Some important properties of B-convex functions

In this paper, B-convex functions which are a class of abstract convex functions are discussed and some important properties of B-convex functions are studied

Hermite-hadamard type inequalities for B-1-convex functions involving generalized fractional integral operators

WOS: 000461186000025B-1-convexity is an abstract convexity type. We obtained Hermite-Hadamard inequality for B-1-convex functions. But now, there are new and more general integral operator types that are fractional integrals. Thus, we need to prove Hermite-Hadamard inequalities involving different fractional integral operator types with this article.Unit of SRP(BAP) of Aksaray University [2017-053]The first author was supported in part by Unit of SRP(BAP) of Aksaray University with 2017-053 project number

Genelleştirilmiş Ortalama Fonksiyonu ve Bazı Önemli Eşitsizliklerin Öğretimi Üzerine

Aritmetik ortalama, Geometrik ortalama, Harmonik ortalama, Kuvadratik ortalama ve bunlar arasındaki ilişkini veren eşitsizlikler, orta öğretim ve üniversite ders programlarında öğrenilen önemli konulardandır. Bu konunun öğretiminde eşiksizlikler tek tek ele alınır ve doğrulukları farklı yollarla kanıtlanır. Bu makalede, bu konunun öğretimi ile bağlı, farklı bir yol izlenilir. Bu ortalamalar, bir Ortalama Fonksiyonunun birer özel durumları olduğundan dolayı, adı geçen Ortalama Fonksiyonunun daha genel durumu olan Ağırlıklı Ortalama Fonksiyonu ele alınır. Bu fonksiyonun monotonluk özelliğine dayanarak ortalamalarla bağlı tüm bilinen eşitsizliklerin (bilinmeyen, çok sayıda diğer eşitsizliklerin de) doğruluğu gösterilir

Radon's and Helly's theorems for B-1-Convex sets

Helly's, Radon's, and Caratheodory's theorems are the basic theorems of convex analysis and have an important place. These theorems have been studied by different authors for different classes of convexity. Caratheodory's theorem for B-1-convex sets has been proved before by Adilov and Yes , ilce. In this article, Helly's and Radon's theorems are discussed and examined for these sets

New Type Inequalities for B−1\mathbb{B}^{-1}-convex Functions involving Hadamard Fractional Integral

Abstract convexity is an important area of mathematics in recent years and it has very significant applications areas like inequality theory. The Hermite-Hadamard Inequality is one of these applications. In this article, we studied Hermite-Hadamard Inequalities for $\mathbb{B}^{-1}$-convex functions via Hadamard fractional integral

A refinement of the Bergstrom inequality

In this paper, the Bergstrom inequality is studied, and a refinement of this inequality is obtained by performing the optimality conditions based on abstract concavity. Some numerical experiments are given to illustrate the efficacy of the refinement

Some integral inequalities for the product of s-convex functions in the fourth sense

n this paper, several novel inequalities are examined for the product of two s-convex functions in the fourth sense. Also, some applications regarding special means and digamma functions are presented