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DC Field | Value | Language |
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dc.contributor.advisor | Prof. Dr. Ertürk, Vedat Suat | - |
dc.contributor.advisor | Prof. Dr. Maden, Selahattin | - |
dc.contributor.author | Kadakal, Huriye | - |
dc.date.accessioned | 2022-08-12T07:07:31Z | - |
dc.date.available | 2022-08-12T07:07:31Z | - |
dc.date.issued | 2018 | - |
dc.date.submitted | 2018 | - |
dc.identifier.uri | http://earsiv.odu.edu.tr:8080/xmlui/handle/11489/1058 | - |
dc.description.abstract | Bu tezde, geometrik-aritmetik konveks fonksiyonlar ve 𝑛-kere diferansiyellenebilir konveks(dışbükey) ve konkav(içbükey) fonksiyonlar için yeni integral eşitsizlikleri verildi. Çalışmanın ilk bölümünde, konveks fonksiyonların tarihi gelişimi ve literatür taraması verildi. İkinci bölümde, literatürdeki konveks fonksiyon çeşitleri tanımlanarak, konveks fonksiyon sınıfları arasındaki hiyerarşi ve literatürde bulunan farklı ortalamalar verildi. Üçüncü bölümde, bu tezde kullanılan klasik eşitsizlikler ve daha sonrada tezin bulgular kısmında kullanılacak olan lemmalar ve teoremler verildi. Dördüncü bölümde ise geometrik- aritmetik(GA) konveks fonksiyonlar ile 𝑛-kere diferansiyellenebilir konveks ve konkav fonksiyonlarla ilgili yeni lemmalar, teoremler, önermeler ve sonuçlar verildi. Elde edilen bu yeni sonuçlar için çeşitli ortalamalar ve 𝑛-kere diferensiyellenebilen konveks ve konkav fonksiyonlar kullanılarak farklı uygulamalar verilmiştir.,In this thesis, new type integral inequalities for geometrically-arithmetically convex functions and 𝑛-time differentiable convex and concave functions are stated. In the first part, the historical developments of the convex functions and the literature review have been clarified. In the second part, classes of convex functions in literature, the hierarchy of convex function classes, and different averages in the literature have been explained. In the third part, the classical inequalities used in this thesis and then the lemmas and theorems to be used in the findings of the thesis are given. In the fourth part, new identities, lemmas, theorems, propositions and results about geometrically arithmetically convex functions and 𝑛-times differentiable convex and concave functions have been presented. For these new results obtained, different applications are provided by using different means and 𝑛-time differentiable convex and concave functions. | en_US |
dc.description.abstract | In this thesis, new type integral inequalities for geometrically-arithmetically convex functions and 𝑛-time differentiable convex and concave functions are stated. In the first part, the historical developments of the convex functions and the literature review have been clarified. In the second part, classes of convex functions in literature, the hierarchy of convex function classes, and different averages in the literature have been explained. In the third part, the classical inequalities used in this thesis and then the lemmas and theorems to be used in the findings of the thesis are given. In the fourth part, new identities, lemmas, theorems, propositions and results about geometrically arithmetically convex functions and 𝑛-times differentiable convex and concave functions have been presented. For these new results obtained, different applications are provided by using different means and 𝑛-time differentiable convex and concave functions. | en_US |
dc.language.iso | tur | en_US |
dc.publisher | Fen Bilimleri Enstitüsü | en_US |
dc.rights | info:eu-repo/semantics/openAccess | en_US |
dc.subject | Hermite-Hadamard İntegral Eşitsizliği, Geometrik-Aritmetik Konveks Fonksiyonlar, Hölder İntegral Eşitsizliği, Power-Mean İntegral Eşitsizliği.,Hermite-Hadamard Integral Inequality, Geometrically Arithmetically Convex Functions, Hölder Integral Inequality, Power-Mean Integral Inequality | en_US |
dc.title | Yeni Tip İntegral Ortalamaları İçin Bazı Eşitsizlikler | en_US |
dc.title.alternative | SOME INEQUALITIES FOR NEW TYPE INTEGRAL MEANS | en_US |
dc.type | doctoralThesis | en_US |
dc.contributor.department | Ordu Üniversitesi | en_US |
dc.contributor.department | Fen Bilimleri Enstitüsü | en_US |
Appears in Collections: | Fen Bilimleri Enstitüsü |
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10217100.pdf | 1.92 MB | Adobe PDF | ![]() View/Open |
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