Bielecki-Ulam stability of a hammerstein-type difference system

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dc.contributor.authorGul Rahmat
dc.contributor.authorSohail Ahmad
dc.contributor.authorMuhammad Sarwar
dc.contributor.authorKamaleldin Abodayeh
dc.contributor.authorSaowaluck Chasreechai
dc.contributor.authorThanin Sitthiwirattham
dc.contributor.correspondenceM. Sarwar; Department of Mathematics, University of Malakand, Khyber Pakhtunkhwa, Pakistan; email: sarwar@uom.edu.pk
dc.date.accessioned2025-07-07T18:16:38Z
dc.date.available2025-07-07T18:16:38Z
dc.date.issued2025
dc.description.abstractIn this study, we investigate the Bielecki-Ulam (B-U) stabilities of two forms of Hammerstein-type difference systems (HT-DS). Specifically, we consider the systems: (0.1){xm+1−xm=M¯mxm+F¯(m,xm,xhm)[∑[j=0][m]G¯(m,j)H¯(j,xj,xhj)]x0=b0,and (0.2){xm+1−xm=M¯mxm+F¯(m,xm,L¯xm,J¯xm)x0=b0,by establishing conditions under which a unique solution exists. We derive sufficient conditions for the existence and uniqueness of solutions that satisfy B-U stability criteria. To demonstrate the theoretical findings, we provide an illustrative example that confirms the validity of our results. • Purpose: In this study, we examine the Bielecki-Ulam (B-U) stabilities of two forms of Hammerstein-type difference systems (HT-DS) to understand the conditions necessary for solution uniqueness and stability. • Methodology: We analyze two specific systems characterized by distinct recursive nonlinear structures and employ the Banach contraction principle under the Bielecki norm to establish stability results. The theoretical development involves verifying boundedness and Lipschitz continuity of the nonlinear terms and ensuring that the involved operators satisfy contractive conditions. • Findings: We derive sufficient conditions (outlined in Theorems 2 and 3) under which the systems possess unique solutions and are shown to be Bielecki-Ulam stable (Theorems 4 and 5). Specifically, these conditions include boundedness of system coefficients, Lipschitz continuity of nonlinear mappings, and the fulfillment of a contraction inequality using the Bielecki norm. Illustrative examples are provided to confirm the applicability of the results. © 2025 The Author(s)
dc.identifier.citationMethodsX
dc.identifier.doi10.1016/j.mex.2025.103422
dc.identifier.issn22150161
dc.identifier.scopus2-s2.0-105008920799
dc.identifier.urihttps://repository.dusit.ac.th/handle/123456789/7300
dc.languageEnglish
dc.publisherElsevier B.V.
dc.rights.holderScopus
dc.subjectDifference equations
dc.subjectHammerstein type difference system (HT-DE)
dc.subjectUlam stability
dc.titleBielecki-Ulam stability of a hammerstein-type difference system
dc.typeArticle
mods.location.urlhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-105008920799&doi=10.1016%2fj.mex.2025.103422&partnerID=40&md5=e4a49c9eb3529532845de8ed452e9074
oaire.citation.volume15
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