Intelligent Comparisons: Analytic Inequalities

This monograph presents recent and original work of the author on inequalities in real, functional and fractional analysis. The chapters are self-contained and can be read independently, they include an extensive list of references per chapter.

The book's results are expected to find applications in many areas of applied and pure mathematics, especially in ordinary and partial differential equations and fractional differential equations. As such this monograph is suitable for researchers, graduate students, and seminars of the above subjects, as well as Science and Engineering University libraries.

Contenu

Fractional Polya Integral Inequality.- Univariate Fractional Polya Integral Inequalities.- About Multivariate General Fractional Polya Integral Inequalities.- Balanced Canavati Fractional Opial Inequalities.- Fractional Representation Formulae and Fractional Ostrowski Inequalities.- Basic Fractional Integral Inequalities.- Harmonic Multivariate Ostrowski and Grüss Inequalities.- Fractional Ostrowski and Grüss Inequalities Using Several Functions.- Further Interpretation of Some Fractional Ostrowski and Grüss Type Inequalities.- Multivariate Fractional Representation Formula and Ostrowski Inequality.- Fractional Representation Formulae and Ostrowski Inequalities.- About Multivariate Lyapunov Inequalities.- Ostrowski Type Inequalities for Semigroups.- About Ostrowski Inequalities for Cosine and Sine Operator Functions.- About Hilbert-Pachpatte Inequalities.- About Ostrowski and Landau Type Inequalities.- Multidimensional Ostrowski Type Inequalities.- About Fractional Representation Formulae and Right Fractional Inequalities.- About Canavati fractional Ostrowski inequalities.- The Most General Fractional Representation Formula.- Rational Inequalities for Integral Operators Using Convexity.- Fractional Integral Inequalities with Convexity.- Vectorial Inequalities for Integral Operators.- Vectorial Splitting Rational Lp Inequalities for Integral Operators.- Separating Rational Lp Inequalities for Integral Operators.- About Vectorial Hardy Type Fractional Inequalities.- About Vectorial Fractional Integral Inequalities Using Convexity.