The sharper version for generalized power mean inequalities with negative exponent

In this study, the generalized power mean inequalities with a negative parameter are refined using an optimality theorem on the generator function. The optimality theorem requires the study of different cases for the exponents and yields a refinement of the inequality in a neighbourhood of the vectors for which the equality occurs. Then, these local inequalities are generalized to all positive vectors by an appropriate selection of parameters. Also, some of the results are exemplified by numerical calculations

Abstract Convexity and Hermite-Hadamard Type Inequalities

<p/> <p>The deriving Hermite-Hadamard type inequalities for certain classes of abstract convex functions are considered totally, the inequalities derived for some of these classes before are summarized, new inequalities for others are obtained, and for one class of these functions the results on <inline-formula> <graphic file="1029-242X-2009-943534-i1.gif"/></inline-formula> are generalized to <inline-formula> <graphic file="1029-242X-2009-943534-i2.gif"/></inline-formula>. By considering a concrete area in <inline-formula> <graphic file="1029-242X-2009-943534-i3.gif"/></inline-formula>, the derived inequalities are illustrated.</p

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

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

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