In　practical　applications,　people　sometimes　do　not　know　whether　the　estimated　function　is　smooth,　and　it　is　reasonable　to　consider　the　consistency　of　an　estimator.　Furthermore,　the　acquired　data　are　usually　contaminated　by　various　random　noises.　In　this　paper,　we　develop　the　wavelet　estimators　for　m-fold　convolutions　of　the　unknown　density　functions　and　consider　their　Lp　(1　＜=　p　＜=　infinity)　consistency　under　noiseless　and　additive　noise　situations,　respectively.　Finally,　simulation　studies　illustrate　the　good　performances　of　our　nonparametric　wavelet　estimators.　(C)　2018　Elsevier　B.V.　All　rights　reserved.