Introduction Sessa [9] generalized the notion of commuting maps given by Jungck [2] and introduced weakly commuting mappings. Further, Jungck [3] introduced more generalized commutativity called compatibility. In 1998, Jungck and Rhoades [4] introduced the notion of weakly compatible maps and showed that compatible maps are weakly compatible but converse need not true. Menger [5] introduced the...

Route suggestions for public transportation has been integrated to different mapping services such as Google Maps or Bing Maps. However, those suggestions are often found to be unreliable for the end-users, mainly because of two reasons. Firstly, these route-finding techniques do not consider traffic conditions on the roads. Secondly, routes are generalized for every user, completely ignoring t...