Functional Equations in Mathematical Analysis

ISBN-13: 9781461400547 / Angielski / Twarda / 2011 / 768 str.

Themistocles M. Rassias; Janusz Brzdek

Opis

The stability problem for approximate homomorphisms, or the Ulam stability problem, was posed by S. M. Ulam in the year 1941. The solution of this problem for various classes of equations is an expanding area of research. In particular, the pursuit of solutions to the Hyers-Ulam and Hyers-Ulam-Rassias stability problems for sets of functional equations and ineqalities has led to an outpouring of recent research. This volume, dedicated to S. M. Ulam, presents the most recent results on the solution to Ulam stability problems for various classes of functional equations and inequalities. Comprised of invited contributions from notable researchers and experts, this volume presents several important types of functional equations and inequalities and their applications to problems in mathematical analysis, geometry, physics and applied mathematics. "Functional Equations in Mathematical Analysis" is intended for researchers and students in mathematics, physics, and other computational and applied sciences.

Spis treści

Preface.- 1. Stability properties of some functional equations (R. Badora).- 2. Note on superstability of Mikusiński’s functional equation (B. Batko).- 3. A general fixed point method for the stability of Cauchy functional equation (L. Cădariu, V. Radu).- 4. Orthogonality preserving property and its Ulam stability (J. Chmieliński).- 5. On the Hyers-Ulam stability of functional equations with respect to bounded distributions (J.-U. Chung).- 6. Stability of multi-Jensen mappings in non-Archimedean normed spaces (K. Ciepliński).- 7. On stability of the equation of homogeneous functions on topological spaces (S. Czerwik).- 8. Hyers-Ulam stability of the quadratic functional equation (E. Elhoucien, M. Youssef, T. M. Rassias).- 9. Intuitionistic fuzzy approximately additive mappings (M. Eshaghi-Gordji, H. Khodaei, H. Baghani, M. Ramezani).- 10. Stability of the pexiderized Cauchy functional equation in non-Archimedean spaces (G. Z. Eskandani, P. Găvruţa).- 11. Generalized Hyers-Ulam stability for general quadratic functional equation in quasi-Banach spaces (J. Gao).- 12. Ulam stability problem for frames (L. Găvruţa, P. Găvruţa).- 13. Generalized Hyers-Ulam stability of a quadratic functional equation (K.-W. Jun, H-M. Kim, J. Son).- 14. On the Hyers-Ulam-Rassias stability of the bi-Pexider functional equation (K.-W. Jun, Y.-H. Lee).- 15. Approximately midconvex functions (K. Misztal, J. Tabor, J. Tabor).- 16. The Hyers-Ulam and Ger type stabilities of the first order linear differential equations (T. Miura, G. Hirasawa).- 17. On the Butler-Rassias functional equation and its generalized Hyers-Ulam stability (T. Miura, G. Hirasawa, T. Hayata).- 18. A note on the stability of an integral equation (T. Miura, G. Hirasawa, S.-E. Takahasi, T. Hayata).- 19. On the stability of polynomial equations (A. Najati, T. M. Rassias).- 20. Isomorphisms and derivations in proper JCQ*-triples (C. Park, M. Eshaghi-Gordji).- 21. Fuzzy stability of an additive-quartic functional equation: a fixed point approach (C. Park, T.M. Rassias).- 22. Selections of set-valued maps satisfying functional inclusions on square-symmetric grupoids (D. Popa).- 23. On stability of isometries in Banach spaces (V.Y. Protasov).- 24. Ulam stability of the operatorial equations (I.A. Rus).- 25. Stability of the quadratic-cubic functional equation in quasi-Banach spaces (Z. Wang, W. Zhang).- 26. μ-trigonometric functional equations and Hyers-Ulam stability problem in hypergroups (D. Zeglami, S. Kabbaj, A. Charifi, A. Roukbi).- 27. On multivariate Ostrowski type inequalities (Z Changjian, W.-S. Cheung).- 28. Ternary semigroups and ternary algebras (A. Chronowski).- 29. Popoviciu type functional equations on groups (M. Chudziak).- 30. Norm and numerical radius inequalities for two linear operators in Hillbert spaces: a survey of recent results (S.S. Dragomir).- 31. Cauchy’s functional equation and nowhere continuous/everywhere dense Costas bijections in Euclidean spaces (K. Drakakis).- 32. On solutions of some generalizations of the Gołąb-Schinzel equation (E. Jabłońska).- 33. One-parameter groups of formal power series of one indeterminate (W. Jabłoński).- 34. On some problems concerning a sum type operator (H.H. Kairies).- 35. Priors on the space of unimodal probability measures (G. Kouvaras, G. Kokolakis).- 36. Generalized weighted arithmetic means (J. Matkowski).- 37. On means which are quasi-arithmetic and of the Beckenbach-Gini type (J. Matkowski).- 38. Scalar Riemann-Hillbert problem for multiply connected domains (V.V. Mityushev).- 39. Hodge theory for Riemannian solenoids (V. Muñoz, R.P. Marco).- 40. On solutions of a generalization of the Gołąb-Schinzel functional equation (A. Mureńko).- 41. On functional equation containing an indexed family of unknown mappings (P. Nath, D.K. Singh).- 42. Two-step iterative method for nonconvex bifunction variational inequalities (M.A. Noor, K.I. Noor, E. Al-Said).- 43. On a Sincov type functional equation (P. K. Sahoo).- 44. Invariance in some families of means (G. Toader, I. Costin, S. Toader).- 45. On a Hillbert-type integral inequality (B. Yang).- 46. An extension of Hardy-Hillbert’s inequality (B. Yang).- 47. A relation to Hillbert’s integral inequality and a basic Hillbert-type inequality (B. Yang, T.M. Rassias).

Blurb

Functional Equations in Mathematical Analysis, dedicated to S.M. Ulam in honor of his 100th birthday, focuses on various important areas of research in mathematical analysis and related subjects, providing an insight into the study of numerous nonlinear problems. Among other topics, it supplies the most recent results on the solutions to the Ulam stability problem.

 

The original stability problem was posed by S.M. Ulam in 1940 and concerned approximate homomorphisms. The pursuit of solutions to this problem, but also to its generalizations and/or modifications for various classes of equations and inequalities, is an expanding area of research, and has led to the development of what is now called the Hyers–Ulam stability theory.

 

Comprised of contributions from eminent scientists and experts from the international mathematical community, the volume presents several important types of functional equations and inequalities and their applications in mathematical analysis, geometry, physics, and applied mathematics. It is intended for researchers and students in mathematics, physics, and other computational and applied sciences.