Earthquake convexity and some new related inequalities

Unfortunately, eleven of our provinces were severely affected due to two severe earthquakes that occurred in our country, the Republic of Turkey, on February 6, 2023. As a result, thousands of buildings were destroyed and tens of thousands of our citizens lost their lives. From past to present, such disasters have occurred in many parts of our world and will continue to happen. In order to raise awareness for researchers and academicians reading our article, we will give a new definition of convexity in this article, and we will call it "earthquake convexity". In this paper, we study some algebraic properties of the earthquake convexity. Then we compare the results obtained with both Hölder, Hölder-Işcan inequalities and power-mean, improved power-mean integral inequalities and show that the results obtained with Hölder-Işcan and improved power-mean inequalities are better than the others. Some applications to special means of real numbers are also given.