Hüseyin Budak

Düzce University

Regular polygonAlgebraMathematical analysisType (model theory)Convex functionFractional calculusGeneralizationHermite polynomialsPure mathematicsDifferentiable functionHermite–Hadamard inequalityIdentity (mathematics)Bounded variationApplied mathematicsMathematicsMidpointBounded functionInequalityHadamard transformQuantum

159Publications

11H-index

563Citations

Publications 154

Extensions of Hermite–Hadamard inequalities for harmonically convex functions via generalized fractional integrals

#2Muhammad Ali (Nanjing Normal University)H-Index: 15

In the paper, the authors establish some new Hermite–Hadamard type inequalities for harmonically convex functions via generalized fractional integrals. Moreover, the authors prove extensions of the Hermite–Hadamard inequality for harmonically convex functions via generalized fractional integrals without using the harmonic convexity property for the functions. The results offered here are the refinements of the existing results for harmonically convex functions.

Quantum Hermite–Hadamard-type inequalities for functions with convex absolute values of second q b q^{b}-derivatives

#1Muhammad Ali (Nanjing Normal University)H-Index: 15

#2Hüseyin Budak (Düzce University)H-Index: 11

Last. Yu-Ming ChuH-Index: 23

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In this paper, we obtain Hermite–Hadamard-type inequalities of convex functions by applying the notion of q^{b}-integral. We prove some new inequalities related with right-hand sides of q^{b}-Hermite–Hadamard inequalities for differentiable functions with convex absolute values of second derivatives. The results presented in this paper are a unification and generalization of the comparable results in the literature on Hermite–Hadamard inequalities.

On generalized Ostrowski, Simpson and Trapezoidal type inequalities for co-ordinated convex functions via generalized fractional integrals

#1Hüseyin Budak (Düzce University)H-Index: 11

#2Fatih Hezenci (Düzce University)

Last. Hasan Kara (Düzce University)H-Index: 2

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In this study, we prove an identity for twice partially differentiable mappings involving the double generalized fractional integral and some parameters. By using this established identity, we offer some generalized inequalities for differentiable co-ordinated convex functions with a rectangle in the plane null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null nu...

Quantum variant of Montgomery identity and Ostrowski-type inequalities for the mappings of two variables

#1Muhammad Ali (Nanjing Normal University)H-Index: 15

#2Yu-Ming ChuH-Index: 3

Last. Manzoor Ahmed Zahid (CUI: COMSATS Institute of Information Technology)H-Index: 1

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In this investigation, we demonstrate the quantum version of Montgomery identity for the functions of two variables. Then we use the result to derive some new Ostrowski-type inequalities for the functions of two variables via quantum integrals. We also consider the particular cases of the key results and offer some new integral inequalities.

New quantum boundaries for quantum Simpson’s and quantum Newton’s type inequalities for preinvex functions

#1Muhammad Ali (Nanjing Normal University)H-Index: 15

#2Mujahid Abbas (Government College University)H-Index: 36

Last. Yu-Ming ChuH-Index: 23

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In this research, we derive two generalized integral identities involving the q^{\varkappa _{2}}-quantum integrals and quantum numbers, the results are then used to establish some new quantum boundaries for quantum Simpson’s and quantum Newton’s inequalities for q-differentiable preinvex functions. Moreover, we obtain some new and known Simpson’s and Newton’s type inequalities by considering the limit q\rightarrow 1^{-}in the key results of this paper.

A new generalization of some quantum integral inequalities for quantum differentiable convex functions

#1Yi-Xia Li (Xiangnan University)

#2Muhammad Ali (Nanjing Normal University)H-Index: 15

Last. Yu-Ming ChuH-Index: 3

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In this paper, we offer a new quantum integral identity, the result is then used to obtain some new estimates of Hermite–Hadamard inequalities for quantum integrals. The results presented in this paper are generalizations of the comparable results in the literature on Hermite–Hadamard inequalities. Several inequalities, such as the midpoint-like integral inequality, the Simpson-like integral inequality, the averaged midpoint–trapezoid-like integral inequality, and the trapezoid-like integral ine...

Weighted Hermite–Hadamard type inclusions for products of co-ordinated convex interval-valued functions

#1Hasan Kara (Düzce University)H-Index: 2

#2Hüseyin Budak (Düzce University)H-Index: 11

Last. Yu-Ming ChuH-Index: 3

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In this paper, we establish some Hermite–Hadamard–Fejer type inclusions for the product of two co-ordinated convex interval-valued functions. These inclusions are generalizations of some results given in earlier works.

#1Muhammad Ali (Nanjing Normal University)H-Index: 15

#2Hüseyin Budak (Düzce University)H-Index: 11

Last. Yu-Ming ChuH-Index: 23

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In this research, we introduce the notions of (p,q)-derivative and integral for interval-valued functions and discuss their fundamental properties. After that, we prove some new inequalities of Hermite–Hadamard type for interval-valued convex functions employing the newly defined integral and derivative. Moreover, we find the estimates for the newly proved inequalities of Hermite–Hadamard type. It is also shown that the results proved in this study are the generalization of some already prove...

#2Muhammad Ali (Nanjing Normal University)H-Index: 15

Last. Yu-Ming ChuH-Index: 23

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In this paper, first we obtain a new identity for quantum integrals, the result is then used to prove midpoint type inequalities for differentiable coordinated convex mappings. The outcomes provided in this article are an extension of the comparable consequences in the literature on the midpoint inequalities for differentiable coordinated convex mappings.

On Some New Fractional Ostrowski- and Trapezoid-Type Inequalities for Functions of Bounded Variations with Two Variables

#1Thanin SitthiwiratthamH-Index: 11

#2Hüseyin BudakH-Index: 11

Last. Jiraporn ReunsumritH-Index: 3

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In this paper, we first prove three identities for functions of bounded variations. Then, by using these equalities, we obtain several trapezoid- and Ostrowski-type inequalities via generalized fractional integrals for functions of bounded variations with two variables. Moreover, we present some results for Riemann–Liouville fractional integrals by special choice of the main results. Finally, we investigate the connections between our results and those in earlier works. Analytic inequalities of ...

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