Approximately Monotone, Hölder, Convex and Affine Functions

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dc.contributor.advisorPáles, Zsolt
dc.contributor.authorGoswami, Angshuman Robin
dc.contributor.departmentMatematika- és számítástudományok doktori iskolahu
dc.date.accessioned2021-07-02T08:55:02Z
dc.date.available2021-07-02T08:55:02Z
dc.date.created2021hu_HU
dc.date.defended2021-10-19
dc.description.abstractIn the dissertation, we described the structural properties of four function classes, determined the error function which is the most optimal one. Then we succeeded to show that the optimal error functions for approximate-monotonicity and approximate-Hölder property must be subadditive and absolutely subadditive, respectively. While the optimal error functions for approximate-convexity and approximate-affinity must possesses a special property, termed as Gamma-property. Then we offered a precise formula for the lower and upper approximately-monotone and approximately-Hölder envelopes. We also derive a formula for the approximately-convex minorant. We introduced a generalization of the classical notion of total variation and we proved an extension of the Jordan Decomposition Theorem known for functions of bounded total variations. Besides, we deduced Ostrowski- and Hermite-Hadamard-type inequalities from the approximate-monotonicity and approximate-Hölder properties, and then we also verified the sharpness of these implications. Using the notions of upper and lower interpolations, we established a characterizations for approximately monotone and approximately-Hölder functions. Finally, we characterized approximately-convex and approximately-affine classes of functions and investigated their relationship with approximately monotone and approximately Hölder functions.hu_HU
dc.format.extent95hu_HU
dc.identifier.urihttp://hdl.handle.net/2437/320486
dc.language.isoenhu_HU
dc.subjectMonotonicityhu_HU
dc.subjectConvexity
dc.subjectOstrowski and Hermite-Hadamard type inequalities
dc.subjectJordan type decomposition
dc.subject.disciplineMatematika- és számítástudományokhu
dc.subject.sciencefieldTermészettudományokhu
dc.titleApproximately Monotone, Hölder, Convex and Affine Functionshu_HU
dc.title.translatedApproximately Monotone, Holder, Convex and Affine Functionshu_HU
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