Çok Boyutlu Fonksiyonların Genelleştirilmiş Konveksliği ve İlgili Hermite-Hadamard Tipi İntegral Eşitsizlikleri

Year 2020, Volume: 10 Issue: 1, 241 - 250, 15.01.2020

Fatma Buğlem Yalçın , Nurgül Okur

https://doi.org/10.17714/gumusfenbil.632639

Abstract

Bu makalede temel amaç, çok boyutlu fonksiyonların genelleştirilmiş konveksliğini incelemek ve onunla ilgili bazı önemli eşitsizlikler elde etmektir. Bu nedenle ilk olarak çok boyutlu genelleştirilmiş konveks fonksiyonlar tanımlanmıştır. Devamında bu fonksiyonların bazı özelliklerinden bahsedilmiştir. Buna bağlı olarak, çok boyutlu genelleştirilmiş konveks fonksiyonlar ile diğer konveks fonksiyonların ilişkisi kurulmuştur. Ek olarak, iki boyutlu genelleştirilmiş konveks fonksiyonlar için Hermite-Hadamard tipli integral eşitsizliği genelleştirilmiştir. Son olarak bu çalışmada, çok boyutlu genelleştirilmiş konveks için Hermite-Hadamard tipli integral eşitsizliği elde edilmiş ve bu eşitsizliği açıklayıcı bir örnek verilmiştir

Keywords

Generalized Convexity, Hermite-Hadamard Inequality, Multidimensional General Convex Functions, n-coordinates

General Convexity of Multidimensional Functions and Related Hermite-Hadamard Type Integral Inequalities

Abstract

The basic goal is to investigate general convexity of multidimensional functions and derive several important inequalities associated with it’s in this paper. For this reason, multidimensional general convex functions were firstly defined. Afterwards, some properties of these functions were mentioned. Accordingly, the relation of multidimensional general convex functions with other convex functions was established. Additionally, a generalization of Hermite-Hadamard type integral inequality was showed for two-dimensional general convex functions. Finally, Hermite-Hadamard type integral inequality for multidimensional general convex functions was verified and an explanatory example for this inequality was given in this study.

 

Keywords

Genelleştirilmiş Konvekslik, Hermite-Hadamard Eşitsizliği, Çok Boyutlu Genelleştirilmiş Konveks Fonksiyonlar, n-boyutlu koordinatlar

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