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
Summary
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 < ∞.
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