Hermite-Hadamard Type Inequalities for the Functions Whose Absolute Values of First Derivatives are $p$-Convex

Abstract

In this paper, we extend some estimates of a Hermite-Hadamard type inequality for functions whose absolute values of the first derivatives are p-convex. By means of the obtained inequalities, some bound functions involving beta functions and hypergeometric functions are derived as applications. Also, we suggest an upper bound for error in numerical integration of p-convex functions via composite trapezoid rule.

An Analysis of the Effect of the 1878 Berlin Treaty on Diplomatic Policy Making

“…Furthermore, the Young Turk governments' nationalistic agenda was aimed at cultivating a Turkish identity for the Muslims that had fled from the Balkans, Central Asia, and South Caucasus, which were culturally different from the population of Anatolia. 42 Their only binding to the Ottoman state was their historical ties to the tribes of Oguz, who migrated to Anatolia in the early 11th Century, and that they shared a common religion. For the government, this presented a split in policy goals.…”

“…45 The refugee crisis of 1878 created an economic burden on the Ottoman Empire and would lead to the expulsion of the remainder of Ottoman influence in the Balkans. 46 Many Turks and Muslims fled the Balkans starting from 1877 due to fears of Russian and Bulgarian attacks. 47 During the war, up to 1.5 million Turks and Muslims fled to Rumelia and Anatolia according to immigration archives investigated by Justin McCarthy and Ilgın Barut.…”

“…The additional burden on the railway network also put a major strain on military logistics due to the scarcity of locomotives and railway tracks. 49 Therefore, Ottoman logistics were stretched thinly, even doubling the number of shifts to service the army and the population failed to adequately supply both. As a result, on many occasions the sick and wounded military personnel had to be left behind in order to evacuate the civilians, ramping up the human cost of the conflict immensely.…”