... The stability problem for the **cubic** **functional** **equation** was proved by Jun and Kim [21] for mappings f : X ® Y, where X is a real normed space and Y is a Banach space. In this article, we show that ...

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... the **cubic** **functional** **equation** was proved by Jun and Kim [5] for mappings f: X ® Y, where X is a real normed space and Y is a Banach ...of **cubic** **functional** **equation** were discussed ...

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... of **equation** g ax a s gx a, s ∈ N, a ≥ 2 in random normed spaces and derive from it results on stability of **equation** f4x 10f2x − ...additive-**cubic** **functional** **equation** ...linear ...

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... -Dimensional **Cubic** **Functional** **Equation** in Felbin’s Type Spaces: Direct and Fixed Point Methods, International Conference on Mathematical Sciences, (ICMS 2014), Elsevier Publication, 81-88, ...

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... We now investigate the generalized Hyers-Ulam-Rassias stability problem for **functional** **equation** 1.6. From now on, let X be a real vector space, and let Y be a Banach space. Now before taking up the main ...

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... Intmodellingtappliedtproblemstonlytpartialtinformationtmaytbet knownt(or)ttheretmaytbetatdegreetoftuncertaintytintthetparame terstusedtintthetmodeltortsometmeasurementstmaytbetimpreci se[r] ...

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... Hyers’ theorem was generalized by Aoki 15 for additive mappings and by Th. M. Rassias 16 for linear mappings by considering an unbounded Cauchy diﬀerence. The paper of Th. M. Rassias 16 has provided a lot of influence in ...

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... In this paper, we consider the general solution of 1.5 and prove the stability theorem of this equation in the space Rn of Schwartz tempered distributions and the space Ᏺ Rn of Fouri[r] ...

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... 19. Ulam, SM: Problems in Modern Mathematics. Chapter VI. Science Editions. Wiley, New York (1964) 20. Hyers, DH: On the stability of the linear **functional** **equation**. Proc. Natl. Acad. Sci. USA 27, 222-224 ...

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... a **functional** **equation** is related to the question of Ulam [] concerning the stability of group homomorphisms and aﬃr- matively answered for Banach spaces by Hyers ...

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... of **functional** equations araised as follows: 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 ...

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... that **Equation** (1.2) is called a **cubic** **functional** **equation** and every solution of this **cubic** **functional** **equation** is said to be a **cubic** func- ...a **cubic** ...

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... the **functional** **equation** (2), which is called a **cubic** **functional** **equation** and every solution of the **cubic** **functional** **equation** is said to be a **cubic** ...

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... the **functional** **equation** 1.2, which is called a **cubic** **functional** **equation** and every solution of the **cubic** **functional** **equation** is said to be a **cubic** ...

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... **equation**. Every solution of the **cubic** **functional** **equation** is said to be a **cubic** mapping. Jun and Kim proved that a mapping f between two real vector spaces X and Y is a solution of 1.1 ...

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... is thus called a **cubic** **functional** **equation**. Every solution of the **cubic** **functional** **equation** is said to be a **cubic** function. Also, Jun and Kim proved that a function f ...

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... a **cubic** **functional** **equation**, because the **cubic** function f (x) = cx 3 is a solution of the **equation** ...the **functional** **equation** ...

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... additive **functional** equa- tion, the quadratic **functional** **equation** ...the **cubic** **functional** **equation** (.) and the quartic **functional** **equation** ...

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... 1.3, which is thus called a **cubic** **functional** **equation**. Every solution of the **cubic** **functional** **equation** is said to be a **cubic** function. Jun and Kim proved that a function f ...

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... Now, we will investigate the stability of the given cubic functional equation (1) using the alternative fixed point.. Before proceeding the proof, we will state the theorem, the alterna[r] ...

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