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E-book

Title Stability of some advanced functional equations in various spaces / Hemen Dutta, Vediyappan Govindan, Choonkil Park, R. Vadivel
Published Cham : Springer, 2023

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Description 1 online resource (260 p.)
Series Studies in Systems, Decision and Control ; v. 479
Studies in systems, decision and control ; v. 479.
Contents Intro -- Preface -- Contents -- About the Authors -- 1 Functional Equations -- 1.1 Fundamentals of Functional Equation -- 1.2 Definition of Functional Equations -- 1.3 Solution of Functional Equations -- 1.4 Applications of Functional Equations -- 1.5 Stability of Functional Equations -- 1.6 Fixed Point Theory on Stability of Functional Equations -- 2 Additive Functional Equations -- 2.1 Additive Functional Equation -- 2.2 General Solution of Additive Functional Equation -- 2.3 Additive Functional Equation: Odd Case-Direct Method -- 2.4 Functional Equation: Odd Case-Fixed Point Method
2.5 Examples -- 3 Additive Functional Equations in Banach Algebras -- 3.1 Banach Algebra-Additive Functional Equation -- 3.2 Additive Functional Equation: Odd Case-Direct Method -- 3.3 Additive Functional Equation: Odd Case-Fixed Point Method -- 4 n-Dimensional Additive Functional Equations in Random 2-Normed Spaces -- 4.1 n-Dimensional Additive Functional Equation -- 4.2 Solutions of n-Dimensional Additive Functional Equation -- 4.3 n-Dimensional Additive Functional Equation-Direct Method -- 4.4 n-Dimensional Additive Functional Equation-Fixed Point Method -- 5 Quadratic Functional Equations
5.1 Quadratic Functional Equation -- 5.2 General Solution of Quadratic Functional Equation -- 5.3 Quadratic Functional Equation: Even Case-Direct Method -- 5.4 Stability Quadratic Functional Equation: Even Case-Fixed Point Method -- 5.5 Applications -- 6 Quadratic Functional Equations in Banach Algebras -- 6.1 Banach Algebra-Quadratic Functional Equation -- 6.2 Quadratic Functional Equation: Even Case-Direct Method -- 6.3 Quadratic Functional Equation: Even Case-Fixed Point Method -- 7 n-Dimensional Quadratic Functional Equations in Generalized 2-Normed Spaces
7.1 n-Dimensional Quadratic Functional Equation -- 7.2 Solution of n-Dimensional Quadratic Functional Equation -- 8 Additive-Quadratic Functional Equations -- 8.1 Additive Quadratic Functional Equation -- 8.2 Additive Quadratic Functional Equation: Mixed Case-Direct Method -- 8.3 Additive Quadratic Functional Equation: Mixed Case-Fixed Point Method -- 9 Additive-Quadratic Functional Equations in Banach Algebras -- 9.1 Banach Algebra-Additive Quadratic Functional Equation -- 9.2 Additive Quadratic Functional Equation: Mixed Case-Direct Method
9.3 Additive Quadratic Functional Equation: Mixed Case-Fixed Point Method -- 10 3-Dimensional Cubic Functional Equations -- 10.1 3-Dimensional Cubic Functional Equation -- 10.2 General Solution of 3-Dimensional Cubic Functional Equation -- 10.3 3-Dimensional Cubic Functional Equation-Direct Method -- 10.4 3-Dimensional Cubic Functional Equation-Fixed Point Method -- 10.5 Stability of 3-Dimensional Cubic Functional Equation-Direct Method -- 10.6 Stability of 3-Dimensional Cubic Functional Equation-Fixed Point Method -- 10.7 Examples -- 11 4-Dimensional Cubic Functional Equations
Summary The book aims to present several new results concerning solution and various stabilities of some functional equations in various spaces. The chapters consider various spaces to investigate stabilities justifying that stability results hold well in those spaces. It also includes results proving new insight to analyze approximate solutions to a given equation whenever uncertainty occurs. The presentation of the book should be useful for graduated students and researchers interested in the theory of functional equations to understand the useful ideas involved and problems to study further
Notes 11.1 4-Dimensional Cubic Functional Equation
Subject Functional equations.
Form Electronic book
Author Dutta, Hemen, 1981-
Govindan, Vediyappan
Park, Choonkil.
Vadivel, R
ISBN 9783031337048
3031337042