Ulam Stability of Zero Point Equations

On the Ulam stabilities of nonlinear integral equations and integro‐differential equations

“…Later, as the next steps, the concepts of the Hyers–Ulam stability (HUS), the Hyers–Ulam–Rassias stability (HURS) and some generalized HURS were constructed by researchers during the investigations. Hence, the Ulam stability, the HUS, the HURS, the generalized HURS, the existence and uniqueness of solutions were applied and investigated extensively to FEs, ordinary differential equations (ODEs), functional differential equations (FDEs), integro‐differential equations (IDEs), integral equations (IEs), partially differential equations (PDEs), fractional differential equations (FrDEs) and so on by numerous researchers (see, in particular, the books or papers of Abbas et al [2], Akkouchi [3], Biçer and Tunç ([4–6]), Castro and Simoes [7, 8], Huang and Li [9], Janfada and Sadeghi [10], Jung ([11–13]), Khan et al [14], Kucche et al ([15, 16]), Kucche and Shikhare [17], Li and Shen [18, 19]), Lungu and Popa [20], Ngoc and Vinh [21], Obloza [22], Otrocol and Ilea [23], Petru et al ([24–26]), Popa and Raça [27], Rus and Petruşel [28], Tunç and Biçer [29], Radu [30], Petruşel and Rus [31] and the references therein). We should also mention that, today, the theory of the Ulam stabilities is one of the most important topics of the modern theory of FEs, ODEs, FDEs, IDEs, IEs, PDEs, FrDEs and more.…”

Best Decision-Making on the Stability of the Smoke Epidemic Model via Z-Numbers and Aggregate Special Maps

“…To clarify the issue, let us introduce the notion of Ulam-type stability of an operator equation [16,17]. We consider the Banach space (X , ∥ .…”