Analysis of Hardy-type Inequalities Involving Green Functions and Taylor’s Polynomial Approximation
DOI:
https://doi.org/10.29020/nybg.ejpam.v18i1.5694Keywords:
Green function; Fink’s Identity; Hardy Type Inequalities; Gr¨uss type inequalities; Mean value Theorem, n-Exponential Convexity.Abstract
Herein, we study the Hardy type inequalities using two-point right focal problem’s green functions that are convex for both variables involved along with the n−convex function. Furthermore, we analyze the aforementioned inequality by using Fink’s identity. In the later part, we gave Ostrowski type and Gr¨uss type inequalities by using the Cebyˇsev functional. Finally, we define ˇa functional obtained from our results that is employed to develop the mean value theorem and n-exponential convexity.
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Copyright (c) 2025 Anjum Mustafa Khan Abbasi, Matloob Anwar
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