Advances in Mathematical Analysis and its Applications

✍ Scribed by Bipan Hazarika, Santanu Acharjee, H. M. Srivastava

• Publisher: CRC Press/Chapman & Hall
• Year: 2022
• Tongue: English
• Leaves: 358
• Category: Library

✦ Synopsis

Advances in Mathematical Analysis and its Applications is designed as a reference text and explores several important aspects of recent developments in the interdisciplinary applications of mathematical analysis (MA), and highlights how MA is now being employed in many areas of scientific research. It discusses theory and problems in real and complex analysis, functional analysis, approximation theory, operator theory, analytic inequalities, the Radon transform, nonlinear analysis, and various applications of interdisciplinary research; some topics are also devoted to specific applications such as the three-body problem, finite element analysis in fluid mechanics, algorithms for difference of monotone operators, a vibrational approach to a financial problem, and more.

Features:

• The book encompasses several contemporary topics in the field of mathematical analysis, their applications, and relevancies in other areas of research and study.
• It offers an understanding of research problems by presenting the necessary developments in reasonable details
• The book also discusses applications and uses of operator theory, fixed-point theory, inequalities, bi-univalent functions, functional equations, and scalar-objective programming, and presents various associated problems and ways to solve such problems
• Contains applications on wavelets analysis and COVID-19 to show that mathematical analysis has interdisciplinary as well as real life applications.

The book is aimed primarily at advanced undergraduates and postgraduate students studying mathematical analysis and mathematics in general. Researchers will also find this book useful.

✦ Table of Contents

Cover
Half Title
Title Page
Copyright Page
Contents
Preface
Editors
Contributors
1. Some applications of double sequences
1.1. Introduction
1.1.1. Double sequences
1.1.2. Selection principles
1.1.3. Asymptotic analysis
1.2. S1 selection principle and double sequences
1.3. α2-selection principle and double sequences
1.4. Double sequences and the exponent of convergence
Bibliography
2. Convergent triple sequences and statistical cluster points
2.1. Introduction
2.2. Known definitions and properties
2.3. I3-statistical cluster points of triple sequences
2.3.1. ГI3-statistical convergence
2.4. Lacunary I3-statistical cluster points
Bibliography
3. Relative uniform convergence of sequence of positive linear Functions
3.1. Introduction
3.2. Preliminaries and definitions
3.3. Relative uniform convergence of single sequence of functions
3.4. Statistical convergence of sequence
3.5. Double sequences
3.6. Relative uniform convergence of difference double sequence of positive linear functions
Bibliography
4. Almost convergent sequence spaces defined by Nörlund matrix and generalized difference matrix
4.1. Introduction and preliminaries
4.2. Main results
Bibliography
5. Factorization of the infinite Hilbert and Cesàro operators
5.1. Introductions and preliminaries
5.2. Hilbert matrix
5.3. Hausdorff matrix
5.4. Cesàro matrix of order n
5.5. Copson matrix
5.6. Gamma matrix of order n
5.7. Factorization of the infinite Hilbert operator
5.7.1. Factorization of the Hilbert operator based on Cesàro operator
5.7.2. Factorization of the Hilbert operator based on gamma operator
5.7.3. Factorization of the Hilbert operator based on the generalized Cesàro operator
5.8. Factorization of the Cesàro operator
Bibliography
6. On theorems of Galambos-Bojanic-Seneta type
6.1. Introduction
6.2. Known results
6.2.1. Classes ORVs and ORVf and their subclasses
6.2.2. Rapid and related variations
6.3. New result
Bibliography
7. On the spaces of absolutely p-summable and bounded q-Euler difference sequences
7.1. Introduction
7.1.1. Euler matrix of order 1 and sequence spaces
7.1.2. Quantum calculus
7.2. q-Euler difference sequence spaces eqp(▽) and eq∞(▽)
7.3. Alpha-, beta-, and gamma-duals
7.4. Matrix transformations
Bibliography
8. Approximation by the double sequence of LPO based on multivariable q-Lagrange polynomials
8.1. Introduction
8.2. Double sequence of Kꞵ(1)n,q,... ,ꞵ(r)(.)(x)
8.3. Approximation by using power series summability method (p.s.s.m)
8.3.1. Illustrative example
8.4. A-statistical convergence of operators Kn2,qn2n1,qn1(.)(x)
8.4.1. Application of Theorem 8.4.4.
8.5. A-statistical convergence by GBS operators
Bibliography
9. Results on interpolative Boyd-Wong contraction in quasi-partial b-metric space
9.1. Introduction and preliminaries
9.2. Main results
Bibliography
10. Applications of differential transform method on some functional differential equations
10.1. Introduction
10.2. Preliminaries
10.2.1. Definition of differential transform
10.2.2. Faà di Bruno’s formula and Bell polynomials
10.2.3. Description of the method
10.2.4. Convergence results
10.2.5. Error estimate
10.3. Applications
10.3.1. Example 1
10.3.2. Example 2
10.3.3. Example 3
10.3.4. Example 4
10.3.5. Example 5
Bibliography
11. Solvability of fractional integral equation via measure of noncompactness and shifting distance functions
11.1. Introduction
11.1.1. Some notations
11.1.2. Measure of noncompactness
11.2. Main result
11.3. Application
Bibliography
12. Generalized fractional operators and inequalities integrals
12.1. Introduction
12.2. Integral inequalities with some integral operators
12.2.1. Generalized integral operators
12.2.2. Generalized fractional integral operators
12.2.3. Weighted integral operators
12.3. A general formulation of the notion of convex function
12.4. Integral inequalities and fractional derivatives
Bibliography
13. Exponentially biconvex functions and bivariational inequalities
13.1. Introduction
13.2. Preliminary results
13.3. Properties of exponentially biconvex functions
13.4. Bivariational inequalities
Bibliography
14. On a certain subclass of analytic functions defined by Bessel functions
14.1. Introduction
14.2. Coefficient bounds
14.3. Neighborhood property
14.4. Partial sums
Bibliography
15. A note on meromorphic functions with positive coefficients defined by differential operator
15.1. Introduction
15.2. Coefficient inequality
15.3. Distortion theorem
15.4. Integral operators
15.5. Convex linear combinations and convolution properties
15.6. Neighborhood property
Bibliography
16. Sharp coefficient bounds and solution of the Fekete-Szegö problem for a certain subclass of bi-univalent functions associated with the Chebyshev polynomials
16.1. Introduction
16.1.1. Bi-univalent function
16.1.2. Subordination
16.1.3. Chebyshev polynomials
16.1.4. The function class CHΣ (λ, μ, x)
16.2. Coefficient estimates for the class CHΣ (λ, μ, x)
16.2.1. Some immediate consequences of the theorem
Bibliography
17. Some differential sandwich theorems involving a multiplier transformation and Ruscheweyh derivative
17.1. Differential subordination and superordination
17.2. Strong differential subordination and superordination
Bibliography
18. A study on self similar, nonlinear and complex behavior of the spread of COVID-19 in India
18.1. Introduction
18.2. On the importance of the tests performed
18.3. Theory
18.3.1. Calculation of moving averages
18.3.2. Calculation of Hurst exponent by finite variance scaling method
18.3.3. Estimation of fractal dimension by Higuchi’s method
18.3.4. Multifractal analysis by multifractal detrended fluctuation analysis
18.3.5. Analysis for non-linearity using delay vector variance method
18.3.6. 0-1 test for chaos detection
18.3.7. Mathematical aspects of self-organized criticality
18.4. Data
18.5. Results
Bibliography
Index