Browsing by Author "Bicer, Emel"

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New Theorems for Hyers-Ulam Stability of Lienard Equation With Variable Time Lags
(Lebanese Univ, 2018) Bicer, Emel; Tunc, Cemil
We investigate a modified Lienard equation (LE) with multiple variable time lags and find assumptions for the Hyers-Ulam stability (HUS) and Hyers-Ulam-Rassias stability (HURS) of the modified (LE) considered. We obtain two results on (HUS) and (HURS) of the equation considered where we use Banach's contraction principle (BCP).
Stability To a Kind of Functional Differential Equations of Second Order With Multiple Delays by Fixed Points
(Hindawi Ltd, 2014) Tunc, Cemil; Bicer, Emel
We discuss the stability of solutions to a kind of scalar Lienard type equations with multiple variable delays by means of the fixed point technique under an exponentially weighted metric. By this work, we improve some related results from one delay to multiple variable delays.
Hyers-Ulam Stability for a First Order Functional Differential Equation
(inst Teknologi Bandung, 2015) Tunc, Cemil; Bicer, Emel
In this paper, by using the fixed point method, we prove two new results on the Hyers-Ulam-Rassias and the Hyers-Ulam stability for the first order delay differential equation of the form y'(t) = F(t, y(t), y(t - tau)). Our results improve some related results in the literature.
On the Hyers-Ulam Stability of Second Order Noncanonical Equations With Deviating Argument
(inst Applied Mathematics, 2023) Bicer, Emel; Tunc, Cemil
. In this paper, we consider a nonlinear differential equation of second order including a variable deviating argument. In the noncanonical case, we investigate Hyers-Ulam stability of the considered differential equation on a finite interval. We prove three new theorems on the Ulam type stability. The proofs of the new outcomes of this paper are based on Banachs fixed point theorem. As the new contributions of the present paper, here, we improve and extend the outcomes that can be found in the earlier literature. The present paper also allows complementary outcomes for Hyers-Ulam stability of nonlinear differential equation of second order with and without deviating arguments. Finally, a concrete example with plots of the behaviours of solutions is given for illustrations.