In this paper, we prove the Hyers-Ulam stability and the Hyers-Ulam-Rassias stability of the following two functional equationswhich is an open problem raised by Berinde and Khan [
In this paper, we generalize two types of Volterra integral equations given on time scales and examine their Hyers-Ulam and Hyers-Ulam-Rassias stabilities. We also prove these stability results for the non-homogeneous nonlinear Volterra integral equation on time scales and provide an example to support these results. Moreover, we show that the general Volterra type integral equation given on time scales has the Hyers-Ulam-Rassias stability. Our results extend and improve some recent developments announced in the current literature.
In this paper, we introduce the concepts of the Ulam-Hyers-Rassias stability and the limit shadowing property of a fixed point problem and the P-property of a mapping in partial cone b-metric space. Also, we give such results by using the mapping which is studied by Fernandez et al. (Filomat 30(10) (2016)) in partial cone b-metric space and provide some numerical examples to support our results. The results presented here extend and improve some recent results announced in the current literature.
In this paper, we show that the iterative sequence which is a simplified form of the iteration method introduced by Ullah and Arshad (SpringerPlus, (2016)5:1616), is convergent strongly to the solution of a nonlinear Volterra integral equation with delay in a complete metric space. Furthermore, we prove a data dependence result for the solution of this integral equation.
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