Karatas, RamazanGelisken, AliAri, Murat2025-01-102025-01-1020242227-7390https://doi.org/10.3390/math12223531https://hdl.handle.net/20.500.13091/9766Rational difference equations have a wide range of applications in various fields of science. To illustrate, the equation xn+1=a+bxnc+dxn,n=0,1,..., known as the Riccati difference equation, has been applied in the field of optics. In this study, the global asymptotic stability of the difference equation xn+1=Axn-2k+j+1B+Cxn-(k+j)xn-2k+j+1,n=0,1,..., is proved. The solutions of this difference equation are obtained by applying the standard iteration method, and the periodicity of these solutions is determined. Furthermore, this difference equation represents a generalisation of the results obtained in previous studies.eninfo:eu-repo/semantics/openAccessDifference EquationStabilityGlobally AsymptoticallyBoundednessPeriodicityArticle10.3390/math122235312-s2.0-85211063103