فهرست مطالب huseyin budak
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International Journal Of Nonlinear Analysis And Applications, Volume:15 Issue: 3, Mar 2024, PP 1 -10This paper proves an equality for the case of twice-differentiable convex functions involving conformable fractional integrals. Using the established equality, we give new Simpson-type inequalities for the case of twice-differentiable convex functions via conformable fractional integrals. We also consider some special cases which can be deduced from the main results.Keywords: Simpson type inequality, fractional conformable integrals, Fractional calculus, convex function}
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In this paper, we prove an equality for the case of twice-differentiable convex functions with respect to the conformable fractional integrals. With the help of this equality, we establish several Simpson-type inequalities for twice-differentiable convex functions by using conformable fractional integrals. Sundry significant inequalities are obtained by taking advantage of the convexity, the H\"{o}lder inequality, and the power mean inequality. By using the specific selection of our results, we give several new and well-known results in the literature.
Keywords: Simpson-type inequality, fractional conformable integrals, fractional conformable derivatives, fractional calculus, convex function} -
International Journal Of Nonlinear Analysis And Applications, Volume:14 Issue: 1, Jan 2023, PP 375 -391In this article, we first establish weighted identities based on twice partially differentiable mappings. Moreover, utilizing this equality, we derive the weighted Hermite-Hadamard type inequalities via co-ordinated convex mappings in a rectangle from the plane $\mathbb{R}^{2}$. More specifically, we establish new inequalities using the Holder and power-mean inequalities. In addition, we obtain new results with special choices.Keywords: Fejer inequality, co-ordinated convex functions, Integral inequalities, Trapezoid Inequality}
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In the literature, several papers are devoted to inequalities of Simpson-type in the case of differentiable convex functions and fractional versions. Moreover, some papers are focused on inequalities of Simpson-type for twice differentiable convex functions. In this research article, we obtain an identity for twice differentiable convex functions. Then, we prove several fractional inequalities of Simpson-type for convex functions.Keywords: Simpson type inequalities, Twice differentiable convex functions, Riemann-Liouville fractional integrals, Fractional calculus}
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We first construct new Hermite-Hadamard type inequalities which include generalized fractional integrals for convex functions by using an operator which generates some significant fractional integrals such as Riemann-Liouville fractional and the Hadamard fractional integrals. Afterwards, Trapezoid and Midpoint type results involving generalized fractional integrals for functions whose the derivatives in modulus and their certain powers are convex are established. We also recapture the previous results in the particular situations of the inequalities which are given in the earlier works.Keywords: Hermite-Hadamard inequalities, Generalized fractional integrals, Convex functions}
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International Journal Of Nonlinear Analysis And Applications, Volume:13 Issue: 2, Summer-Autumn 2022, PP 1165 -1182
n this paper, we firstly obtain some identities via generalized fractional integrals which generalize some important fractional integrals such as the Riemann-Liouville fractional integrals, the Hadamard fractional integrals, etc. Then by utilizing these equalities we establish some Ostrowski and Trapezoid type inequalities for functions of bounded variation with two variables. Moreover, we give some inequalities involving Hadamard fractional integrals as special cases of our main results.
Keywords: Function of bounded variation, Ostrowski inequalities, generalized fractional integral} -
On Some New Extensions of Inequalities of Hermite-Hadamard Type for Generalized Fractional IntegralsIn this paper, we establish some inequalities for generalized fractional integrals by utilizing the assumption that the second derivative of $phi (x)=varpi left( frac{kappa _{1}kappa _{2}}{mathcal{varkappa }}right) $ is bounded. We also prove again a Hermite-Hadamard type inequality obtained in [34] under the condition $phi ^{prime }left( kappa_{1}+kappa _{2}-mathcal{varkappa }right) geq phi ^{prime }(mathcal{varkappa })$ instead of harmonically convexity of $varpi $. Moreover, some new inequalities for $k$-fractional integrals are given as special cases of main results.Keywords: Hermite-Hadamard inequality, convex function, Bounded function}
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In this paper, we first establish two new identities for differentiable function involving generalized fractional integrals. Then, by utilizing these equalities, we obtain some midpoint type inequalities involving generalized fractional integrals for mappings whose derivatives in absolute values are convex. We also give several results as special cases of our main results.Keywords: Hermite-Hadamard inequality, generalized fractional integral, Convex function}
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In this paper, we first obtain two weighted identities for twice partially differentiablemappings. Moreover, utilizing these equalities, we establish the weighted Herrmite-Hadamard typeinequalities and weighted Simpson type inequalities for co-ordinated convex functions in a rectanglefrom the plane R2, respectivelly. The results given in this paper provide generalizations of someresult established in earlier works.
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The purpose of this paper is to establish some Hermite-Hadamard type inequalities for h-convex functions utilizing generalized fractional integrals. We also obtain some generalized trapezoidand midpoint type inequalities for the mapping whose first derivatives absolutely value are h-convex.The results proved in this paper generalize the several inequalities obtained earlier works.
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In this paper, we establish some Trapezoid and Midpoint type inequalities for generalized fractional integrals by utilizing the functions whose second derivatives are bounded . We also give some new inequalities for $k$-Riemann-Liouville fractional integrals as special cases of our main results. We also obtain some Hermite-Hadamard type inequalities by using the condition $f^{prime }(a+b-x)geq f^{prime }(x)$ for all $xin left[ a,frac{a+b}{2}right] $ instead of convexity.Keywords: Hermite-Hadamard inequality, convex function, Bounded function}
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International Journal of Mathematical Modelling & Computations, Volume:10 Issue: 3, Summer 2020, PP 203 -225In this study, we first introduce the co-ordinated hyperbolic ρ-convex functions. Then we establish some Hermite-Hadamard type inequalities for co-ordinated hyperbolic ρ-convex functions. The inequalities obtained in this study provide generalizations of some results given in earlier works.Keywords: Convex function, hyperbolic ρ-convex functions, Hermite-Hadamard inequality, integral inequality}
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International Journal Of Nonlinear Analysis And Applications, Volume:12 Issue: 1, Winter-Spring 2021, PP 979 -996
In this paper, authors discover two interesting identities regarding Gauss--Jacobi and trapezium type integral inequalities. By using the first lemma as an auxiliary result, some new bounds with respect to Gauss--Jacobi type integral inequalities for a new class of functions called strongly $(h_{1},h_{2})$--preinvex of order $sigma>0$ with modulus $mu>0$ via general fractional integrals are established. Also, using the second lemma, some new estimates with respect to trapezium type integral inequalities for strongly $(h_{1},h_{2})$--preinvex functions of order $sigma>0$ with modulus $mu>0$ via general fractional integrals are obtained. It is pointed out that some new special cases can be deduced from main results. Some applications to special means for different real numbers and new approximation error estimates for the trapezoidal are provided as well. These results give us the generalizations of some previous known results. The ideas and techniques of this paper may stimulate further research in the fascinating field of inequalities.
Keywords: Hermite–Hadamard inequality, Gauss–Jacobi type quadrature formula, H¨olderinequality, power mean inequality, general fractional integrals} -
International Journal Of Nonlinear Analysis And Applications, Volume:12 Issue: 1, Winter-Spring 2021, PP 782 -789
In this study, we present the new Hermite-Hadamard type inequality for functions which are $h$-convex on fractal set $mathbb{R}^{alpha }$ $(0<alpha leq 1)$ of real line numbers. Then we provide the special cases of the result using different type of convex mappings.
Keywords: Hermite-Hadamard inequality, fractal set, h- convex function} -
International Journal Of Nonlinear Analysis And Applications, Volume:10 Issue: 2, Summer-Autumn 2019, PP 275 -299In the present work, we prove a parametrized identity for a differentiable function via generalized integral operators. By applying the established identity and the new so-called generalized m-convex function, some generalized trapezium, Ostrowski and Simpson type integral inequalities have been discovered. Various special cases have been studied as well. Some applications of the present results to special means and new error estimates for the trapezium and midpoint quadrature formula have been investigated. It is hoped that the methods and techniques of this paper could further stimulate the research conducted in the field of integral inequalities.Keywords: Trapezium inequality, Ostrowski inequality, Simpson inequality, convexity, general fractional integrals}
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Some new generalized Hermite-Hadamard inequalities for generalized convex functions and applications
In this paper, some new inequality for generalized convex functions are obtained. Some applications for some generalized special means are also given.
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Yang-Laplace transform method Volterra and Abel's integro-differential equations of fractional orderInternational Journal Of Nonlinear Analysis And Applications, Volume:9 Issue: 2, Summer-Autumn 2018, PP 203 -214This study outlines the local fractional integro-differential equations carried out by the local fractional calculus. The analytical solutions within local fractional Volterra and Abel’s integral equations via the Yang-Laplace transform are discussed. Some illustrative examples will be discussed. The obtained results show the simplicity and efficiency of the present technique with application to the problems for the local fractional integral equations.Keywords: Local fractional calculus, Volterra, Abel’s integral equations, Yang-Laplace transform}
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International Journal Of Nonlinear Analysis And Applications, Volume:8 Issue: 2, Winter - Spring 2017, PP 209 -222In this paper, a new inequality for generalized convex functions which is related to the left side of generalized Hermite-Hadamard type inequality is obtained. Some applications for some generalized special means are also given.Keywords: Generalized Hermite-Hadamard inequality, Generalized H{o}lder inequality, Generalized convex functions}
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In this paper, a generalization of trapezoid inequality for functions of two independent variables with bounded variation and some applications are given.Keywords: Bounded Variation, Ostrowski type inequalities, Riemann, Stieltjes, Trapezoid Inequality}
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