Generalized Sin (1 / X) - Continuum, A Continuous Self Mapping The Stability Of The Periodic Orbit,

The stability of periodic orbits of self-maps on a closed, bounded interval was proven by L. Block in 1981. it means that, for any continuous self-map f on a closed interval I with a periodic orbit of period n, there is neighborhood U of f in C(I,I) such that for every g ∈ U and every position integer m with to the right of n in the Sarkovskii ordering, g has a periodic orbit of period m. In this paper, thestability of periodic orbits of self-maps on a generalized sin1/x-continuum isobtained.