All legal publications and notices of whatever kind or character that may by law be required to be published a certain number of days or a certain number of weeks shall be legally published when they have been published in one issue in each week in a daily, semiweekly, or triweekly newspaper, such publication in such daily, semiweekly, or triweekly paper or papers to be made upon any one day of the week upon which such paper is published, except Sunday. Nothing in this section shall be construed as preventing the publication of such legal notices and publications in weekly newspapers. Any newspaper publishing such legal notices or publications, as hereinbefore provided, must be otherwise qualified under existing law to publish such notices or publications. All legal publications and all notices of whatever kind or character that may be required by law to be published a certain number of days or a certain number of weeks, shall be and hereby are declared to be legally published when they shall have been published once a week in a weekly, semiweekly, triweekly, or daily newspaper for the number of weeks, covering the period of publication. For the purpose of this section, when a newspaper is published regularly four or more times each week, it shall be deemed a daily newspaper.