Intelligent Analysis: Fractional Inequalities and Approximations Expanded (Studies in Computational Intelligence, 886)

✍ Scribed by George A. Anastassiou

• Publisher: Springer
• Tongue: English
• Leaves: 525
• Category: Library

✦ Synopsis

This book focuses on computational and fractional analysis, two areas that are very important in their own right, and which are used in a broad variety of real-world applications. We start with the important Iyengar type inequalities and we continue with Choquet integral analytical inequalities, which are involved in major applications in economics. In turn, we address the local fractional derivatives of Riemann–Liouville type and related results including inequalities. We examine the case of low order Riemann–Liouville fractional derivatives and inequalities without initial conditions, together with related approximations. In the next section, we discuss quantitative complex approximation theory by operators and various important complex fractional inequalities. We also cover the conformable fractional approximation of Csiszar’s well-known f-divergence, and present conformable fractional self-adjoint operator inequalities. We continue by investigating new local fractional M-derivatives that share all the basic properties of ordinary derivatives. In closing, we discuss the new complex multivariate Taylor formula with integral remainder. Sharing results that can be applied in various areas of pure and applied mathematics, the book offers a valuable resource for researchers and graduate students, and can be used to support seminars in related fields.

✦ Table of Contents

Preface
Contents
1 General Ordinary Iyengar Inequalities
1.1 Introduction
1.2 Main Results
References
2 Caputo Fractional Iyengar Inequalities
2.1 Introduction
2.2 Main Results
References
3 Canavati Fractional Iyengar Inequalities
3.1 Background
3.2 Main Results
References
4 General Multivariate Iyengar Inequalities
4.1 Background
4.2 Main Results
References
5 Multivariate Iyengar Inequalities for Radial Functions
5.1 Background
5.2 Main Results
References
6 Multidimensional Fractional Iyengar Inequalities for Radial Functions
6.1 Background
6.2 Main Results
6.3 Appendix
References
7 General Multidimensional Fractional Iyengar Inequalities
7.1 Background
7.2 Main Results
7.3 Appendix
References
8 Delta Time Scales Iyengar Inequalities
8.1 Introduction
8.2 Background
8.3 Main Results
8.4 Applications
References
9 Time Scales Nabla Iyengar Inequalities
9.1 Introduction
9.2 Background
9.3 Main Results
9.4 Applications
References
10 Choquet–Iyengar Advanced Inequalities
10.1 Background—I
10.2 Background—II
10.3 Main Results
References
11 Fractional Conformable Iyengar Inequalities
11.1 Background
11.2 Main Results
References
12 Iyengar Fuzzy Inequalities
12.1 Introduction
12.2 Background
12.3 Main Results
References
13 Choquet Integral Analytical Type Inequalities
13.1 Background
13.2 Main Results
References
14 Local Fractional Taylor Formula
14.1 Introduction
14.2 Main Results
References
15 Negative Domain Local Fractional Inequalities
15.1 Introduction
15.2 Background
References
16 Fractional Approximation by Riemann–Liouville Fractional Derivatives
16.1 Introduction
16.2 Main Results
References
17 Riemann–Liouville Fractional Fundamental Theorem of Calculus and Riemann–Liouville Fractional Polya Integral Inequality and the Generalization to Choquet Integral Case
17.1 Introduction
17.2 Background
17.3 Main Results
References
18 Low Order Riemann–Liouville Fractional Inequalities with Absent Initial Conditions
18.1 Introduction
18.2 Main Results
References
19 Low Order Fractional Riemann–Liouville Inequalities on a Spherical Shell
19.1 Main Results
References
20 Complex Korovkin Theory
20.1 Introduction
20.2 Background
20.3 Main Results—I
20.4 Main Results—II
References
21 Left Caputo Fractional Complex Inequalities
21.1 Introduction
21.2 Background
21.3 Main Results
References
22 Complex Opial Inequalities
22.1 Introduction
22.2 Background
22.3 Main Results
References
23 Complex Multivariate Montgomery Identity and Ostrowski and Grüss Inequalities
23.1 Introduction
23.2 Main Results
References
24 Complex Multivariate Fink Identity and Complex Multivariate Ostrowski and Grüss Inequalities
24.1 Introduction
24.2 Main Results
24.3 Applications
References
25 Fractional Conformable Approximation of Csiszar's f-Divergence
25.1 Background—I
25.2 Background—II
25.3 Main Results—I
25.4 Background—III
25.5 Main Results—II
References
26 Fractional Conformable Self Adjoint Operator Analytic Inequalities
26.1 Background—I
26.2 Background—II
26.3 Main Results
References
27 Fractional Left Local General M-Derivative
27.1 Introduction
27.2 Main Results
References
28 Fractional Right Local General M-Derivative
28.1 Introduction
28.2 Main Results
References
29 Complex Multivariate Taylor Formula
29.1 Main Results
References