Abstract
We construct a subclass of Copson’s integral inequality in this article. In order to achieve this goal, we attempt to use the Steklov operator for generalizing different inequalities of the Copson type relevant to the situations ρ>1 as well as ρ<1. We demonstrate the inequalities with the guidance of basic comparison, Holder’s inequality, and the integration by parts approach. Moreover, some new variations of Hardy’s integral inequality are also presented with the utilization of Steklov operator. We also formulate many remarks and two examples to show the novelty and authenticity of our results.
Highlights
IntroductionNumerical inequalities became a significant part of current science in the 20th century through the spearheading work entitled Inequalities by Hardy, Littlewood, and P‘olya, which is the first composition to be released in 1934 [1]
This section is related to the generalizations of Hardy style integral inequalities with the application of the Steklov operator
Inequalities are considered in rather general forms and contain various special integral and discrete inequalities
Summary
Numerical inequalities became a significant part of current science in the 20th century through the spearheading work entitled Inequalities by Hardy, Littlewood, and P‘olya, which is the first composition to be released in 1934 [1] This distinctive publication symbolizes a framework of precise logic filled with inequalities for the betterment pf relevant technologies in mathematics. The classical Hardy inequality declares that if ψ1 > 1 and g is a non-negative measurable function on ( a, b), (2) is valid except g ≡ 0, i.e., in ( a, b), where constant here is the best possible contant This inequality stays relevant providing that 0 < a < b < 1.
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