03871nam 2200445 450 991058332980332120230120002722.00-12-809830-90-12-809829-5(CKB)4100000001786945(MiAaPQ)EBC5217415(EXLCZ)99410000000178694520180209h20182018 uy 0engurcnu||||||||rdacontentrdamediardacarrierUlam stability operators /authors, Janusz Brzdek [and three others] ; series editor, Themistocles M. RassiasLondon, England :Academic Press,2018.©20181 online resource (238 pages) illustrationsMathematical Analysis and its ApplicationsIncludes bibliographical references at the end of each chapters and index.Machine generated contents note:1.Introduction to Ulam stability theory --1.Historical background --2.Stability of additive mapping --3.Approximate isometries --4.Other functional equations and inequalities in several variables --5.Stability of functional equations in a single variable --6.Iterative stability --7.Differential and integral equations --8.Superstability and hyperstability --9.Composite type equations --10.Nonstability --References --2.Operators in normed spaces --1.Introduction --2.Ulam stability with respect to gauges --3.Closed operators --4.Some differential operators on bounded intervals --5.Stability of the linear differential operator with respect to different norms --6.Some classical operators from the approximation theory --6.1.Bernstein operators --6.2.Szasz-Mirakjan operators --6.3.Other classical operators --6.4.Integral operators --6.5.Bernstein-Schnabl operators --References --3.Ulam stability of differential operators --1.Introduction --2.Linear differential equation of the first order --3.Linear differential equation of a higher order with constant coefficients --4.First-order linear differential operator --5.Higher-order linear differential operator --6.Partial differential equations --7.Laplace operator --References --4.Best constant in Ulam stability --1.Introduction --2.Best constant for Cauchy, Jensen, and Quadratic functional equations --3.Best constant for linear operators --3.1.Stancu operators --3.2.Kantorovich operators --3.3.An extremal property of K(Bn) --4.Ulam stability of operators with respect to different norms --References --5.Ulam stability of operators of polynomial form --1.Introduction --2.Auxiliary results --3.A general stability theorem --4.Complementary results for the second-order equations --5.Linear difference equation with constant coefficients --6.Difference equation with a matrix coefficient --7.Linear functional equations with constant coefficients --8.Linear differential equations --9.Integral equations --References --6.Nonstability theory --1.Preliminary information --2.Possible definitions of nonstability --3.Linear difference equation of the first order --4.Linear difference equation of a higher order --5.Linear functional equation of the first order --6.Linear functional equation of a higher order --References.Functional equationsFunctional equations.515.75Brzdȩk Janusz1249176Brzdȩk JanuszRassias Themistocles M.MiAaPQMiAaPQMiAaPQBOOK9910583329803321Ulam stability operators2894942UNINA