Table of Contents:
Preface
1. Existence for set Differential Equations via Multivalued
Operator Equations (Ravi P. Agarwal and Donald O'Regan)
2. Nonlocal Cauchy Problem for Abstract Functional
Integrodifferential Equations (K. Balachandran and R. Ravi Kumar)
3. Existence Results for Discontinuous Functional Evolution
Equations in Abstract Spaces (S. Carl and S. Heikkila)
4. A Generalized Solution of the Black-Scholes Partial
Differential Equation (Constantin Chilarescu, Alin Pogan and
Ciprian Preda)
5. Optimality and Duality for Multiobjective Fractional
Programming with Generalized Invexity (Do Sang Kim, Hun Suk Kang
and Sung Je Kim)
6. Markovian Approach to the Backward Recurrence Time (Jongwoo
Kim and Eui Yong Lee)
7. A Multiplicity Result of Singular Boundary Value Problems for
Second Order Impulsive Differential Equations (Eun Kyoung Lee and
Yong-Hoon Lee)
8. Extremal Solutions of Initial Value Problem for Nonlinear
Second Order Impulsive Integro-Differential Equations of Volterra
Type in Banach Spaces (Lishan Liu, Lixin Yu and Yeol Je Cho)
9. Construction of Upper and Lower Solutions for Singular p-Laplacian
Equations with Sign Changing Nonlinearities (Haishen L? and Donal
O'Regan)
10. A Qualitative Hamiltonian Model for Human Motion (Charles E.M.
Pearce and Vladimir Ivancevic)
11. Newton's Method for Matrix Polynomials (Edgar Pereira,
Rogerio Serodio and Jose Vitoria)
12. Admissibility and Non-Uniform Dichotomy for Differential
Systems (Ciprian I. Preda and Sever S. Dragomir)
13. Boundary Value Problems of Fuzzy Differential Equations on an
Infinite Interval (Seiji Saito and Hiroaki Ishii)
14. An Ultimate Boundedness Result for a Certain System of Fourth
Order Nonlinear Differential Equations (Cemil Tunc)
15. The Initial Value Problems for the First Order System of
Nonlinear Impulsive Integro-Differential Equations (Shengli Xie
and Jiang Zhu)
16. Generic Well-Posedness of Nonconvex Optimal Control Problems
(Alexander J. Zaslavski)
Binding: Flexback
Pub. Date: 2006
ISBN: 1-59454-878-1
Book Description:
This volume deals with new topics in the areas of fixed point
theory, variational inequality and complementarity problem
theory, nonlinear ergodic theory, difference, differential and
integral equations, control and optimization theory, dynamic
system theory, inequality theory, stochastic analysis and
probability theory, and their applications.
Table of Contents:
Preface
1. On the Semilocal Convergence of Newton's Method Under Unifying
Conditions (Ioannis K. Arygos and Jose Guteirrez)
2. Inequalities and Fixed Points in Menger Convex Metric Spaces (Ismat
Beg and Mujahid Abbas)
3. Applications of the Perov's Fixed Point Theorem to Delay
Integro-Differential Equations (Alexandru Bica and Sorin Muresan)
4. On Vector Equilibrium Problems with Multifunctions (In Ja Bu,
Moon Hee Kim and Gue Myung Lee)
5. Fixed Points in Generalized Metric Spaces and the Stability of
a Cubic Functional Equation (Liviu Cadariu and Viorel Radu)
6. Sensitivity Analysis of Solution Set for a New Class of
Generalized Implicit Quasi-Variational Inclusions (Xie Ping Ding)
7. Continuous Selection and Coincidence Theorems on Product G-Convex
Spaces (Xie Ping Ding)
8. Fixed Points in Probabilistic-Quasi-Metric Spaces (Mariusz T.
Grabiec)
9. Common Fixed Point Theorems for Condensed Mappings (Jingchang
Li, Hongyan Guan, Zeqing Liu and Shin Min Kang)
10. The Strongly Convergence Theorems of Fixed Points for Local
Strictly Φ-Pseudocontractive Mappings in Banach Spaces (Wang Lin)
11. On Generalized Nonlinear Variational Inequalities (Zeqing
Liu, Haiyan Gao, Soo Hak Shim and Shin Min Kang)
12. A Note on a Paper of Had?i? and Pap (Dorel Mihe?)
13. The Ishiwaka and Mann Iteration Methods (with errors),
Stability, and Three-Step Iteration Methods (M.O. Osilike)
14. On Certain Applications of Leray-Schauder Alternate (B.G.
Pachpatte)
15. Remarks on Concepts of Generalized Convex Spaces (Sehie Park)
16. Generic Existence and Non-Existence of Approximate Fixed
Points (Simeon Reich and Alexander J. Zaslavski)
17. General System of Relaxed g-γ-r-Pseudococoercive Nonlinear
Variational Inequalities and Projection Methods (Ram U. Verma)
18. Three-Step Iteration Methods with Errors for Nonexpansive
Mappings in Uniformly Convex Banach Spaces (Weili Wang, Zhefu An,
Shin Min Kang and Kang Hak Kim)
19. On Nonnegative Linear Composite Games of NTU-Game (Fengrong
Zhang, Shengkai Zhang and Shin Min Kang)
20. Probabilistic Contractor and Nonlinear Operator Equations
with Set-Valued Operator in Probabilistic Normed Spaces (Tatjana
Zikic-Dosenovic)
Binding: Flexback
Pub. Date: 2006
ISBN: 1-59454-877-3
Book Description:
The aim of this volume is to introduce and exchange recent new
topics on the areas of inequality theory and their applications
dealing in pure and applied mathematics.
Table of Contents:
Preface
1. A Perturbed Trapezoid Inequality in Terms of the Third
Derivative and Applications (N.S. Barnett and S. S. Dragomir)
2. On Odd Zeta and Other Special Function Bounds (P. Cerone)
3. Stolarsky and Gini Divergence Measures in Information Theory (P.
Cerone and S.S. Dragomir)
4. Bounds for the Eigenvalues and the Singular Values of a Block-Schwarz
Matrix (Cecilia Costa and Jose Vitoria)
5. Inequalities for Compound Means (Iulia Costin and Gheorghe
Toader)
6. Gruss Type Discrete Inequalities in Inner Product Spaces,
Revisited (Sever S. Dragomir)
7. On the Trapezoid Inequality for the Riemann-Stieltjes Integral
with Holder Continuous Integrand and Bounded Variation
Integrators (S.S. Dragomir, Y.J. Cho and Y.H. Kim)
8. An Approximation of Hankel Transform for the Functions of
Bounded Variation (N.M. Dragomir, S.S. Dragomir and G.W. Baxter)
9. Note on Integral Version of the Gruss Inequality for Complex
Functions (S.S. Dragomir, J.E. Pecaric and B. Tepes)
10. Sharp Inequality for the BAYES Prediction RISK (L. Gajek and
V. Lipinska)
11. A New Subclass of p-Valently Starlike Functions with Negative
Coefficients (Muhammet Kamali and Murat Ozdemir)
12. On Some New Discrete Inequalities and Their Application (Young-ho
Kim and Themistocles M. Rassias)
13. On a New Integral Inequality Applicable to Certain Partial
Integrodifferential Equations (B.G. Pachpatte)
14. Strengthened Forms of an Integral Inequality Arising in
Connection with the Large Sieve (C.E.M. Pearce amd J. Pecaric)
15. Relative Divergence Measures and Information Inequalities(Inder
Jeet Taneja)
16. Stability on Approximate Isometries (Shuhuang Xiang)
17. The Weighted Elementary Symmetric Mean (Zhi-hua Zhang and
Zhen-gang Xiao)
Binding: Flexback
Pub. Date: 2006
ISBN: 1-59454-875-7
Book Description:
The aim of this volume is to introduce and exchange recent new
topics on the areas of inequality theory and their applications
dealing in pure and applied mathematics.
Table of Contents:
Preface
1. Instability and Super-Additivity (Trandafir Balan and Maria
Predoi)
2. Some Remarks on the Noiseless Coding Theorem (N.S. Barnett and
S.S. Dragomir)
3. Functional Measure and Inf-Compactness of Integral Functionals
(Abdelhamid Bourass, Bouchaib Ferrahi and Nourddin Saidou)
4. Estimation of Relative Entropy Using Novel Taylor-Like
Representations (P. Cerone)
5. Generalized Games and Generalized Vector Quasi-Equilibria in G-Convex
Spaces (Xie Ping Ding and Fu Quan Xia)
6. A Generalisation of an Ostrowski Inequality in Inner Product
Spaces (Sever S. Dragomir and Anca C. Gosa)
7. On the Remainder Estimate in the Generalised Taylor's Formula
(S.S. Dragomir and C.I. Preda)
8. A Perturbed Version of the Generalised Taylor's Formula and
Applications (S.S. Dragomir and A. Sofo)
9. Characteristic Property for Inequalities of Bounded Linear
Operators (C.S. Lin and Y.J. Cho)
10. Improved Bounds on Entropy Measures for Mixed Populations (M.
Matic, C.E.M. Pearce and J. Pecaric)
11. Algebra Homomorphisms in C*-Algebras (Chun-Gil Park)
12. On the Lin-Wong Divergence Measure of Entropy (C.E.M. Pearce
and J. Pecaric)
13. Algebraically Determined p-Series (A. Sofo, S.S. Dragomir and
Y.J. Cho)
14. Some Bounds for the Logarithmic Function (Flemming Topsoe)
15. Error Inequalities for an Optimal 2-Point Quadrature Formula
of Open Type (Nenad Ujevic)
16. A Strong Invariance Principle for Quasi-Associated Sequences
(Wen Sheng Wang)
17. Pareto Optimal Trajectories in a Model with Discrete
Innovations (Alexander J. Zaslavski)
Binding: Flexback
Pub. Date: 2006
ISBN: 1-59454-874-9
Book Description:
This new book provides the reader with a self-contained treatment
of the classical operator theory with significant applications to
abstract differential equations, and an elegant introduction to
basic concepts and methods of the repidly growing theory of the
so-called p-adic operator theory.
Table of Contents:
1 Banach and Hilbert Spaces . . . . . . . . . . . . . . . . . . .
. .
1.1 Banach Spaces. . . . . . . . . . . . . . . . . . . . . . . .
. . .
1.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . .
. . .
1.1.2 Basic Definitions . . . . . . . . . . . . . . . . . . . . .
. .
1.1.3 Examples of Banach Spaces . . . . . . . . . . . . . . . .
1.2 Hilbert Spaces . . . . . . . . . . . . . . . . . . . . . . .
. . .
1.2.1 Pre-Hilbert Spaces . . . . . . . . . . . . . . . . . . . .
. . .
1.2.2 Hilbert Spaces . . . . . . . . . . . . . . . . . . . . . .
. . .
1.2.3 Projections . . . . . . . . . . . . . . . . . . . . . . . .
. .
1.3 Bibliographical Notes . . . . . . . . . . . . . . . . . . . .
. .
2 Bounded Linear Operators on Classical and
p-adic Hilbert Spaces . . . . . . . . . . . . . . . . . . . . . .
. .
2.1 Bounded Linear Operators on Hilbert Spaces . . . . . .
2.1.1 Basic Definitions and Examples . . . . . . . . . . . . .
2.1.2 The Adjoint of An Operator . . . . . . . . . . . . . . . .
2.1.3 The Inverse of An Operator . . . . . . . . . . . . . . . .
2.1.4 Normal and Self-adjoint Operators . . . . . . . . . .
XII Contents
2.1.5 Square Root of a Positive Self-adjoint Operator
2.1.6 Compact Operators . . . . . . . . . . . . . . . . . . . . .
. .
2.1.7 Hilbert-Schmidt Operators . . . . . . . . . . . . . . . . .
2.2 Bounded Linear Operators on p-adic Hilbert Spaces Ew
2.2.1 Absolute Value on a Field . . . . . . . . . . . . . . . . .
.
2.2.2 Construction of the Field of p-adic Numbers . .
.............
2.2.3 Ultrametric Banach Spaces . . . . . . . . . . . . . . . . .
2.2.4 Free Banach Spaces . . . . . . . . . . . . . . . . . . . .
. . .
2.2.5 The p-adic Hilbert Space Ew . . . . . . . . . . . . . . .
2.2.6 Bounded Linear Operators Ew . . . . . . . . . . . . . .
2.3 p-adic Hilbert-Schmidt Operators . . . . . . . . . . . . . .
. .
2.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . .
. . .
2.3.2 Hilbert-Schmidt Operators on Ew . . . . . . . . . . .
2.3.3 Further Properties of Hilbert-Schmidt
Operators on Ew . . . . . . . . . . . . . . . . . . . . . . . . .
.
2.3.4 Applications . . . . . . . . . . . . . . . . . . . . . . .
. . .
2.4 Bibliographical Notes . . . . . . . . . . . . . . . . . . . .
. .
2.5 Open Problems . . . . . . . . . . . . . . . . . . . . . . . .
. .
3 Unbounded Linear Operators on Classical and
p-adic Hilbert Spaces . . . . . . . . . . . . . . . . . . . . . .
. .
3.1 Basic Definitions and Examples . . . . . . . . . . . . . . .
. . .
3.1.1 Examples of Unbounded Operators . . . . . . . . .
3.1.2 Closed and Closable Linear Operators . . . . . .
3.1.3 Invariant Subspaces for Unbounded Linear
Operators. . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . .
Contents XIII
3.1.4 Semigroups of Linear Operators . . . . . . . . . . . .
3.1.5 Spectral Theory for Unbounded Linear
Operators. . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . .
3.1.6 Symmetric and Self-adjoint Linear Operators . ............
3.1.7 Maximal Linear Operators . . . . . . . . . . . . . . . .
3.1.8 Algebraic Sum of Linear Operators . . . . . . . . .
3.2 Unbounded Linear Operators on p-adic Hilbert
Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . .
3.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . .
. . .
3.2.2 The p-adic Hilbert Space Ew1 × Ew2 × ...× Ewn
3.2.3 Unbounded Linear Operators On Ew . . . . . . . .
3.3 Closed Linear Operators on Ew . . . . . . . . . . . . . . . .
. .
3.4 The Diagonal Operator on Ew . . . . . . . . . . . . . . . . .
. .
3.5 The Equation Ax = y on Ew . . . . . . . . . . . . . . . . . .
. .
3.5.1 The Bounded Case . . . . . . . . . . . . . . . . . . . . .
. . .
3.5.2 Application to the Perturbation of Bases on Ew
3.5.3 The Unbounded Case . . . . . . . . . . . . . . . . . . . .
.
3.6 Bibliographical Notes . . . . . . . . . . . . . . . . . . . .
. .
3.7 Open Problems . . . . . . . . . . . . . . . . . . . . . . . .
. .
4 Applications To Abstract Differential Equations .
.................
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . .
. . .
4.2 Basic Definitions and Notations . . . . . . . . . . . . . . .
. .
4.2.1 Almost Automorphic Functions . . . . . . . . . . . . .
4.2.2 Almost Periodic Functions . . . . . . . . . . . . . . . . .
4.2.3 Pseudo Almost Periodic Functions . . . . . . . . . .
4.3 The Equation u0(t) = Au(t) + Bu(t) + f(t) . . . . . . . .
XIV Contents
4.3.1 Almost Automorphic Mild Solutions . . . . . . . . .
4.3.2 Almost Periodic Mild Solutions . . . . . . . . . . . . .
4.4 The Method of Invariant Subspaces for Unbounded
Linear Operators . . . . . . . . . . . . . . . . . . . . . . . .
. . .
4.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . .
. . .
4.4.2 Almost Automorphic Solutions . . . . . . . . . . . . .
4.4.3 Applications to Some Second-Order
Differential Equations . . . . . . . . . . . . . . . . . . . . .
4.4.4 Almost Automorphic Solutions to Some
Second-Order Hyperbolic Equations . . . . . . . . .
4.5 Pseudo Almost Periodic Solutions to Some
Second-Order Equations . . . . . . . . . . . . . . . . . . . . .
. . .
4.5.1 Pseudo Almost Periodic Solutions . . . . . . . . .
4.5.2 Applications . . . . . . . . . . . . . . . . . . . . . . .
. . .
4.6 Existence and Uniqueness of Almost Automorphic
Mild Solutions . . . . . . . . . . . . . . . . . . . . . . . . .
. . .
4.6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . .
. . .
4.6.2 Existence and Uniqueness of Mild Solutions .
4.6.3 Case of Bounded Perturbations . . . . . . . . . . . .
4.6.4 Applications . . . . . . . . . . . . . . . . . . . . . . .
. . .
4.7 Bibliographical Notes . . . . . . . . . . . . . . . . . . . .
. .
4.8 Open Problems . . . . . . . . . . . . . . . . . . . . . . . .
. .
References . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . .
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. .
Binding: Hardcover
Pub. Date: 2006
ISBN: 1-59454-424-7