oh, i totally get you. and i don't want to try to analyze your situation. (i am neither qualified, nor is it my place to do that) i am just making general comments how i would see the situation if it occurred to me.
the thing that i initially picked up on was when you said "When I stopped putting effort, even these relationship got eroded. This was the moment I realized that there is no such thing as friendship which author described." because i think it is possible to keep staying friends without putting in effort to keep in touch. the only effort that is needed is that if my friend contacts me, that i do not ignore them because that sends a confusing signal. but if we both stop communicating then we should be able to resume later. again, i am not saying that this should have happened to you. and it doesn't always happen to me like that either.
what i am trying to get at is, that just because you couldn't experience it yet, doesn't mean it doesn't exist.
good friends are rare. but they do exist.
Well, I would just talk with them as if nothing happened
which is what i would do too.
However, the conversation always end up with most of them asking something from me.
but then what happens? do they keep asking for favors without giving you the feeling that you are still friends? that would be unfortunate. and i would not know how to deal with that either. if it happens rarely and they are not big favors i might not think much of it. maybe it is just part of their struggle to keep in touch. maybe follow up with asking them something in return. how they have been, i don't know. this is something i struggle with, because i am uncomfortable with small talk. to start a conversation i need to have a reason, or a topic to talk about.
but what ever it is, it doesn't mean the friendship is over, or that it can't be reactivated. frankly, if someone is upset because i didn't keep in touch, then that's their problem. if they think, for you to be worthy of their friendship requires effort on your part, then they probably weren't good friends to begin with.
but the same goes the other way around. if others asking for favors is a problem, i'd think about why that is so.