Ostrowski and Čebyšev type inequalities for interval-valued functions and applications

Area of Science:

• Mathematical Analysis
• Set-Valued Analysis

Background:

• Ostrowski and Čebyšev inequalities are fundamental in classical analysis.
• Non-additive integral inequalities, including Sugeno and Choquet integrals, are widely applicable.
• Set-valued analysis generalizes classical analysis with applications in economics and control theory.

Purpose of the Study:

• To establish specific Ostrowski and Čebyšev type inequalities for interval-valued functions.
• To extend the theory of inequalities to the domain of interval analysis.
• To demonstrate the utility of these inequalities through applications.

Main Methods:

• Development of novel interval-valued inequalities based on existing classical forms.
• Application of set-valued analysis techniques.
• Error estimation for quadrature rules using the derived inequalities.

Main Results:

• Novel Ostrowski and Čebyšev type inequalities for interval-valued functions were successfully established.
• The derived inequalities provide a framework for analyzing interval-valued functions.
• Error bounds for quadrature rules were effectively estimated.

Conclusions:

• The paper successfully extends Ostrowski and Čebyšev inequalities to interval-valued functions.
• The results have practical implications for numerical integration and error analysis.
• The presented mathematical methods are applicable and demonstrated through examples.