We discuss a differential equations treatment of the implicit functions problem. Our approach allows a precise and complete description of the solution, of continuity and differentiability properties. The critical case is also considered. The investigation is devoted to dimension two and three, but extensions to higher dimension are possible. MSC: 26B10, 34A12, 53A05. keywords: implicit functio...

The aim of the present paper is to introduce the concept of joint common limit range property ((JCLR) property) for single-valued and set-valued maps in non-Archimedean fuzzy metric spaces. We also list some examples to show the difference between (CLR) property and (JCLR) property. Further, we establish common fixed point theorems using implicit relation with integral contractive condition. Se...

The asymptotical limit of the trajectory deened by the continuous steepest descent method for a proper closed convex function f on a Hilbert space is characterized in the set of minimizers of f via an asymp-totical variational principle of Brezis-Ekeland type. The implicit discrete analogue (prox method) is also considered.

Uncertainty is an inevitable factor that influences the function analysis, design, and safe operation in engineering systems. Due to complexity property unclear failure mechanism, uncertainty intrinsic of slope engineering. Hence, stability analysis design cannot meet demands based on traditional deterministic method, which deal with uncertainty. In this study, a practical reliability approach ...

We present in this note an alternative yet simple approach to obtain the Devaney-Nitecki horseshoe region for the Hénon maps. Our approach is based on the anti-integrable limit and the implicit function theorem. We also highlight an application to the logistic maps.