dc.contributor.advisor	Páles, Zsolt
dc.contributor.author	Ali, Ali Hasan
dc.contributor.department	Matematika- és számítástudományok doktori iskola	hu
dc.contributor.submitterdep	Természettudományi és Technológiai Kar::Matematikai Intézet::Analízis Tanszék
dc.date.accessioned	2024-04-19T20:13:12Z
dc.date.available	2024-04-19T20:13:12Z
dc.date.defended	2024-06-17
dc.date.issued	2024-04-15
dc.description.abstract	The aim of this dissertation is to develop an extension of the Taylor theorem related to linear differential operators with constant coefficients. For this aim, we employ divided differences with repeated arguments to describe the characteristic element from the kernel of the differential operator. We establish the extension of the Taylor theorem concerning exponential polynomials and investigate its implications, incorporating integral remainder terms and mean value type theorems. Furthermore, we establish various factorization results and utilize them to derive estimates for linear functionals through a generalized Taylor theorem. Moreover, we establish several error bounds, including their applications to the trapezoidal rule and a Simpson formula rule.
dc.format.extent	101
dc.identifier.uri	https://hdl.handle.net/2437/369097
dc.language.iso	en
dc.subject	Generalized Taylor theorem
dc.subject	differential operator
dc.subject	characteristic solution
dc.subject	exponential polynomial
dc.subject	factorization of linear functional
dc.subject	quadrature rule
dc.subject	trapezoidal rule
dc.subject	Simpson rule
dc.subject.discipline	Matematika- és számítástudományok	hu
dc.subject.sciencefield	Természettudományok	hu
dc.title	Extensions of Taylor's theorem and norm estimations of linear functionals
dc.title.translated	A Taylor-tétel kiterjesztései és lineáris funkcionálok normáinak becslései
dc.type	PhD, doktori értekezés	hu

Extensions of Taylor's theorem and norm estimations of linear functionals

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