Mathematical Analysis: Theory and Applications, 1st Edition

Cover
Half Title
Title Page
Copyright Page
Contents
Preface
Editor Biographies
List of Contributors
Chapter 1 Developments, Applications and Open Problems in Fixed Point Theory
	1.1 INTRODUCTION
	1.2 EXTENSIONS OF THE CONTRACTION PRINCIPLE
	1.3 FIXED POINT WITHOUT CONTINUITY
	1.4 SOME APPLICATIONS OF FIXED POINT THEOREMS
		1.4.1 Applications in Linear Equations
		1.4.2 Applications in Differential Equations
		1.4.3 Applications in Integral Equations
	1.5 OPEN PROBLEMS IN METRIC FIXED POINT THEORY
	References
Chapter 2 Several Recent Episodes on the Metric Completeness
	2.1 INTRODUCTION
	2.2 PRELIMINARIES
	2.3 HISTORICAL BACKGROUND OF METRIC COMPLETENESS
	2.4 BASIC FIXED POINT THEOREMS
	2.5 COMPLETENESS OF QUASI-METRIC SPACES
	2.6 THEOREMS DUE TO SUZUKI ET AL
		2.6.1 Suzuki [24] in 2008
		2.6.2 Suzuki [25] in 2008
		2.6.3 Kikkawa and Suzuki [9] in 2008
		2.6.4 Kikkawa and Suzuki [10] in 2008
		2.6.5 Enjouji, Nakanishi, and Suzuki [6] in 2009
		2.6.6 Nakanishi and Suzuki [13] in 2010
	2.7 OTHER AUTHORS’ COMMENTS RELATED TO SUZUKI ET AL
	2.8 EPILOGUE
	References
Chapter 3 Fixed Point Theorems in p-Normed Spaces
	3.1 INTRODUCTION
	3.2 SOME BASIC RESULTS OF P-VECTOR SPACES
	3.3 FIXED POINT THEOREMS IN P-NORMED SPACE
	References
Chapter 4 New Versions of Kannan-Type Map
	4.1 INTRODUCTION
	4.2 PRELIMINARIES
	4.3 MAIN RESULTS
		4.3.1 A New Form of Kannan-Type Map on S-Metric Spaces
		4.3.2 A New Form of Kannan-Type Map on b-Metric Spaces
	4.4 INTEGRAL APPROACH TO KANNAN-TYPE MAP
	References
Chapter 5 Some Applications of a Kittaneh Inequality to Operator-Valued Integrals on Hilbert Spaces
	5.1 INTRODUCTION
	5.2 MAIN RESULTS
	5.3 SOME RELATED RESULTS
	5.4 APPLICATIONS VIA POLAR DECOMPOSITION
	References
Chapter 6 Frozen Derivative Iterative Methods of High Order for Equations
	6.1 INTRODUCTION
	6.2 LOCAL CONVERGENCE
	6.3 CONCLUSION
	References
Chapter 7 Application of Some Classes of Mittag-Leffler Functions in Solving Conformal Fractional Differential Equations
	7.1 INTRODUCTION
	7.2 PRELIMINARIES
	7.3 MAIN RESULTS
	7.4 EXAMPLES
	7.5 APPLICATIONS
	7.6 CONCLUSION
	7.7 FUNDING
	References
Chapter 8 The Non-Population Conserving SIR Model on Time Scales
	8.1 INTRODUCTION
	8.2 PRELIMINARIES
	8.3 THE NON-POPULATION CONSERVING SIR MODEL ON TIME SCALES (SIR-NC)
	8.4 THE SIR-NC MODEL WITH IMPORTED INFECTIONS
	8.5 ACKNOWLEDGMENTS
	References
Chapter 9 Stability Criteria of Nonlinear Generalized Proportional Fractional Delayed Systems
	9.1 INTRODUCTION
	9.2 PRELIMINARIES
	9.3 FINITE TIME STABILITY OF DELAYED GPFS
	9.4 APPLICATIONS
	9.5 CONCLUSION
	9.6 FUNDING
	References
Chapter 10 On the Hamburger-Oberhettinger-Soni Modular Relations
	10.1 THE FOURIER-BESSEL EXPANSION AND ITS VARIANT
	10.2 SOME SUMMATION FORMULAS ACCORDING TO THE PRINCIPLE
	10.3 SUMMATION FORMULAS
		10.3.1 Proof
	10.4 VARIANT OF THE PRINCIPLE
		10.4.1 The Case of Gupta and Maji
		10.4.2 The Case of Krätzel
	10.5 EQUIVALENTS TO THE RIEMANN FUNCTIONAL EQUATION
	References
Chapter 11 Extended and Efficient Secant-Type Methods Based on Generalized Schmidt-Schwetlick Conditions
	11.1 INTRODUCTION
	11.2 LOCAL ANALYSIS OF CONVERGENCE
	11.3 SEMI-LOCAL ANALYSIS OF CONVERGENCE
	11.4 CONCLUSION
	References
Chapter 12 Summation of Schlömilch-Type Series
	12.1 INTRODUCTION
	12.2 BESSEL AND RELATED FUNCTIONS
	12.3 ANGER AND WEBER FUNCTIONS
	12.4 SERIES OVER BESSEL OR STRUVE FUNCTIONS
		12.4.1 Series over Spherical Bessel Functions
		12.4.2 Series over Struve Functions
		12.4.3 Summation Based on Poisson’s Formula
	12.5 SERIES OVER ANGER AND WEBER FUNCTIONS
	12.6 SERIES OVER BOURGET FUNCTIONS
	12.7 SERIES OVER A PRODUCT OF BESSEL FUNCTIONS
		12.7.1 Summation Based on the Gegenbauer Integral
		12.7.2 Summation Based on the Anger-Weber Integral
		12.7.3 Application of Poisson’s Formula
	12.8 PRODUCT OF A TRIGONOMETRIC AND A SPECIAL FUNCTION
		12.8.1 Product of Bessel or Struve Functions and a Trigonometric Function
		12.8.2 Closed-Form Cases
		12.8.3 Product of Anger or Weber Functions and a Trigonometric Function
		12.8.4 Product of a Trigonometric Function and Two Bessel Functions
	12.9 SERIES OVER NEUMANN OR MACDONALD FUNCTIONS
	12.10 APPENDIX – TABLES
	References
Chapter 13 Cross-Diffusion-Driven Instability and Non-Linear Analysis in a Spatio-Temporal Oncolytic Therapeutic Model
	13.1 INTRODUCTION AND MATHEMATICAL MODEL
	13.2 STABILITY WITHOUT DIFFUSION
	13.3 TURING INSTABILITY
		13.3.1 Non-Turing Bifurcation without Cross- Diffusion
		13.3.2 Turing Instability Induced by Cross-Diffusion
	13.4 NON-LINEAR ANALYSIS
		13.4.1 Amplitude Equations
		13.4.2 Analysis of the Amplitude Equations
	13.5 NUMERICAL SIMULATIONS AND CONCLUSIONS
	References
Chapter 14 From Metric Spaces to O-Metric Spaces: Generalizing the Metrical Triangle Inequality
	14.1 INTRODUCTION
		14.1.1 The Class of b-Metric Spaces and Some Extensions
		14.1.2