Intelligent Comparisons: Analytic Inequalities

Description

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.   Front Matter....Pages i-xv Fractional Polya Integral Inequality....Pages 1-7 Univariate Fractional Polya Integral Inequalities....Pages 9-21 About Multivariate General Fractional Polya Integral Inequalities....Pages 23-55 Balanced Canavati Fractional Opial Inequalities....Pages 57-66 Fractional Representation Formulae Using Initial Conditions and Fractional Ostrowski Inequalities....Pages 67-94 Basic Fractional Integral Inequalities....Pages 95-130 Harmonic Multivariate Ostrowski and Grüss Inequalities Using Several Functions....Pages 131-158 Fractional Ostrowski and Grüss Inequalities Using Several Functions....Pages 159-173 Further Interpretation of Some Fractional Ostrowski and Grüss Type Inequalities....Pages 175-187 Multivariate Fractional Representation Formula and Ostrowski Inequality....Pages 189-198 Multivariate Weighted Fractional Representation Formulae and Ostrowski Inequalities....Pages 199-207 About Multivariate Lyapunov Inequalities....Pages 209-216 Ostrowski Type Inequalities for Semigroups....Pages 217-230 About Ostrowski Inequalities for Cosine and Sine Operator Functions....Pages 231-244 About Hilbert-Pachpatte Inequalities for Semigroups, Cosine and Sine Operator Functions....Pages 245-258 About Ostrowski and Landau Type Inequalities for Banach Space Valued Functions....Pages 259-289 Multidimensional Ostrowski Type Inequalities for Banach Space Valued Functions....Pages 291-340 About Fractional Representation Formulae and Right Fractional Inequalities....Pages 341-369 About Canavati Fractional Ostrowski Inequalities....Pages 371-390 The Most General Fractional Representation Formula for Functions and Consequences....Pages 391-399 Rational Inequalities for Integral Operators Using Convexity....Pages 401-438 Fractional Integral Inequalities with Convexity....Pages 439-475 Vectorial Inequalities for Integral Operators Involving Ratios of Functions Using Convexity....Pages 477-513 About Vectorial Hardy Type Fractional Inequalities....Pages 515-548 About Vectorial Fractional Integral Inequalities Using Convexity....Pages 549-583 Back Matter....Pages 585-622 ....Pages 623-659