Generalizations and stability of convexity

dc.contributor.advisorPáles, Zsolt
dc.contributor.authorMolnár, Gábor Marcell
dc.contributor.departmentMatematika- és számítástudományok doktori iskolahu
dc.contributor.submitterdepTermészettudományi és Technológiai Kar::Matematikai Intézet::Analízis Tanszék
dc.date.accessioned2024-01-24T20:41:46Z
dc.date.available2024-01-24T20:41:46Z
dc.date.created2024
dc.date.defended2024-04-26
dc.description.abstractThis dissertation consists of two distinct topics, separated into two main chapters. In Chapter 1, we introduce and investigate the algebraic structures called cornets. Our primary focus is on extending the well-regarded Rådström cancellation principle to these specific objects. This chapter aims to delve into the adaptation and application of the cancellation principle within the context of cornets. Additionally, we establish the fundamental properties of cornets, covering essential aspects such as convexity properties, topological notions and, boundedness. In Chapter 2, we broaden the concepts of convex, concave, and affine sequences by introducing the novel notions of q-convex, q-concave, and q-affine sequences. This chapter not only unveils foundational results but also highlights an unexpected correlation between these sequences and Chebyshev polynomials. Furthermore, we present two practical applications of q-convex, q-concave, and q-affine sequences. The first involves addressing a minimax-type problem, while the second is an application in fixed point theory.
dc.description.correctorhbk
dc.format.extent123
dc.identifier.urihttps://hdl.handle.net/2437/365499
dc.language.isoen
dc.language.isohu
dc.subjectRådström cancellation theorem
dc.subjectordered commutative semigroup
dc.subjectcornet
dc.subjectconvexity
dc.subjectboundedness and closedness in cornets
dc.subjectq-convex sequence
dc.subjectq-concave sequence
dc.subjectq-affine sequence
dc.subjectChebyshev polynomials of the first and second kind
dc.subjectcontraction
dc.subject.disciplineMatematika- és számítástudományokhu
dc.subject.sciencefieldTermészettudományokhu
dc.titleGeneralizations and stability of convexity
dc.title.translatedKonvexitás általánosításai és stabilitása
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