When a notice is required to be given by publication in a newspaper, it shall mean a newspaper published in the county where the subject matter is situated, pending or to be heard, or a newspaper published within the State which has a general circulation. In any case, in its discretion, the court may cause such notice to be further published in a newspaper which circulates in the neighborhood of the persons interested. Whenever a notice of any kind is required to be given by publication in a newspaper prior to a certain date for a certain number of weeks successively, it may be given by an insertion prior to such date once a week, for the number of successive weeks required, either in a daily, semiweekly, or weekly newspaper. If such publication is in a daily or semiweekly newspaper, such notice shall be inserted on the same day of each successive week.