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
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New time scale generalizations of the Ostrowski-Grüss type inequality for k points [PDF]
Journal of Inequalities and Applications, 2017 Two Ostrowski-Grüss type inequalities for k points with a parameter λ ∈ [ 0 , 1 ] $\lambda\in[0, 1]$ are hereby presented. The first generalizes a recent result due to Nwaeze and Tameru, and the second extends the result of Liu et al. to k points.
Eze R Nwaeze +2 more
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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
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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
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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
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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
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Extended Jensen’s Functional for Diamond Integral via Hermite Polynomial
Journal of Function Spaces, 2021 In this paper, with the help of Hermite interpolating polynomial, extension of Jensen’s functional for n-convex function is deduced from Jensen’s inequality involving diamond integrals.
Rabia Bibi +3 more
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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
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Construction of New Ostrowski’s Type Inequalities By Using Multistep Linear Kernel
Cumhuriyet Science Journal, 2023 In this paper, we construct a generalisation of Ostrowski’s type inequalities with the help of new identity. By using this identity, we construct further results for ģ^'∈L^1 [c ̇,d ̆ ],ģ^'∈L^2 [c ̇,d ̆ ],ģ^''∈L^2 [c ̇,d ̆ ].
Yasır Qayyum +3 more
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General Opial Type Inequality and New Green Functions
Axioms, 2022 In this paper we provide many new results involving Opial type inequalities. We consider two functions—one is convex and the other is concave—and prove a new general inequality on a measure space (Ω,Σ,μ).
Ana Gudelj +2 more
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