A Fixed Point Approach to the Stability of a Volterra Integral Equation

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We will apply the fixed point method for proving the Hyers-Ulam-Rassias stability of a Volterra integral equation of the second kind.

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Applications of fixed point theorems to the Hyers-Ulam stability of functional equations–a survey (2012, methodology): “The fixed point method is also a useful tool for proving the Hyers– Ulam stability of differential (see [7, 28]) and integral equations (see for instance [12, 21, 27]).”
ULAM STABILITY OF ORDINARY DIFFERENTIAL EQUATIONS (2009, background): “For the Ulam stability of some integral equations see [13] and [21].”
Hyers‐Ulam‐Rassias stability of nonlinear integral equations through the Bielecki metric (2018, unknown): “and jyðxÞ−y0ðxÞj≤ σðbÞ 1−M 2þ Lη ð Þ ð ÞσðaÞ (26)”
Ulam-Hyers Stability for Operatorial Equations (2011, result): “Our results are connected to some recent papers of Castro-Ramos [3], Jung [9] and Rus [15], [16] (where integral and differential equations are considered), Rus [13] and Petru-PetruşelYao [11] (where the Ulam-Hyers stability of the fixed point problem are discussed).”
Ulam stability for a delay differential equation (2013, result): “Our results are connected to some recent papers of Castro and Ramos [2] and Jung [5] (where integral and differential equations are considered), Bota-Boriceanu and Petrușel [1], and Petru et al.”