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On Some Inequalities Arising from Montgomery's Identity (Montgomery's Identity)
Journal of Computational Analysis and Applications, 2003A Montgomery identity is an identity of type \[ f(x)= M(f)+ M(P(x,.)f'), \] where \(M(f)\) is the integral mean of \(f\) on \([a,b]\), and \(P(x, t)= t-a\) on \([a,x]\) and \(=t-b\) on \([x,b]\). The authors combine such identity with applications of Grüss and Chebyshev integral inequalities in order to deduce results on generalized functionals ...
S S Dragomir
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MULTIVARIATE MONTGOMERY IDENTITIES AND OSTROWSKI INEQUALITIES
Numerical Functional Analysis and Optimization, 2002ABSTRACT Multivariate Montgomery type identities are developed involving, among others, integrals of mixed partial derivatives. These lead to new multivariate Ostrowski type inequalities. These inequalities in their right-hand sides involve Lp -norms of the engaged mixed partials. An application is given at the end to Probability.
George Anastassiou
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Georgian Mathematical Journal, 2014
Abstract. We present a weighted Montgomery identity for the fractional integral of a function f with respect to another function g and use it to obtain weighted Ostrowski type inequalities for fractional integrals involving functions whose first derivatives belong to Lp spaces. These inequalities are generally sharp in
Josip Pečarić +2 more
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Abstract. We present a weighted Montgomery identity for the fractional integral of a function f with respect to another function g and use it to obtain weighted Ostrowski type inequalities for fractional integrals involving functions whose first derivatives belong to Lp spaces. These inequalities are generally sharp in
Josip Pečarić +2 more
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Complex Multivariate Montgomery Identity and Ostrowski and Grüss Inequalities
Studies in Computational Intelligence, 2020We give a general complex multivariate Montgomery type identity which is a representation formula for a complex multivariate function. Using it we produce general tight complex multivariate high order Ostrowski and Gruss type inequalities. The estimates involve \(L_{p}\) norms, any \(1\le p\le \infty \). We include also applications. See also [1].
George Anastassiou
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Generalizations of the Weighted Hermite-Hadamard and Fejér Inequalities via the Montgomery Identity [PDF]
Results in MathematicszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Josip Pečarić, M Ribičič Penava
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On Fractional Inequalities via Montgomery Identities
International Journal of Open Problems in Complex Analysis, 2014In the present work we give several new integral inequalities via Riemann-Liouville fractional integral and Montgomery ...
Mehmet Zeki Sarikaya +2 more
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Generalizations of Sherman’s inequality by Montgomery identity and Green function
Electronic Journal of Mathematical Analysis and Applications, 2017In this paper, we give generalization of Sherman inequality by using Green function and Montgomery identity. We present Gr¨uss and Ostrowskitype inequalities related to generalized Sherman inequality. We give mean value theorems and n-exponential convexity for the functional associated to generalized inequality. We also give a family of functions which
Khan, M. A., Khan, J., Pečarić, Josip
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SCREENING L.M. MONTGOMERY: HERITAGE, NOSTALGIA AND NATIONAL IDENTITY
British Journal of Canadian Studies, 2004I don't know why I keep on going to see my favourite books screened. The result is always a disappointment. (Montgomery, Selected Journals, vol. 111: 26)
Philippa Gates, Stacy Gillis
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Asian-European Journal of Mathematics, 2018
We consider discrete and continuous cyclic refinements of Jensen’s inequality and generalize them from convex function to higher order convex function by means of Lagrange Green’s function and Montgomery identity. We give application of our results by formulating the monotonicity of the linear functionals obtained from generalized identities utilizing ...
Mehmood, Nasir +2 more
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We consider discrete and continuous cyclic refinements of Jensen’s inequality and generalize them from convex function to higher order convex function by means of Lagrange Green’s function and Montgomery identity. We give application of our results by formulating the monotonicity of the linear functionals obtained from generalized identities utilizing ...
Mehmood, Nasir +2 more
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