Yazar "Kadakal, Huriye" seçeneğine göre listele

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    Better approximations for quasi-convex functions
    (Univ Babes-Bolyai, 2024) Kadakal, Huriye
    In this paper, by using Holder-(center dot)Iscan, Holder integral inequality and an general identity for differentiable functions we can get new estimates on generalization of Hadamard, Ostrowski and Simpson type integral inequalities for functions whose derivatives in absolute value at certain power are quasi-convex functions. It is proved that the result obtained Holder-(center dot)Iscan integral inequality is better than the result obtained Holder inequality.
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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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    Generalization of Some Integral Inequalities for Arithmetic Harmonically Convex Functions
    (2022) Kadakal, Huriye
    In this study, by using an integral identity, Hölder integral inequality and modulus properties we obtain some new general inequalities of the Hermite-Hadamard and Bullen type for functions whose derivatives in absolute value at certain power are arithmetically harmonically (AH) convex. In the last part of the article, applications including arithmetic mean, geometric mean, harmonic mean, logarithmic mean and p-logarithmic mean, which are some special means of real numbers, are given by using arithmetic harmonically convex functions.
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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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    Harmonic trigonometrically convexity
    (Univ Nis, Fac Sci Math, 2023) Kadakal, Huriye
    In this study, we introduce and study the concept of harmonic trigonometrically convex functions and their some algebric properties. We prove two Hermite-Hadamard type inequalities for the newly introduced class of functions. We also obtain some refinements of the Hermite-Hadamard inequality for functions whose first derivative in absolute value, raised to a certain power which is greater than one, respectively at least one, is harmonic trigonometrically convex.
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    INEQUALITIES OF HERMITE-HADAMARD TYPE FOR n-TIMES DIFFERENTIABLE ARITHMETIC-HARMONICALLY FUNCTIONS
    (Honam Mathematical Soc, 2022) Kadakal, Huriye
    In this work, by using an integral identity together with both the Holder and the power-mean integral inequalities we establish several new inequalities for n-times differentiable arithmetic-harmonically-convex function. Then, using this inequalities, we obtain some new inequalities connected with means. In special cases, the results obtained coincide with the well-known results in the literature.
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    MULTIPLICATIVELY PREINVEX P-FUNCTIONS
    (Editura Bibliotheca-Bibliotheca Publ House, 2023) Kadakal, Huriye; Kadakal, Mahir
    In this study, using both Holder's integral inequality and Holder-Iccan integral inequality, some inequalities of Hermite Hadamard type obtained for multiplicatively preinvex P -functions are given. Afterwards, the result obtained with Holder-Iccan inequality has been shown to be better than that obtained with Holder's integral inequality.
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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.
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    STRONGLY HYPERBOLIC TYPE CONVEXITY AND SOME NEW INEQUALITIES
    (Editura Bibliotheca-Bibliotheca Publ House, 2023) Kadakal, Huriye; Kadakal, Mahir
    In this study, we introduce and study the concept of strongly hyperbolic type convexity functions and their some algebraic properties. We obtain Hermite-Hadamard type inequalities for the strongly hyperbolic type convex functions. After that, by using an identity, we get some inequalities for strongly hyperbolic type convex functions. In addition, we compare the results obtained with both Holder, Holder-Iscan inequalities and power-mean, improved power-mean integral inequalities.