Ahmet YantirDuygu SoyogluYantir, AhmetSoyoglu, Duygu2025-10-0620151303-50102651-477X10.15672/HJMS.20154494122-s2.0-84961678021http://dx.doi.org/10.15672/HJMS.2015449412https://gcris.yasar.edu.tr/handle/123456789/6659https://doi.org/10.15672/HJMS.2015449412https://search.trdizin.gov.tr/en/yayin/detay/174004https://search.trdizin.gov.tr/en/yayin/detay/480160In this article we prove an existence theorem regarding the weak solutions to the hyperbolic-type partial dynamic equation z(Gamma Delta)(x y) = f(x y z(x y)) x(x 0) = 0 z(0 y) = 0 x is an element of T-1 y is an element of T-2 in Banach spaces. For this purpose by generalizing the definitions and results of Cichon et. al. we develop weak partial derivatives double integrability and the mean value results for double integrals on time scales. DeBlasi measure of weak noncompactness and Kubiaczyk's fixed point theorem for the weakly sequentially continuous mappings are the essential tools to prove the main result.Englishinfo:eu-repo/semantics/closedAccessHyperbolic partial dynamic equation, Banach space, measure of weak noncompactness, time scaleDIFFERENTIAL-EQUATIONS, CAUCHY-PROBLEM, INTEGRATION, EXISTENCE, SETHyperbolic Partial Dynamic EquationMeasure of Weak NoncompactnessMatematikBanach SpaceTime ScaleBilgisayar Bilimleri, Teori Ve MetotlarArticle