(u) ? X. If the limit limu?? y(u) = s exists then we say that x = x(u) is convergent to s with respect to the summability method A, and write x(u) ? s(A). One of the basic notions in our talk is the notion of speed of convergence. Let ? = ?(u) be a positive function from X such that ?(u) ? ? as u ? ?. We say that a function x = x(u) is convergent to s with speed ? if the finite limit limu?? ?(u) [x(u) ? s] exists. We say that x is convergent with speed ? with respect to the summability method A if the function Ax = y = y(u) ? X is convergent with speed ?. 2. We discuss a Riesz-type family {A?} of summability methods A? where ? > ?0 and ?0 is some fixed number and which transform functions x = x(u) into functions A?x = y?(u). This family is defined with the help of relation A? = C?,? ? A? (? > ? > ?0), where C?,? is certain integral transformation (see e.g. [2]). For example, the Riesz methods (R, ?) and certain generalized N¨orlund methods (N, p?(u), q(u)) form Riesz-type families. It is important to be able to compare the speed of convergence of x = x(u) with respect to different methods in family {A?} For a given speed ? = ?(u) and a fixed number ? > ?0 the speeds ?? = ??(u) and ?? = ??(u) can be found (see [2]) such that for all ? > ? > ? the next implications are true: ?(u) [y? (u) ? s] ? t =? ??(u) [y?(u) ? s] ? t, ?(u) [y? (u) ? s] = O(1), ??(u) [y?(u) ? s] ? t =? ??(u) [y?(u) ? s] ? t.en_US
dc.identifier.citationSheletski, A. (2009). Comparison of speeds of convergence in some families of summability methods for functions. Maltepe Üniversitesi. s. 105.en_US
dc.identifier.endpage106en_US
dc.identifier.startpage105en_US
dc.identifier.urihttps://www.maltepe.edu.tr/Content/Media/CkEditor/03012019014112056-AbstractBookICMS2009Istanbul.pdf#page=331
dc.identifier.urihttps://hdl.handle.net/20.500.12415/2433
dc.institutionauthorSheletski, Anna
dc.language.isoenen_US
dc.publisherMaltepe Üniversitesien_US
dc.relation.ispartofInternational Conference of Mathematical Sciencesen_US
dc.relation.publicationcategoryUluslararası Konferans Öğesi - Başka Kurum Yazarıen_US
dc.rightsCC0 1.0 Universal*
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.rights.urihttp://creativecommons.org/publicdomain/zero/1.0/*
dc.snmzKY07798
dc.titleComparison of speeds of convergence in some families of summability methods for functionsen_US
dc.typeConference Object
dspace.entity.typePublication

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