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- MakaleAçık Erişim2025Scopus SJRQ2Some novel fractional Milne-type inequalities for twice differentiable s−convex functions in the second sense
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.
AtıfScopus1WoS1OpenAlex1
İncele - MakaleAçık Erişim2023Scopus SJRQ3Harmonic trigonometrically convexity
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.
AtıfScopus10WoS12OpenAlex11İncele - MakaleAçık Erişim2023Scopus SJRQ3Semi P-geometric-arithmetically functions and some new related inequalities
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.
AtıfScopus5WoS4OpenAlex3İncele - MakaleAçık Erişim2022Scopus SJRQ3Approximating Functions in the Power-Type Weighted Variable Exponent Sobolev Space by the Hardy Averaging Operator
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.
AtıfScopus3WoS4OpenAlex3İncele - MakaleAçık Erişim2019Scopus SJRQ2Uniform boundedness of kantorovich operators in variable exponent Lebesgue spaces
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.
AtıfScopus3WoS3OpenAlex3İncele - DergiFilomat