In this paper, we investigate the stability of an additive-quadratic-quartic functional equation f(x+2y)+f(x-2y) - 2f(x+y) - 2f(-x-y) - 2f(x-y) - 2f(y-x)+4f(-x)+2f(x) - f(2y) - f(-2y)+4f(y)+4f(-y)=0 by the direct method in the sense of Găvruta.
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In this paper, we obtain Hyers-Ulam stability of the functional equations f(x+y, z+w) + f(x-y, z-w) = 2f(x, z) + 2f(y, w), f(x+y, z-w) + f(x-y, z+w) = 2f(x, z) + 2f(y, w) and f(x+y, z-w) + f(x-y, z+w) = 2f(x, z) - 2f(y, w) in 2-Banach spaces. The quadratic forms ax2+bxy+cy2, ax2+by2 and axy are solutions of the above functional equations, respectively.
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In this paper, existence and uniqueness of solution for a coupled impulsive Hilfer-Hadamard type fractional differential system are obtained by using Kransnoselskii’s fixed point theorem. Different types of Hyers-Ulam stability are also discussed. We provide an example demonstrating consistency to the theoretical findings.
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In this manuscript, we deal with a class and coupled system of implicit fractional differential equations, having some initial and impulsive conditions. Existence and uniqueness results are obtained by means of Banach’s contraction mapping principle and Krasnoselskii’s fixed point theorem. Hyers–Ulam stability is investigated by using classical technique of nonlinear functional analysis. Finally, we provide illustrative examples to support our obtained results.
In this paper, we present a Hyers–Ulam stability result for the approximately linear recurrence in Banach spaces. An example is given to show the results in more tangible form.
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We have proved the Hyers-Ulam stability and the hyperstability of the quadratic functional equation f(x+y+z) +f(x+y−z) +f(x−y+z) +f(−x+y+z) = 4[f(x) +f(y) +f(z) ] in the class of functions from an abelian group G into a Banach space.
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We establish the Hyers-Ulam stability (HUS) of certain first-order linear constant coefficient dynamic equations on time scales, which include the continuous (step size zero) and the discrete (step size constant and nonzero) dynamic equations as important special cases. In particular, for certain parameter values in relation to the graininess of the time scale, we find the minimum HUS constants. A few nontrivial examples are provided. Moreover, an application to a perturbed linear dynamic equation is also included.
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