Özcan, Serap; Kadakal, Mahir; Iscan, Imdat; Kadakal, Huriye

As 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.

İncele

Kadakal, Huriye; Kadakal, Mahir

In 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 Hölder-İşcan and improved power-mean integral inequalities give a better approach than Hölder and power-mean inequalities.

İncele

Kadakal, Mahir; Agarwal, Praveen; İŞcan, İMdat

In this study, by using an integral identity together with both the Hölder 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.

AtıfOpenAlex1

İncele

Kadakal, Mahir; Iscan, İMDAT; Kadakal, Huriye

The 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 Hölder and Hölder–˙ I¸scan inequalities and show that the result obtained with Hölder–˙ I¸scan inequalities give better approach than the others. Some applications to special means of real numbers are also given.

İncele

Gülsu, Nagihan kurt; Iscan, Imdat; Kadakal, Mahir; Bekar, Kerim

In 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.

İncele

Ozcan, Serap; Kadakal, Mahir; Iscan, Imdat; Kadakal, Huriye

In 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.

AtıfWoS1·OpenAlex1

İncele

Kadakal, Huriye; Kadakal, Mahir

In 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 ρ-convex. We also show that our results coincide with previous results.

AtıfScopus3·OpenAlex1

İncele

Kadakal, Mahir; İşcan, İmdat

In 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.

AtıfScopus1

İncele

Kadakal, Mahir; İmdat, Işcan; Kadakal, Huriye

In 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 Hölder and power-mean integral inequalities. Then, the authors compare the results obtained with both Hölder, Hölder-İşcan integral inequalities and prove that the Hölder-İşcan integral inequality gives a better approximation than the Hölder integral inequality. Also, some applications to special means of real numbers are also given.

AtıfScopus1·WoS2

İncele

Kadakal, Mahir

In 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.

AtıfScopus1·WoS2

İncele

Kadakal, Mahir; Işcan, 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 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.

AtıfWoS1·OpenAlex3

İncele

Özcan, Serap; Kadakal, Mahir; İşcan, İmdat; 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 Hölder–İşcan 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.

AtıfScopus5·WoS5·OpenAlex6

İncele

Ayazoglu, Rabil; Kadakal, Mahir; Akkoyunlu, Ebubekir

We consider the parabolic-elliptic chemotaxis system with the exponents depending on the spatial variables logistic source and nonlinear signal production: ut = ∆u−χ∇·(u∇υ)+f(x, u), (x, t) ∈ Ω×(0, T), 0 = ∆υ−υ+uγ in a bounded domain Ω ⊂ RN (N ≥ 1) with smooth boundary, subject to nonnegative initial data and homogeneous Neumann boundary conditions, where χ > 0, γ ≥ 1 and ∂ν∂ denotes the outward normal derivative on ∂Ω. The logistic function f fulfilling f(x, s) ≤ ηs− µsα(x)+1, η ≥ 0, µ > 0 for all s > 0 with f(x, 0) ≥ 0 ∀x ∈ Ω, where α : Ω → [1, ∞) is a measurable function. It is proved that if 1 ≤ α(x) < ∞ for all x ∈ Ω such that essinfx∈Ω α(x) > γ or essinfx∈Ω α(x) = γ with µ > χ, then there exists a nonnegative classical solution (u, υ) that is global-in-time and bounded. In addition, under the particular conditions γ = 1 and f(x, s) = µ(s − sα(x)+1), if µ is sufficiently large, the global bounded solution (u, υ) satisfies ∥u(·, t) − 1∥L∞(Ω) + ∥υ (·, t) − 1∥L∞(Ω) ≤ Ce− Nk+2 t for all t > 0 with k = min n χ42 12o , 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.

AtıfScopus11·WoS9·OpenAlex11

İncele

Kadakal, Mahir; İşcan, İmdat; Kadakal, Huriye

In 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" pre-viously 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 Hölder, Hölder-İşcan and power-mean, improved-power-mean integral inequalities show that the results give a better approach than the others. Finally, we conclude our paper with applications containing some means.

AtıfScopus7·WoS7·OpenAlex7·TR Dizin1

İncele

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.

AtıfWoS2·OpenAlex2

İncele

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.

AtıfWoS19

İncele

Kadakal, Mahir; İşcan, İmdat; Kadakal, Huriye

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 Hölder and Hölder-İşcan integral inequalities with the help of an identity. Then, the aouthors compare the results obtained with both Hölder, Hölder-İşcan integral inequalities and prove that the Hölder-İşcan integral inequality gives a better approximation than the Hölder integral inequality. Also, some applications to special means of real numbers are also given.

AtıfScopus5·WoS4·OpenAlex3

İncele

Ataman, Canan; Kadakal, Mahir; İşcan, İmdat

In this paper, we introduce and study the concept of strongly n-polynomial convexity functions and their some algebraic properties. We prove two Hermite-Hadamard type inequalities for the newly introduced class of functions. In addition, we 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 strongly n-polynomial convexity. Also, we compare the obtained results with both Hölder, Hölder-İşcan inequalities and power-mean, improved-power-mean integral inequalities and show that the result obtained with Hölder-İşcan and improved power-mean inequalities give better approach than the others.

AtıfScopus4·OpenAlex4

İncele

Kadakal, Mahir

In this manuscript, we introduce and study the concept of (m1, m2)-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 (m1, m2)-GA-convex functions by using both well-known power mean and Hölder’s integral inequalities.

AtıfScopus2

İncele

Kadakal, Mahir

In this study, we introduced the concept of (α, m1, m2)-GG convex functions; then we obtained Hermite-Hadamard type inequalities for these type of function classes via gamma and incomplete gamma functions together with Hölder, power-mean, Hölder-İşcan and improved power-mean integral inequalities.

İncele