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The classical Grüss and related inequalities have spurred a range of improvements, refinements, generalizations, and extensions. In the present article, we provide generalizations of Sokolov's inequality in weighted Lebesgue L ω Ω , A , μ spaces by employing the weighted Sonin's identity and Čebyšev functional. As a result, we provide a generalized Grüss inequality in which the bounding constants are improved with bounding functions in L ω p Ω , A , μ spaces. As an application, we provide several new bounds for Jensen–Grüss type differences. [ABSTRACT FROM AUTHOR]

Our aim is to improve and further generalize the result of integral Ostrowski-Grüss type inequalities involving differentiable functions and then apply these obtained inequalities to probability theory, special means and numerical integration.

Ostrowski inequality is one of the celebrated inequalities in Mathematics. The main purpose of our study is to generalize the result of Ostrowski-Gruss type inequality for first differentiable mappings and apply it to probability density functions, composite quadrature rules and special means. [ABSTRACT FROM AUTHOR]

We obtain new generalizations of Ostrowski inequality by using generalized Riemann-Liouville fractional integrals. Some special cases are also discussed. [ABSTRACT FROM AUTHOR]

Our aim is to improve and further generalize the result of integral Ostrowski-Grüss type inequalities involving differentiable functions and then apply these obtained inequalities to probability theory, special means and numerical integration. [ABSTRACT FROM AUTHOR]