Mathematical Analysis And Applications (springer Optimization And Its Applications)

Main subject categories: • Mathematical analysis • Real functions • Measure and integration • Functions of a complex variable • Several complex variables and analytic spaces • Partial differential equations • Game theory, economics, finance, and other social and behavioral sciencesAn international community of experts scientists comprise the research and survey contributions in this volume which covers a broad spectrum of areas in which analysis plays a central role. Contributions discuss 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 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.This volume is useful to graduate students and researchers working in mathematics, physics, engineering, and economics. Preface Contents Exact Solution to Systems of Linear First-Order Integro-Differential Equations with Multipointand Integral Conditions 1 Introduction 2 Definitions and Preliminary Results 3 Main Results 4 Conclusions References A Variational Approach to the Financial Problem with Insolvencies and Analysis of the Contagion 1 Introduction 2 The Financial Model and the Equilibrium Conditions 2.1 Presentation of the Model 2.2 The Equilibrium Flows and Prices 2.3 Existence Theorem 2.4 An Example of a Markowitz-Type Risk Measure 3 The Duality for the Financial Equilibrium Problem 3.1 The New Infinite-Dimensional Duality Theory 3.2 Existence of Lagrange Multipliers 3.3 The Viewpoints of the Sector and of the System 3.4 Regularity Results 3.5 The Contagion Problem 4 A Numerical Example 5 Conclusions References Fixed Point Theorems for a System of Mappings in Generalized b-Metric Spaces 1 Introduction 2 Main Results 2.1 Basic Theorem 2.2 Local Theorems References Inequalities and Approximations for the Finite Hilbert Transform: A Survey of Recent Results 1 Introduction 2 Inequalities for Some Classes of Functions 2.1 Some Estimates for α-Hölder Continuous Mappings 2.2 Some Results for Monotonic Functions 2.3 Some Results for Convex Functions 3 Inequalities of Trapezoid Type 3.1 Trapezoid Type Inequalities 3.2 Agarwal-Dragomir Type Inequalities 3.3 Compounding Trapezoid Type Inequalities 4 Inequalities of Midpoint Type 4.1 Midpoint Type Inequalities 4.2 Other Midpoint Type Inequalities 4.3 Compounding Midpoint Type Inequalities 5 Estimates for Derivatives of Bounded Variation 5.1 Some Integral Inequalities 5.2 A Quadrature Formula for Equidistant Divisions 5.3 A More General Quadrature Formula 6 Estimates for Absolutely Continuous Derivatives 6.1 Ostrowski Type Inequalities 6.2 A Quadrature Formula 7 Inequalities for Convex Derivatives 7.1 An Inequality on the Interval ( a,b) 7.2 An Inequality on an Equidistant Division of ( a,b) 7.3 The Case of Non-equidistant Partitioning 8 Inequalities for Products 8.1 Some Basic Inequalities 8.2 Further Estimates 9 Estimates via Taylor's Expansion 9.1 Inequalities on the Whole Interval [ a,b] 9.2 The Composite Case References On Hyperstability of the Two-Variable Jensen Functional Equation on Restricted Domain 1 Introduction 2 Auxiliary Results 3 Hyperstability Results for Equation (8) 4 Some Applications and Examples References On the Study of Circuit Chains Associated with a Random Walk with Jumps in Fixed, Random Environments: Criteria of Recurrence and Transience 1 Introduction 2 Preliminaries 3 Circuit and Weight Representations 3.1 Fixed Environments 3.2 Random Environments 4 Recurrence and Transience 4.1 Fixed Environments 4.2 Random Environments References On Selections of Some Generalized Set-Valued Inclusions 1 Introduction 2 Selections of Set-Valued Mappings 3 Set-Valued Dynamics and Applications References Certain Fractional Integral and Differential Formulas Involving the Extended Incomplete Generalized Hypergeometric Functions 1 Introduction 2 Fractional Calculus Operators and Their Formulas 3 Incomplete Gamma Functions and Their Generalizations 4 Fractional Integral Formulas Involving Extended Incomplete Generalized Hypergeometric Functions 4.1 Special Cases 5 Fractional Differential Formulas Involving the Extended Incomplete Generalized Hypergeometric Functions 5.1 Special Cases 6 Integral Transform Formulas of the Extended Incomplete Generalized Hypergeometric Functions 6.1 Beta Transform 6.2 Laplace Transform 6.3 Whittaker Transform 7 Fractional Kinetic Equations 8 Solution of Generalized Fractional Kinetic Equations Involving Extended Incomplete Generalized Hypergeometric Functions 9 Conclusion References On the Stability of the Triangular Equilibrium Points in the Elliptic Restricted Three-Body Problem with Radiation and Oblateness 1 Introduction 2 Equations of Motion and Triangular Equilibrium Points 3 Stability of the Triangular Equilibrium Points 4 Numerical Results 5 Conclusions References Some Different Type Integral Inequalities and Their Applications 1 Introduction 2 Main Results 3 Applications to Special Means 4 Conclusion References Extensions of Kannappan's and Van Vleck's Functional Equations on Semigroups 1 Introduction 2 Solutions of Equation (9) on Semigroups 3 Solutions of Equation (10) on Semigroups 4 Solutions of Equation (11) 5 Solutions of Equation (12) References Recent Advances of Convexity Theory and Its Inequalities 1 Introduction 2 Generalized Convex Functionals in Normed Linear Spaces 3 Some New Basic Inequalities 4 New Generalized Hermite-Hadamard Type Inequalities 5 Strongly Convex Functionals in Normed Linear Spaces 6 New Schur, Jensen, Hermite-Hadamard Type Inequalities References Additive Functional Inequalities and Partial Multipliers in Complex Banach Algebras 1 Introduction and Preliminaries 2 Additive Functional Inequality (1) 3 Additive Functional Inequality (2) 4 Partial Multipliers in C*-Algebras 5 Partial Multipliers in Lie C*-Algebras 6 Partial Multipliers in JC*-Algebras 7 Partial Multipliers in C*-Ternary Algebras References Additive ρ-Functional Inequalities and Their Applications 1 Introduction and Preliminaries 2 Additive ρ-Functional Inequality (1) 3 Additive ρ-Functional Inequality (2) 4 Homomorphisms and Derivations in C*-Algebras 5 Homomorphisms and Derivations in Lie C*-Algebras 6 Homomorphisms and Derivations in JC*-Algebras References Graphic Contraction Principle and Applications 1 Introduction 2 Two General Results on Graphic Contractions 3 Relevant Examples of Graphic Contractions 4 Some General Results on Non-self Graphic Contractions 5 Data Dependence and Stability Results for Graphic Contractions 6 Operators on a Complete Metric Space Which Are Graphic Contractions on an Invariant Subset 7 Open Questions and New Research Directions 7.1 Generalized Contractions as Graphic Contractions 7.2 Nonlinear Graphic Contractions 7.3 Generalized Metric Spaces 7.4 Coupled Fixed Point Problems Via Graphic Contraction Conditions 7.5 Y-Contractions References A New Approach for the Inversion of the AttenuatedRadon Transform 1 Introduction 2 The Radon Transform 3 The Inversion of the Radon Transform 3.1 Preliminaries 3.2 The Radon Transform Pair 3.2.1 The Direct Problem: A -Problem 3.2.2 The Inverse Problem: A Riemann–Hilbert Problem 4 The Attenuated Radon Transform 5 The Inversion of the Attenuated Radon Transform 5.1 The Attenuated Radon Transform Pair 5.2 A Novel Equivalent Formula 6 The Attenuated Spline Reconstruction Technique 6.1 The Evaluation of the Function M and Its Derivative Mρ 6.2 The Evaluation of the Function F 6.3 The Evaluation of the Function G and Its Derivative Gρ References On Algorithms for Difference of Monotone Operators 1 Introduction 2 DC Programming and DCA 3 Proximal Point Algorithm for DC Program 4 Inertial Proximal Algorithm for Difference of Two Maximal Monotone Operators References Finite Element Analysis in Fluid Mechanics 1 Introduction 2 Preliminaries and Basic Theorems 3 The Stokes Problem 3.1 A Priori Error Estimates 3.2 A Posteriori Error Estimates 3.3 Crouzeix–Raviart Finite Element Discretization and Finite Volume Scheme 4 Advection–Diffusion Equation 4.1 The Galerkin Formulation 4.2 The Stabilized Finite Element Methods 4.3 The Variational Multiscale Method 4.4 The Discontinuous Galerkin (DG) Method 5 The Navier–Stokes Problem 5.1 Streamline–Upwind/Petrov–Galerkin (SUPG) 5.2 Variational Multiscale Method (VMS) and Stabilized FEM 5.3 Characteristic Based Split (CBS) Method and Two-Step Methods 5.4 Gradient Smoothed Method (GSM) 5.5 Discontinuous and Adaptive Galerkin Method 6 Conclusions References On a Hilbert-Type Integral Inequality in the Whole Plane Related to the Extended Riemann Zeta Function 1 Introduction 2 An Example and Two Lemmas 3 Main Results and a Few Corollaries 4 Operator Expressions References On Metric Structures of Normed Gyrogroups 1 Introduction 2 Preliminaries 3 Normed Gyrogroups and Concrete Examples 3.1 The Definition and Basic Properties 3.2 Concrete Examples 3.2.1 An n-Dimensional Euclidean Version of the Einstein Gyrogroup 3.2.2 An n-Dimensional Euclidean Version of the Möbius Gyrogroup 4 Topological and Geometric Structures 4.1 Topological and Geometric Properties 4.2 A Characterization of Normed Gyrogroups 4.3 Sufficient Conditions to be a Topological Gyrogroup References Birelator Spaces Are Natural Generalizations of Not Only Bitopological Spaces, But Also Ideal Topological Spaces 1 Some Basic Facts on Topological Spaces 2 Some Basic Facts on Relator Spaces 3 Some Important Structures Derived from Relators 4 Some Important Unary Operations for Relators 5 Some Basic Theorems on Fat and Dense Sets 6 Some Further Theorems on Fat and Dense Sets 7 Proximal Closures and Interiors Derived from Ordered Pairs of Relators 8 Some Further Theorems on the Induced Proximal Closures and Interiors 9 Topological Closures and Interiors Derived from Ordered Pairs of Relators 10 Fat and Dense Sets Derived from Ordered Pairs of Relators 11 Proximally Open and Closed Sets Derived from Ordered Pairs of Relators 12 Topologically Open and Closed Sets Derived from Ordered Pairs of Relators 13 The Real Line as a Prime Example for Birelator Spaces References PPF Dependent Fixed Points in Razumikhin Metrical Chains 1 Introduction 2 Preliminaries 3 Meir-Keeler Relations 4 Geometric Contractions in OMS 5 Razumikhin Chains 6 Conditional Result 7 Full Razumikhin Chains 8 Linear Aspects References Equivalent Properties of Parameterized Hilbert-Type Integral Inequalities 1 Introduction 2 Some Lemmas 3 The Case of the Conjugate Exponents p>1(q>1) 4 The Case of the Conjugate Exponents 0