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Öğe Construction of a new generalization for n-polynomial convexity with their certain inequalities(Hacettepe Univ, Fac Sci, 2024) Kadakal, Mahir; Iscan, Imdat; Kadakal, HuriyeIn this paper, we first construct a new generalization of n-polynomial convex function. That is, this study is a generalization of the definition of n-polynomial convexity previously found in the literature. By making use of this construction, we derive certain inequalities for this new generalization and show that the first derivative in absolute value corresponds to a new class of n-polynomial convexity. Also, we see that the obtained results in the paper while comparing with H & ouml;lder, H & ouml;lder-& Idot;& scedil;can and power-mean, improvedpower-mean integral inequalities show that the results give a better approach than the others. Finally, we conclude our paper with applications containing some means.Öğe DYNAMICS IN A PARABOLIC-ELLIPTIC CHEMOTAXIS SYSTEM WITH LOGISTIC SOURCE INVOLVING EXPONENTS DEPENDING ON THE SPATIAL VARIABLES(Amer Inst Mathematical Sciences-Aims, 2024) Ayazoglu, Rabil; Kadakal, Mahir; Akkoyunlu, EbubekirWe consider the parabolic-elliptic chemotaxis system with the exponents depending on the spatial variables logistic source and nonlinear signal production: ut = Delta u-chi del (u del upsilon)+f (x, u), (x, t) is an element of Omega x (0, T), 0 = Delta upsilon - upsilon +u(gamma) in a bounded domain Omega subset of R-N (N > 1) with smooth boundary, subject to non negative initial data and homogeneous Neumann boundary conditions, where chi > 0, gamma >= 1 and partial derivative/partial derivative nu denotes the outward normal derivative on partial derivative Omega. The logistic function f fulfilling f (x, s) <= eta s - mu s(alpha(x)+1), eta >= 0, mu > 0 for all s > 0 with f (x, 0) >= 0 for all x is an element of Omega, where alpha : Omega -> [1, infinity) is a measurable function. It is proved that if 1 <= alpha (x) < infinity for all x is an element of Omega such that ess inf(x is an element of Omega) alpha (x) > gamma or ess inf(x is an element of Omega) alpha (x) = gamma with mu > chi, then there exists a nonnegative classical solution (u, upsilon) that is global-in-time and bounded. In addition, under the particular conditions gamma = 1 and f (x, s) = mu (s - s(alpha(x)+1)), if mu is sufficiently large, the global bounded solution (u, upsilon) satisfies IIu (, t) - 1II(L)infinity(Omega) + II upsilon (, t) - 1II(L)infinity(Omega) <= Ce (- k/N+2t) for all t > 0 with k = min{ chi 2/4 , 1/2 } , C > 0. The global-in-time existence and uniform-in-time boundedness of solutions are established under specific parameter conditions, which improves the known results.Öğe EARTHQUAKE -FUNCTIONS WITH SOME RELATED INEQUALITIES AND THEIR APPLICATIONS(Editura Bibliotheca-Bibliotheca Publ House, 2025) Ozcan, Serap; Kadakal, Mahir; Iscan, Imdat; Kadakal, HuriyeAs researchers, our primary commitment is to engage in the creation of scientific and academic knowledge. Recognizing the importance of societal impact, we also strive to contribute to social awareness through our work. Natural disasters, such as floods, earthquakes, avalanches, landslides, tsunamis, and others, frequently afflict regions globally, resulting in profound human losses and extensive material damage. Notably, the earthquake that struck our country on February 6, 2023, marked as the disaster of the century, deeply affected eleven provinces, leading to a tragic loss of tens of thousands of lives. In this paper, we investigate the concept of earthquake P-functions. We establish the Hermite-Hadamard inequality for this class of functions and derive several refinements of the Hermite-Hadamard type inequality for functions whose first derivative, in absolute value, at a certain power, is an earthquake P-function. We present some applications of the trapezoidal formula. We also provide new bounds for special means of different non-negative real numbers.Öğe Earthquake convexity and some new related inequalities(Walter De Gruyter Gmbh, 2024) Kadakal, Mahir; Iscan, Imdat; Kadakal, HuriyeUnfortunately, 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.Öğe Exponential Convex Functions with Respect to s(Univ Maragheh, 2024) Kadakal, MahirIn this paper, we study the concept of exponential convex functions with respect to s and prove Hermite-Hadamard type inequalities for the newly introduced this class of functions. In addition, we get some refinements of the Hermite-Hadamard (HH) inequality for functions whose first derivative in absolute value, raised to a certain power which is greater than one, respectively at least one, is exponential convex with respect to s. Our results coincide with the results obtained previously in special cases.Öğe GENERALIZED n-POLYNOMIAL P- FUNCTIONS WITH SOME RELATED INEQUALITIES AND THEIR APPLICATIONS(Editura Bibliotheca-Bibliotheca Publ House, 2024) Ozcan, Serap; Kadakal, Mahir; Iscan, Imdat; Kadakal, HuriyeIn this paper, we introduce the notion of generalized n-polynomial Pfunction. We explore some algebraic properties of this function class. Additionally, we establish a new trapezium type inequality for this generalized class of functions and derive several refinements of the trapezium type inequality for functions whose first derivative in absolute value at a certain power is generalized n-polynomial P-function. Finally, we conclude our paper by exploring some applications of the results we have obtained in the context of special means. Our novel findings generalize previously known results in the literature.Öğe Generalized strongly n-polynomial convex functions and related inequalities(Springer, 2024) Ozcan, Serap; Kadakal, Mahir; Iscan, Imdat; Kadakal, HuriyeThis 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.Öğe HERMITE-HADAMARD TYPE INTEGRAL INEQUALITIES FOR SEMIHARMONICALLY P-FUNCTIONS(Rocky Mt Math Consortium, 2025) Kadakal, Mahir; Iscan, Imdat; Kadakal, HuriyeThe authors introduce the concept of semiharmonically P-functions and establish some Hermite-Hadamard type integral inequalities for these classes of functions. Also, the authors compare the results obtained H & ouml;lder and H & ouml;lder-I-center dot,scan inequalities and show that the result obtained with H & ouml;lder-I-center dot,scan inequalities give better approach than the others. Some applications to special means of real numbers are also given.Öğe HG-CONVEX FUNCTIONS(Editura Bibliotheca-Bibliotheca Publ House, 2024) Gulsu, Nagihan kurt; Iscan, Imdat; Kadakal, Mahir; Bekar, KerimIn this paper, the concept of Hg-convex function is given for the first time in the literature. Some inequalities of Hadamard's type for Hg-convex functions are given. Some algebraic properties of Hg-convex functions and special cases are discussed. In addition, we establish some new integral inequalities for Hg-convex functions by using an integral identity.Öğe INVERSE TRIGONOMETRICALLY CONVEXITY AND BETTER APPROXIMATIONS(Univ Miskolc Inst Math, 2025) Kadakal, Huriye; Kadakal, MahirIn this paper, we introduce and study the concept of inverse trigonometrically convex functions and their some algebraic properties. We prove some Hermite-Hadamard type integral 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 is inverse trigonometrically convex. Moreover, we proved that Holder-I(center dot)s, can and improved power-mean integral inequalities give a better approach than Holder and power-mean inequalities.Öğe LOGARITHMIC SEMI P-FUNCTION AND SOME NEW INEQUALITIES(Erhan SET, 2024) Kadakal, Mahir; İşcan, İmdatIn this study, we introduce and study the concept of logarithmic semi P functions and their some algebraic properties. Then, we obtain the Hermite-Hadamard integral inequality for the log semi-P-functions. After that, we obtain some new inequalities by using Hölder, Hölder-İşcan and power-mean integral inequalities and show that the result obtained with Hölder-İşcan inequality gives better approach than the Hölder integral inequality. Some applications to special means of real numbers are also given. © 2024, Erhan SET. All rights reserved.Öğe (m1, m2) Geometric Arithmetically Convex Functions and Related Inequalities(2022) Kadakal, MahirIn this manuscript, we introduce and study the concept of $\\left( m_{1},m_{2}\\right) $-geometric arithmetically (GA) convex functions and their some algebric properties. In addition, we obtain Hermite-Hadamard type inequalities for the newly introduced this type of functions whose derivatives in absolute value are the class of $\\left( m_{1},m_{2}\\right) $ -GA-convex functions by using both well-known power mean and Hölder's integral inequalities.Öğe MULTIPLICATIVELY PREINVEX P-FUNCTIONS(Editura Bibliotheca-Bibliotheca Publ House, 2023) Kadakal, Huriye; Kadakal, MahirIn 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.Öğe Semi P-geometric-arithmetically functions and some new related inequalities(Univ Nis, Fac Sci Math, 2023) Kadakal, Mahir; Kadakal, Huriye; Iscan, ImdatIn 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.Öğe Some Hermite-Hadamard type integral inequalities for functions whose first derivatives are trigonometrically ?-convex(SINUS Association, 2024) Kadakal, Huriye; Kadakal, MahirIn this manuscript, we obtain refinements of the Hermite-Hadamard type inequalites for functions whose first derivative in absolute value, raised to a certain power which is greater than one, respectively at least one, is trigonometrically ?-convex. We also show that our results coincide with previous results. © 2024, SINUS Association. All rights reserved.Öğe SOME NEW INEQUALITIES FOR DIFFERENTIABLE ARITHMETIC-HARMONICALLY CONVEX FUNCTIONS(Univ Kragujevac, Fac Science, 2025) Kadakal, Mahir; Agarwal, Praveen; Iscan, ImdatIn this study, by using an integral identity together with both the H & ouml;lder and the power-mean inequalities for integrals we establish several new inequalities for differentiable arithmetic-harmonically-convex function. Also, we give some applications for special means.Öğe Some New Integral Inequalities for Exponential Type P-functions(Univ Craiova, 2024) Kadakal, Mahir; Iscan, Imdat; Kadakal, HuriyeIn this paper, by using an identity we obtain some new Hermite-Hadamard type inequalities for functions whose first derivative in absolute value is exponential type P- function by using Holder and power-mean integral inequalities. Then, the authors compare the results obtained with both Holder, Holder-I-center dot,scan integral inequalities and prove that the Holder-I-center dot,scan integral inequality gives a better approximation than the Holder integral inequality. Also, some applications to special means of real numbers are also given.Öğe STRONGLY HYPERBOLIC TYPE CONVEXITY AND SOME NEW INEQUALITIES(Editura Bibliotheca-Bibliotheca Publ House, 2023) Kadakal, Huriye; Kadakal, MahirIn 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.
