Seren SALAŞ, Erdal ÜNLÜYOL, Dilan YARDIMCIEL

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

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

Anahtar Kelimeler:

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

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

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,

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