[PDF] Top 20 Orthogonal stability of functional equations with the fixed point alternative

... several orthogonal- ity notions on a real normed space such as Birkhoff-James, Boussouis, Singer, Carlsson, unitary-Boussouis, Roberts, Phythagorean, isosceles and Diminnie (see ... See full document

... Let (X, D) be a generalized metric space. An operator T : X → X satisfies a Lipschitz condition with Lipschitz constant L if there exists a constant L ≥  such that d(Tx, Ty) ≤ Ld(x, y) for all x, y ∈ X. If the Lipschitz ... See full document

... f(x + y) = f (x) + f (y), (x, y ∈ A, x⊥y) (1.1) in which ⊥ is an abstract orthogonally was first investigated by S. Gudder and D. Strawther [7]. R. Ger and J. Sikkorska discussed the orthogonal stability of ... See full document

... Now we are able to formulate a stability result for the Jensen functional equation. Theorem 3.2. Let (X, · ) be a real normed linear space with dim ≥ 2 and with Birkhoff- James orthogonality and let (Y , · ) ... See full document

... 13. Nikodem, K: On quadratic set-valued functions. Publ Math Debrecen. 30, 297 – 301 (1984) 14. Nikodem, K: On Jensen ’ s functional equation for set-valued functions. Radovi Mat. 3, 23 – 33 (1987) 15. Nikodem, K: ... See full document

... in which ⊥ is an abstract orthogonality relation, was first investigated by Gudder and Strawther [3]. They defined ⊥ by a system consisting of five axioms and described the general semi-continuous real-valued solution of ... See full document

... The stability problem of functional equations originated from the following question of Ulam [18]: Under what condition does there exist an additive mapping near an approximately additive mapping? In ... See full document

... The stability problem of functional equations originated from a question of Ulam 12 concerning the stability of group ...Hyers-Ulam stability or as Hyers- Ulam-Rassias stability ... See full document

... a fixed point method was proposed, by showing that many theorems concerning the stability of Cauchy, Jensen, quadratic, cubic, quartic, and monomial functional equations are ... See full document

... Hyers-Ulam-Rassias stability of functional ...several stability problems for various func- tional equations have been investigated in [, , , –, , ...quadratic functional ... See full document

... the fixed point alternative. The stability of several functional equations have been extensively investigated by a number of mathematicians and there are many interesting results ... See full document

... The fixed point alternative methods are implemented to give generalized Hyers-Ulam-Rassias stability for the Pexiderized quadratic functional equation in the fuzzy ...the ... See full document

... In the last section, we prove the stability problem in the sense of Hyers-Ulam-Rassias for the functional equations 1.1 and 1.2 on Multi-Banach spaces by using fixed point approach.. We [r] ... See full document

... The stability problem of functional equations originated from a question of Ulam 1 concerning the stability of group ...Hyers-Ulam stability of functional ...The stability ... See full document

... The stability concept that was introduced by Rassias’ theorem provided a large influence to a number of mathematicians to develop the notion of what is known today with the term Hyers-Ulam-Rassias stability ... See full document

... of stability theory of functional equations for the proof of new fixed point theorems with ...the fixed point method, the stability problems of several ... See full document

... quintic functional equation f x 3y − 5fx 2y 10fx y − 10fx 5fx − y − fx − 2y 120fy and the sextic functional equation fx 3y − 6fx 2y 15f x y − 20f x 15f x − y − 6f x − 2y f x − 3y 720f y ...the ... See full document

... general functional equations one can ask the following question ...given functional inequality, when can assert that the solutions of the inequality lie near to the solutions of the strict equation? ... See full document

... of functional equations is the following: “When is it true that a function which approximately satisfies a functional equation must be close to an exact solution of the equation?” If the problem ... See full document

... non-linear functional analysis involved is the stability problem of functional equations as follows: “When is it true that a mathematical object satisfying a certain property approximately ... See full document