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On weighted generalization of opial type inequalities in two variables
Huseyin Budak,Mehmet Zeki Sarikaya,Artion Kashuri 강원경기수학회 2020 한국수학논문집 Vol.28 No.4
In this paper, we establish some weighted generalization of Opial type inequalities in two independent variables for two functions. We also obtain weighted Opial type inequalities by using $p$-norms. Special cases of our results reduce to the inequalities in earlier study.
FRACTIONAL TRAPEZOID AND NEWTON TYPE INEQUALITIES FOR DIFFERENTIABLE S-CONVEX FUNCTIONS
Fatih Hezenci,Huseyin Budak,Muhammad Aamir Ali 호남수학회 2023 호남수학학술지 Vol.45 No.1
In the present paper, we prove that our main inequality reduces to some trapezoid and Newton type inequalities for differentiable s-convex functions. These inequalities are established by using the wellknown Riemann-Liouville fractional integrals. With the help of special cases of our main results, we also present some new and previously obtained trapezoid and Newton type inequalities.
Fatih Hezenci,Huseyin Budak 강원경기수학회 2023 한국수학논문집 Vol.31 No.2
In this paper, an equality is established by twice-differentiable convex functions with respect to the conformable fractional integrals. Moreover, several Simpson-type inequalities are presented for the case of twice-differentiable convex functions via conformable fractional integrals by using the established equality. Furthermore, our results are provided by using special cases of obtained theorems.
More on reverse of Holder's integral inequality
Bouharket Benaissa,Huseyin Budak 강원경기수학회 2020 한국수학논문집 Vol.28 No.1
In 2012, Sulaiman [7] proved integral inequalities concerning reverse of Holder's. In this paper two results are given. First one is further improvement of the reverse H\"{o}lder inequality. We note that many existing inequalities related to the H\"{o}lder inequality can be proved via obtained this inequality in here. The second is further generalization of Sulaiman's integral inequalities concerning reverses of Holder's [7].
Note on Newton-type inequalities involving tempered fractional integrals
Fatih Hezenci,Huseyin Budak 강원경기수학회 2024 한국수학논문집 Vol.32 No.2
We propose a new method of investigation of an integral equality associated with tempered fractional integrals. In addition to this, several Newton-type inequalities are considered for differentiable convex functions by taking the modulus of the newly established identity. Moreover, we establish some Newton-type inequalities with the help of H\"{o}lder and power-mean inequality. Furthermore, several new results are presented by using special choices of obtained inequalities.
Muhammad Aamir Ali,Huseyin Budak,Sadia Sakhi 강원경기수학회 2020 한국수학논문집 Vol.28 No.4
In this study, some new inequalities of Hermite-Hadamard type for convex and co-ordinated convex functions via Riemann-Liouville fractional integrals are derived. It is also shown that the results obtained in this paper are the extension of some earlier ones.
ON NEW INEQUALITIES OF SIMPSON'S TYPE FOR GENERALIZED CONVEX FUNCTIONS
Sarikaya, Mehmet Zeki,Budak, Huseyin,Erden, Samet The Kangwon-Kyungki Mathematical Society 2019 한국수학논문집 Vol.27 No.2
In this paper, using local fractional integrals on fractal sets $R^{\alpha}(0<{\alpha}{\leq}1)$ of real line numbers, we establish new some inequalities of Simpson's type based on generalized convexity.
New quantum variants of Simpson-Newton type inequalities via $(\alpha,m)$-convexity
Saad Ihsan Butt,Qurat Ul Ain,Huseyin Budak 강원경기수학회 2023 한국수학논문집 Vol.31 No.2
In this article, we will utilize $(\alpha, m)$-convexity to create a new form of Simpson-Newton inequalities in quantum calculus by using $q_{\varrho_{1}}$-integral and $q_{\varrho_{1}}$-derivative. Newly discovered inequalities can be transformed into quantum Newton and quantum Simpson for generalized convexity. Additionally, this article demonstrates how some recently created inequalities are simply the extensions of some previously existing inequalities. The main findings are generalizations of numerous results that already exist in the literature, and some fundamental inequalities, such as H\"{o}lder's and Power mean, have been used to acquire new bounds.