Abstract

The aim of paper is to develop the inequalities for L∞, Lp and L1 norms. Applications for some special weight functions and Perturbed expressions are also determined via Chebychev functional. We recaptured the previous results for different weights.

Highlights

  • In 1938, Ostrowski established the interesting integral inequality for differentiable mappings with bounded derivative [10]

  • Let f : J, k → R be continuous on J, kand differentiable mapping on J, k, the following weighted peano kernel, define G (., .) : J, k → R as:

  • Let f : J, k → R be continuous on J, kand differentiable mapping on J, k, whose first derivative f : J, k → R is bounded on J, k, following weighted integral inequalities

Read more

Summary

Introduction

In 1938, Ostrowski established the interesting integral inequality for differentiable mappings with bounded derivative [10]. Let the functional S f ; ; J, kbe defined as: S f ; ; J, k = f (z) − Mf ; ; J, k , (1.1) Where f (z) : J, k → R be a continuous mapping, Mf ; ; J, kis weighted integral mean and is defined as: The functional S f ; Mf ; We assume non-negative weight function : (J, k) → [0, ∞) is integrable k (r)dr < ∞.

Results
Conclusion
Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call