فهرست مطالب artion kashuri
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In this study, we established the Hermite-Hadamard type, Simpson type, Ostrowski type and midpoint type integral inequalities for the s-convex functions in the second sense via Katugampola fractional integrals. By using Katugampola fractional integral operators, we obtained several new identities and presented new results for the s-convex function in the second sense. We made connections of our results with various results recognized in the literature. Finally, applications to special means are examined to verify the efficiency of the established results.Keywords: Hermite-Hadamard Type Inequalities, Simpson Type Inequalities, Ostrowski Type Inequalities, Holder's Inequality, Young's Inequality, S-Convex Function, Katugampola Fractional Integral Operators, Special Means}
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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} -
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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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 945 -962
In this article, we first presented a new integral identity concerning differentiable mappings defined on m-invex set. By using the notion of generalized relative semi-$(r; m, p, q, h_1, h_2)$-preinvexity and the obtained identity as an auxiliary result, some new estimates with respect to Ostrowski type conformable fractional integral inequalities are established. It is pointed out that some new special cases can be deduced from main results of the article.
Keywords: Ostrowski type inequality, H¨older’s inequality, Minkowski’s inequality, power meaninequality, m–invex} -
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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International Journal Of Nonlinear Analysis And Applications, Volume:8 Issue: 2, Winter - Spring 2017, PP 109 -124In the present paper, the notion of generalized (r;g,s,m,φ)-preinvex function is applied to establish some new generalizations of Ostrowski type integral inequalities via Caputo k-fractional derivatives. At the end, some applications to special means are given.Keywords: Ostrowski type inequality, H{o}lder's inequality, Minkowski's inequality, s-convex function in the second sense, m-invex}
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