A city may levy a special assessment against the real estate located in a business improvement district, to the extent of the special benefit thereto, for the purpose of paying all or any part of the total costs and expenses of performing any authorized work, except maintenance, repair, and reconstruction costs, within such district. The amount of each special assessment shall be determined by the city council sitting as a board of equalization. Assessments shall be levied in accordance with the method of assessment proposed in the ordinance creating the district. If the city council finds that the proposed method of assessment does not provide a fair and equitable method of apportioning costs, then it may assess the costs under such method as the city council finds to be fair and equitable. Notice of a hearing on any special assessments to be levied under the Business Improvement District Act shall be given to the landowners in such district by publication of the description of the land, the amount proposed to be assessed, and the general purpose for which such assessment is to be made one time each week for three weeks in a daily or weekly newspaper of general circulation published in the city. The notice shall provide the date, time, and place of hearing to hear any objections or protests by landowners in the district as to the amount of assessment made against their land. A direct appeal to the district court of the county in which such city is located may be taken from the decision of the city council in the same manner and under like terms and conditions as appeals may be taken from the amount of special assessments levied in street improvement districts in such city as now provided by law. All special assessments levied under the act shall be liens on the property and shall be certified for collection and collected in the same manner as special assessments for improvements and street improvement districts of the city are collected. If any part of a business improvement district overlaps with a riverfront development district in which a special assessment is already being levied pursuant to section 19-5313, the city creating the business improvement district shall not impose the business improvement district’s special assessment within the overlapping area.