Synchronization Analysis of Multiple Integral Inequalities Driven by Steklov Operator

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.

Time‐Scale Integral Inequalities of Copson with Steklov Operator in High Dimension

“…In 2021, Albalawi and Khan generalized the main integral of Hardy and Copson inequalities, using the Steklov operator. e operator is defined in the following formulas with considering conditions in two cases (for more details, see [15]). e aim of this paper is extending the study in [16] that was used for some new Hardy-type inequalities to obtain new special Copson inequalities with the Steklov operator (see [15]) in (TS) versions with high dimension.…”

“…e operator is defined in the following formulas with considering conditions in two cases (for more details, see [15]). e aim of this paper is extending the study in [16] that was used for some new Hardy-type inequalities to obtain new special Copson inequalities with the Steklov operator (see [15]) in (TS) versions with high dimension. e results below are proved in two cases m > μ + 1 and m < μ + 1 by considering some general conditions that can be applied for any variable in the integral.…”

“…s)ds.Remark 11. Assume μ � 0 and θ > λ in Corollary 10; we have Corollary 5 in[15].Theorem 12.a v l s l 􏼁Δs l , with V l (∞) � ∞, and w l (a) � 0, andF t 1 , . .…”