Operator (h,m)-Convexity and Hermite-Hadamard Type Inequalities

Year 2017, Volume: 7 Issue: 2, 367 - 377, 15.12.2017

Seren Salaş Erdal Ünlüyol Dilan Yardımcıel

Abstract

In this paper, firstly we define a new class of operator convex functions in Hilbert space, as
operator (h,m)-convex functions. Later we give some properties of this class. Finally, we obtain
some new inequalities via Hermite-Hadamard inequality for operator (h,m)-convex function

Keywords

Hermite-Hadamard inequality, Operator convex, Operator m-convex, Operator hconvex, Operator (h, m)-convex, Hilbert space

Operatör (h,m)-Konvekslik ve Hermite-Hadamard Tipi Eşitsizlikler

Abstract

Bu çalışmada, ilk olarak Hilbert uzayında yeni bir operatör konveks sınıfı olan “operatör
(ℎ, 𝑚)-konveks fonksiyonlar sınıfı” tanıtıldı. Daha sonra bu sınıfın bazı özellikleri verildi. Son
olarak ise operatör (ℎ, 𝑚)-konveks fonksiyonlar için Hermite-Hadamard tipi eşitsizlikler
yardımıyla bazı yeni eşitsizlikler elde edildi.

Keywords

Hermite-Hadamard tipi eşitsizlik, operatör konveks, operatör m-konveks, operatör ℎ-konveks, operatör (ℎ, 𝑚)-konveks, Hilbert uzayı.

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