In a rather broad brushstroke, Christians are instructed “that supplications, prayers, intercessions, and giving of thanks be made for all men” (1 Tim. 2:1). ALL men! Does that really mean “all”? Well, in James 5:16, we are told to 
“pray for one another” (without any qualifiers limiting those prayers), and in Matthew 5:44, we are told to “pray” for our “enemies” and those who mistreat us (without any qualifiers limiting those prayers). We are to pray for all!
All that is involved in “praying for others” is not specifically spelled out, and each of us surely has our own ideas of what “praying for others” entails. But may I make a suggestion for each of us? When we pray for our enemies, when we pray for those who mistreat us, when we pray for brethren with whom we don’t have the best relationship, rather than merely mentioning their name or praying for them to change, what if we included in that prayer, “…And loving Father, please help me to examine myself and to have a better attitude toward them”? Prayer is not just about changing the world and changing other people. Prayer ought to change me!