THE FIXED POINT ALTERNATIVE AND THE STABILITY OF FUNCTIONAL EQUATIONS

By Viorel Radu. 2003

527 citations recorded by the source corpus.

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Citations in the corpus

REMARKS ON ULAM STABILITY OF THE OPERATORIAL EQUATIONS (2009, methodology): “On the other hand by the analogy with the notion of the Ulam-Hyers stability in the theory of functional equation (see [14], [15], [7], [2], [9], [10]-[13], [21], [25], [26],.”
Fixed Point Theory and the Ulam Stability (2014, methodology): “At present, numerous authors follow Radu’s approach (see [20]) and make use of a theorem of Diaz and Margolis.”
On the stability of the additive Cauchy functional equation in random normed spaces (2008, methodology): “In 2003, Radu [20] proposed a new method for obtaining the existence of exact solutions and error estimations, based on the fixed point alternative.”
Ulam stability for a delay differential equation (2013, unknown): “Very important contributions to this subject were brought by Ulam [15], Rassias [10], Hyers et al. [4], Jung [5], Guo et al. [3], Kolmanovskii and Myshkis [6] and Radu [9].”
A fixed point approach to the stability of isometries (2007, unknown): “[7,22]).”
Applications of fixed point theorems to the Hyers-Ulam stability of functional equations–a survey (2012, methodology): “[38] Let E be a real normed space, F be a real Banach space, θ ∈ [0,∞), p ∈ [0,∞) \ {1} and f : E → F be such that ‖f(x+ y)− f(x)− f(y)‖ ≤ θ(‖x‖ + ‖y‖), x, y ∈ E.”
Approximately generalized additive functions in several variables (2010, methodology): “Recently, Cădariu and Radu [11] applied the fixed point method to the investigation of the Cauchy additive functional equation [12, 55].”
A fixed point approach to the stability of the cubic functional equation (2006, unknown): “[2], [12]).”
A Fixed Point Approach to the Stability of a Volterra Integral Equation (2007, methodology): “Using such a clever idea, they could present another proof for the Hyers-Ulam stability of that equation [13–15].”
Hyers–Ulam stability of delay differential equations of first order (2016, background): “For more details and further discussions concerning generalized Hyers–Ulam stability of functional equations, we refer the readers to [20], [26], [33]–[35], and [15], [19], [21], [22], [25] for the problem of differential equations.”
ULAM STABILITY OF ORDINARY DIFFERENTIAL EQUATIONS (2009, background): “[18], [ 19 ]). There are some results of this type for some dierential equations ([8],”