Nonlinear Analysis

The volume will consist of about 40 articles written by some very influential mathematicians of our time and will expose the latest achievements in the broad area of nonlinear analysis and its various interdisciplinary applications.

Presents some of the latest developments in the broad area of nonlinear analysis Includes applications to concrete problems in areas related to the calculus of variations and stability theory including chaos theory, catastrophe theory, and game theory A valuable source of supplementary material for graduate research and coursework in mathematical optimization Includes supplementary material: sn.pub/extras

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Nonlinear Analysis: Stability, Approximation, and Inequalities presents some of the most recent results in the field of nonlinear analysis. Dedicated to Themistocles M. Rassias on the occasion of his 60th birthday, this volume contains 44 articles on various developments in the field, pertaining to subjects such as the stability of functional equations, variational systems, geometric analysis, analytic inequalities, approximation theory and optimization, as well as their applications. Many of the chapters are related to the seminal contributions of Th. M. Rassias and are based upon his initial findings.

This book is well suited to researchers working in nonlinear analysis and approximation theory, differential equations, variational analysis, optimization and their applications, and also to mathematically oriented engineers. It can be used as a valuable source of supplementary material for graduate research and course work.

Contenu
Preface.- 1. Bounds of Jensen's Type Inequality and Eigenvalues of Sturm-Liouville System (S. Abramovich).- 2. Quadratic Operators and Quadratic Functional Equation (M. Adam, S. Czerwik).- 3. On the Regions Containing All the Zeros of a Polynomial (C. Affane-Aji, N.K. Govil).- 4. Some Remarks on the Group of Isometries of a Metric Space (D. Andrica, V. Bulgarean).- 5. Rationality of the Moduli Space of Stable Pairs over a Complex Curve (I. Biswas, M. Logares, V. Muñoz).- 6. Generalized p-valent Janowski Close-to-Convex Functions and Their Applications to the Harmonic Mappings (D. Breaz, Y. Polatoglu, N. Breaz).- 7. Remarks on Stability of the Linear Functional Equation in Single Variable (J. Brzdk, D. Popa, B. Xu).- 8. On a Curious q-hypergeometric Identity (M. J. Cantero, A. Iserles).- 9. Jensen and Quadratic Functional Equations on Semigroups (E.A. Chávez, P.K. Sahoo).- 10. On Bohr's Inequalities (W.-S. Cheung, G. Leng, J. Peari, D. Zhao).- 11. Orlicz Norm Inequalities for Conjugate Harmonic Forms (S. Ding, Y. Xing).- 12. A Survey on Jessen's Type Inequalities for Positive Functionals (S.S. Dragomir).- 13. On Approximate Bi-quadratic Bi-homomorphisms and Bi-quadratic Bi-derivations in C*-ternary algebras and quasi-Banach algebras (A. Ebadian, N. Ghobadipour).- 14. Fixed points approach to the stability of the quadratic functional equation (E. Elhoucien, M. Youssef).- 15. Bohr's Inequality Revisited (M. Fujii, M. S. Moslehian, J. Mii).- 16. Hyers-Ulam-Rassias Stability of Orthogonal Additive Mappings (P. Gvrua and L. Gvrua).- 17. Approximate Ternary Jordan Homomorphisms on Banach Ternary Algebras (M.E. Gordji, N. Ghobadipour, A. Ebadian, M. B. Savadkouhi, C. Park).- 18. Approximately Cubic nderivations on Nonarchimedean Banach Algebras (F. Habibian, R. Bolghanabadi, M.E. Gordji).- 19. Fuzzy Stability of a Quadratic-additive Type Functional Equation (S. S. Jin, Y.-H. Lee).- 20. Generalized Hyers-Ulam Stability of CauchyJensen Functional Equations (K.-W. Jun, H.-M. Kim, E. Y. Son).- 21. A Fixed Point Approach to the Stability of the Gamma Functional Equation (S.-M. Jung).- 22. Random Stability of An AQCQ Functional Equation: A Fixed Point Approach (H.A. Kenary).- 23. Basis Sets in Banach Spaces (S.V. Konyagin, Y.V. Malykhin).- 24. Inequalities for Trigonometric Sums (S. Koumandos).- 25. On Vandiver's Best Result on FLT1 (P. Mihilescu).- 26. Multiple Orthogonality and Applications in Numerical Integration (G. V. Milovanovi, M.P. Stani).- 27. Approximate C-Algebra Homomorphisms Associated to an Apollonius - Jensen type Additive Mapping; A Fixed Point Approach (F. Moradlou, G. Z. Eskandani).- 28. The Fuík Spectrum for the Negative p-Laplacian with Different Boundary Conditions (D. Motreanu, P. Winkert).- 29. Korovkin Type Approximation Theorem for Almost and Statistical Convergence (M. Mursaleen, S. A. Mohiuddine).- 30. On the Stability of an Additive (A. Najati).- 31. Existence Results for Extended General Nonconvex Quasivariational Inequalities (M.A. Noor, K.I. Noor, E. Al-Said).- 32. Iterative Projection Methods for Solving Systems of General Nonconvex Variational Inequalities (M.A. Noor, K.I. Noor, E. Al-Said).- 33. On the Asymptotic Behavior of Solutions to General Linear Functional Equations (B. Paneah).- 34. On the Stability of an Additive and Quadratic Functional Equation (C. Park).- 35. Classification and Stability of Functional Equations (C. Park, M. E. Gordji, R. Saadati).- 36. Exotic n-d'Alembert PDE's and Stability (A. Prástaro).- 37. Stability of Affine Approximations on Bounded Domains (V.Y. Protasov).- 38. Some Inequalities and Other Results Associated with Certain Subclasses of Univalent and Bi-Univalent Analytic Functions (H. M. Srivastava).- 39. The HyersUlam and the HahnBanach Theorems and Some Elementary Operations on Relations Motivated by Their Set-valued Generalizations (Á. Száz).- 40. Spectral Analysis and Spectral Synthesis (L. Székelyhidi).- 41. Möbius Transformation and Einstein Velocity Addition in the Hyperbolic Geometry of Bolyai and Lobachevsky (A. A. Ungar).- 42. Hilbert-Type Integral Operators: Norms and Inequalities (B. Yang).- 43. On the Stability of the Pexiderized Sine Functional Equation (X. Zhao, X. Yang).- 44. Stability of Additive-quadratic Functional Equations in Intuitionistic Fuzzy Normed Spaces (W. Zhihua, Z. Wanxiong).