## 5 Discussion
The availability isochrone did not cover 13 municipalities' districts, which were split into four zones A-D as shown in Figure 5, as well as the Borik (residential area with city park) district placed in the middle of the municipality's area. Respondents' opinions about the extension of the bike-sharing stations into the districts lacking thisservice were collected in questions Q5, Q6, and Q7. The respondents proceeded logically, and the primacy of the city districts of Zavodie and Budatin is valid. These districts with lack bike-sharing stations are the two closest districts to the city center, located in its immediate vicinity, and the addition of public bicycle stations would be very acceptable (Zavodie in zone A to the west and Budatin in zone D to the north of the center). The identified extension requirements for the bike-sharing service are also reflected in the population estimates of underserved areas living in the area uncovered by the service in Table 5.  
The combination of spatial analysis (isochrone mapping and heatmaps) and the social survey allowed for cross-validation of findings. For example, areas identified as underserved in the spatial analysis (zones A-D) strongly corresponded with the locations respondents most frequently highlighted for station expansion (Q5 and Q6). This alignment strengthens the justification for proposed station placements and shows the value of integrating objective GIS-based data with subjective user experience to shape a future expansion strategy that is both evidence-based and user-informed. The busiest bike-sharing stations showed heatmaps in Figure 4 in the city center (main square close to the train and bus station) and in the middle of the biggest residential Vlince district. The availability of isochrones fully covered the city center, but still respondents proposed the extension of bike-sharing stations to new locations: train station, bus station, streets known for the headquarters of many companies, etc. Problems can be caused by several reasons. The city that does not own the necessary land appears as the most likely, also in cases with Borik, especially the city park area, and in other requiring districts in zones A-D mentioned above. On the other hand, the low usability of bike stations with fewer than 1000 rentals or returns also showed up in the spatial analysis. Reasons for low demand for the service can be split up into three groups. First, the location of the bike-sharing station is not in a well-accessible area, or it is located at a higher altitude (like bike stations UNIZA, Lesopark, Namestie Mladosti). The rebalancing of city-wide stations to maintain bike availability on the stations is an important issue for bike-sharing service [84]. Then, the bike station does not cover a large population in its isochronous availability (OC Max, FRI). And third, the bike-sharing station is located on the outskirts of the municipality for nearby company employees (DPMZ Kvacalova, Stanica Zilina-Zariecie, OC IDEA). Even though multiple methods were used for complex evaluation of the bike-sharing system in the chosen city Zilina (4 th biggest city in Slovakia, identified as a small urban area), the analysis was not related to public transport as one of the indicators of bike-sharing service efficiency. The relationship between bike-sharing services and public transport offers a sustainable urban mobility system [57]. Ref. [50] added that bike-sharing systems complement or replace other ways of transit. The relationship between public transport and bike-sharing service depends upon the length of the trip [85], and wider data, like from a public transport provider or extension of the questionnaire aimed at public transportation, would be needed for the evaluation. The questionnaire was completed by 354 users of the bike-sharing system in Zilina, which is more than required (266 respondents). However, more than 60% of respondents stated their status as students.