Cetin, ErbilTopal, F. Serap2019-10-272019-10-2720121085-33751085-3375https://doi.org/10.1155/2012/707319https://hdl.handle.net/11454/45486Let T subset of R be a periodic time scale in shifts delta(+/-). We use a fixed point theorem due to Krasnosel'ski(sic) to show that nonlinear delay in dynamic equations of the form x(Delta)(t) = -a(t)x(sigma)(t) + b(t)x(Delta)(delta(-)(k, t))delta(Delta)(-)(k, t) + q(t, x(t), x(delta_(k, t)), t is an element of T, has a periodic solution in shifts delta(+/-). We extend and unify periodic differential, difference, h-difference, and q-difference equations and more by a new periodicity concept on time scales.en10.1155/2012/707319info:eu-repo/semantics/openAccessArticleWOS:000308158700001Q1