Tyāga or giving up is an important concept found in the Hindu scriptures.
It has two aspects: giving away something to someone who needs it more; giving up an object feeling that it is not a necessity or even an obstacle to the way of life one has chosen.
The former is known as dāna (See DĀNA for details.) and the latter as vairāgya (renunciation). Dāna has been prescribed as a duty for the householders. Vairāgya is an essential qualification for one who aspires after saṁnyāsa or monastic life.
The Manusmṛti (8.389) forbids a householder from giving up his parents, wife and sons who depend upon him.
The Bhagavadgītā (18.2) gives a general definition of tyāga as giving up the fruits of all actions. It then categorises the tyāga of actions into three types: sāttvika, rājasika and tāmasika.
Sāttvika-tyāga consists in performing one’s prescribed duties but giving up attachment towards them as also the fruits thereof.
Giving up one’s prescribed duties because they entail a lot of physical exertion is rājasika-tyāga.
If the same is done out of delusion or confused understanding, it is tāmasika-tyāga (vide Bhagavadgītā 18.7-9).
The Bhagavadgītā, however, unequivocally declares that works like yajña (sacrifice), dāna (giving gifts) and tapas (austerities) should not be given up, but, must be performed. They always have a purifying effect.