We prove an inequality for the number of periods in a word [Formula: see text] terms length and its initial critical exponent. Next, we characterize all length-[Formula: prefix characteristic Sturmian lazy Ostrowski representation text], use this result to show that our is tight infinitely many words text]. propose two related measures periodicity infinite words. Finally, also consider special ...

A main class of inequalities including generalized Ostrowski and Ostrowski-Grüss inequalities is established in ] , [ 1 b a L and ] , [ b a L spaces. As this class can be corresponded to a weighted approximation formula, new inequalities can be obtained by using its upper and lower bounds. Some illustrative examples such as three new generalizations of Ostrowski and Ostrowski-Grüss inequalities...

Some errors in literatures are pointed out and corrected. A generalization of Ostrowski type inequalities for functions whose derivatives in absolute value are s-convex in the second sense is established. Special cases are discussed.