Aslan, Sinan; Demir, Ümit; Karaduman, Ebru; Akdemir, Ahmet Ocak

In this paper, a special identity for twice differentiable functions, which is available in the literature, is utilized. By combining this identity with Riemann-Liouville fractional integrals, various fractional Milne-type inequalities are obtained for functions whose second derivatives in absolute value are s−convex in the second sense. Moreover, Hölder and Young inequalities are used to prove the different and original results. These approaches contribute to the analysis of s−convex functions and offer new perspectives in the field of fractional analysis.

AtıfScopus1·WoS1·OpenAlex1

İncele

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.

AtıfScopus10·WoS12·OpenAlex11

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

Ayazoglu, Rabil; Ekincioglu, Ismail; Şener, S. Şule

We investigate the problem of approximating function f in the power-type weighted variable exponent Sobolev space (Formula presented), by the Hardy averaging operator (Formula presented). If α(.) x 0 the function f lies in the power-type weighted variable exponent Sobolev space (Formula presented) (0, 1), it is shown that (Formula presented), where C is a positive constant. Moreover, we consider the problem of boundedness of Hardy averaging operator A in power-type weighted variable exponent grand Lebesgue spaces (Formula presented) (0, 1). The sufficient α(.) criterion established on the power-type weight function α(.) and exponent p(.) for the Hardy averaging operator to be bounded in these spaces.

AtıfScopus3·WoS4·OpenAlex3

İncele

Ayazoglu, Rabil; Akbulut, Sezgin; Akkoyunlu, Ebubekir

In this paper, the Kantorovich operators Kn, n ϵ N are shown to be uniformly bounded in variable exponent Lebesgue spaces on the closed interval [0, 1]. Also an upper estimate is obtained for the difference Kn (f) − f for functions f of regularity of order 1 and 2 measured in variable exponent Lebesgue spaces, which is of interest on its own and can be applied to other problems related to the Kantorovich operators.

AtıfScopus3·WoS3·OpenAlex3

İncele