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    Earthquake convexity and some new related inequalities
    (Walter De Gruyter Gmbh, 2024) Kadakal, Mahir; Iscan, Imdat; Kadakal, Huriye
    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 Holder, Holder-Iscan inequalities and power-mean, improved power-mean integral inequalities and show that the results obtained with Holder-Iscan and improved power-mean inequalities are better than the others. Some applications to special means of real numbers are also given.
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    Generalized strongly n-polynomial convex functions and related inequalities
    (Springer, 2024) Ozcan, Serap; Kadakal, Mahir; Iscan, Imdat; Kadakal, Huriye
    This paper focuses on introducing and examining the class of generalized strongly n-polynomial convex functions. Relationships between these functions and other types of convex functions are explored. The Hermite-Hadamard inequality is established for generalized strongly n-polynomial convex functions. Additionally, new integral inequalities of Hermite-Hadamard type are derived for this class of functions using the Holder-Iscan integral inequality. The results obtained in this paper are compared with those known in the literature, demonstrating the superiority of the new results. Finally, some applications for special means are provided.
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    Semi P-geometric-arithmetically functions and some new related inequalities
    (Univ Nis, Fac Sci Math, 2023) Kadakal, Mahir; Kadakal, Huriye; Iscan, Imdat
    In this manuscript, the authors introduce the concept of the semi P-geometric-arithmetically functions (semi P-GA functions) and give their some algebraic properties. Then, they get Hermite-Hadamard's integral inequalities for semi P-GA-functions (geometric-arithmetically convex). In addition, the authors obtain new inequalities by using Holder and Holder-Iscan integral inequalities with the help of an identity. Then, the aouthors compare the results obtained with both Holder, Holder-Iscan integral inequalities and prove that the Holder-Iscan integral inequality gives a better approximation than the Holder integral inequality. Also, some applications to special means of real numbers are also given.