Really?There are three types of feeding relationship identified in biology and it is arguable whether any of them occurs directly as a result of competition.
I presume by "three types of feeding relationship" you mean the trophic levels: producers, herbivores and predators.
And yes, organisms compete at all trophic levels. Producers compete for sunlight. Arboreal herbivores and herbivores with long necks out compete the grazers for leaves and fruit. And faster predators or social hunters often outcompete other predators.
[Where are the scavengers and saprophytes? An alternate classification lumps the herbivores, carnivores and scavengers together as consumers, and calls the saprophytes and related organisms decomposers, yielding these three: producers, consumers and decomposers]