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, M.; İşcan, İ.; Kadakal, H.

In this paper, we establish some new Simpson type inequalities for functions, whose first deriva-tive in absolute value is (s, P)-function by using Hölder, power-mean and Hölder-İşcan inequalities. After that, we 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 inequality. Also, some applications to special means of real numbers are also given.

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