New generalizations of Popoviciu-type inequalities via new Green’s functions and Montgomery identity [PDF]
Journal of Inequalities and Applications, 2017 The inequality of Popoviciu, which was improved by Vasić and Stanković (Math. Balk. 6:281-288, 1976), is generalized by using new identities involving new Green’s functions.
Nasir Mehmood +3 more
doaj +2 more sources
On generalization of refinement of Jensen’s inequality using Fink’s identity and Abel-Gontscharoff Green function [PDF]
Journal of Inequalities and Applications, 2017 In this paper, we formulate new Abel-Gontscharoff type identities involving new Green functions for the ‘two-point right focal’ problem. We use Fink’s identity and a new Abel-Gontscharoff-type Green’s function for a ‘two-point right focal’ to generalize ...
Tasadduq Niaz +2 more
doaj +2 more sources
Trace inequalities of Shisha-Mond type for operators in Hilbert spaces [PDF]
Concrete Operators, 2017 Some trace inequalities of Shisha-Mond type for operators in Hilbert spaces are provided. Applications in connection to Grüss inequality and for convex functions of selfadjoint operators are also given.
Dragomir Sever Silvestru
doaj +3 more sources
Two New Sharp Ostrowski-Grüss Type Inequalities [PDF]
Le Matematiche, 2013 The purpose of this paper is to use a variant of the Grüss inequality to derive two new sharp Ostrowski-Grüss type inequalities related to a perturbed trapezoidal type rule and a perturbed generalized interior point rule, respectively, which provide ...
Zheng Liu
doaj +3 more sources
Generalizations of some q-integral inequalities of Hölder, Ostrowski and Grüss type
AIMS Mathematics, 2023 This paper investigates some well-known inequalities for $ q $-$ h $-integrals. These include Hölder, Ostrowski, Grüss and Opial type inequalities.
Da Shi +5 more
doaj +1 more source
Generalized Čebyšev and Grüss Type Results in Weighted Lebesgue Spaces
Mathematics, 2023 The classical Grüss and related inequalities have spurred a range of improvements, refinements, generalizations, and extensions. In the present article, we provide generalizations of Sokolov’s inequality in weighted Lebesgue LωΩ,A,μ spaces by employing ...
Saad Ihsan Butt +2 more
doaj +1 more source
Generalizations of Hardy-Type Inequalities by Montgomery Identity and New Green Functions
Axioms, 2023 In this paper we extend general Hardy’s inequality by appropriately combining Montgomery’s identity and Green functions. Related Grüss and Ostrowski-type inequalities are also derived.
Kristina Krulić Himmelreich +3 more
doaj +1 more source
Some k-fractional extension of Grüss-type inequalities via generalized Hilfer–Katugampola derivative
Advances in Difference Equations, 2021 In this paper, we prove several inequalities of the Grüss type involving generalized k-fractional Hilfer–Katugampola derivative. In 1935, Grüss demonstrated a fascinating integral inequality, which gives approximation for the product of two functions ...
Samaira Naz +2 more
doaj +1 more source
Some integral inequalities related to Wirtinger's result for p-norms
Cubo, 2021 In this paper we establish several natural consequences of some Wirtinger type integral inequalities for p-norms. Applications related to the trapezoid unweighted inequalities, of Grüss' type inequalities and reverses of Jensen's inequality are also ...
S. S. Dragomir
doaj +1 more source
Extended Jensen’s functional for diamond integral via Green’s function and Hermite polynomial
Journal of Inequalities and Applications, 2022 In this paper, with the help of Green’s function and Hermite interpolating polynomial, an extension of Jensen’s functional for n-convex functions is deduced from Jensen’s inequality involving diamond integrals.
Fazilat Bibi +3 more
doaj +1 more source