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In this paper, we introduce an iterative numerical method to solve systems of nonlinear equations. The third-order convergence of this method is analyzed. Several examples are given to illustrate the efficiency of the proposed method.
We establish a generalized Ulam-Hyers stability theorem in a Šerstnev probabilistic normed space briefly, Šerstnev PN-space endowed with ΠM. In particular, we introduce the notion of approximate Jensen mapping in PN-spaces and prove that if an approximate Jensen mapping in a Šerstnev PN-space is continuous at a point then we can approximate it by an… (More)
In this article, we prove the Hyers-Ulam stability of exact second-order linear differential equations. As a consequence, we show the Hyers-Ulam stability of the following equations: second-order linear differential equation with constant coefficients, Euler differential equation, Hermite's differential equation, Cheybyshev's differential equation, and… (More)
We show that, given a weak compactness condition which is always satisfied when the underlying space does not contain an isomorphic copy of c 0 , all the operators in the weakly closed algebra generated by the real and imaginary parts of a family of commuting scalar-type spectral operators on a Banach space will again be scalar-type spectral operators,… (More)
We show that a quaternary Jordan derivation on a quaternary Banach algebra associated with the equation f (x + y + z 4) + f (3x − y − 4z 4) + f (4x + 3z 4) = 2f (x). is satisfied in generalized Hyers–Ulam stability.