Avatirya, Avatīrya: 3 definitions
Introduction:
Avatirya means something in Buddhism, Pali, Hinduism, Sanskrit. If you want to know the exact meaning, history, etymology or English translation of this term then check out the descriptions on this page. Add your comment or reference to a book if you want to contribute to this summary article.
In Hinduism
Shaivism (Shaiva philosophy)
Source: Brill: Śaivism and the Tantric TraditionsAvatīrya (अवतीर्य) refers to “taking up an incarnation”, as mentioned in the Malhar or Junwani copper plate inscription (647CE, see Bakker 2000 and 2015; Sanderson 2012).—Accordingly, “[…] reaching the present Kali age, the venerable Lord Lakulīśa took up an incarnation (avatīrya) and was born in the family of a Brahmin called Somaśarman. He was initiated into the Great Observance by him (?) [and became] the Moon of the World. Then by him, Musalīśa [was initiated], then, by the unbroken tradition starting with Soma, the local Master Rudrasoma, his disciple Tejasoma, whose pupil is the venerable Bhīmasoma […]”.

Shaiva (शैव, śaiva) or Shaivism (śaivism) represents a tradition of Hinduism worshiping Shiva as the supreme being. Closely related to Shaktism, Shaiva literature includes a range of scriptures, including Tantras, while the root of this tradition may be traced back to the ancient Vedas.
Purana and Itihasa (epic history)
Source: archive.org: Shiva Purana - English TranslationAvatīrya (अवतीर्य) refers to “having incarnated (in order to be beneficial to the worlds)”, according to the Śivapurāṇa 2.3.44 (“Menā regains consciousness”).—Accordingly, as Viṣṇu said to Menā: “[...] Brahmā and I are created thereafter. Then, with the three attributes, Śiva Himself, incarnated (avatīrya) in order to be beneficial to the worlds. The Vedas originated from Him. The gods sprang up from Him. Whatever mobile and immobile there is in the universe, sprang up from him. Who has described His form? By whom can it be known? Even Brahmā and I were not able to gauge him. [...]”.

The Purana (पुराण, purāṇas) refers to Sanskrit literature preserving ancient India’s vast cultural history, including historical legends, religious ceremonies, various arts and sciences. The eighteen mahapuranas total over 400,000 shlokas (metrical couplets) and date to at least several centuries BCE.
In Buddhism
Mahayana (major branch of Buddhism)
Source: academia.edu: A Study and Translation of the GaganagañjaparipṛcchāAvatīrya (अवतीर्य) refers to “having descended (from the open space)”, according to the Gaganagañjaparipṛcchā: the eighth chapter of the Mahāsaṃnipāta (a collection of Mahāyāna Buddhist Sūtras).—Accordingly: “Then five hundred widows, having departed from the city of Rājagṛha and proceeded to the place where the Bodhisatva Gaganagañja stayed, said this to him: ‘If you fulfill the wishes of all living beings, O Good man, please return our husbands’. Immediately after that, by the magical presence of the Bodhisatva Gaganagañja, five hundred men resembling their deceased husbands in colors, distinguishing marks, and appearances, having descended from the open space (gaganād avatīrya), settled down in front of the Bodhisatva Gaganagañja. [...]”.

Mahayana (महायान, mahāyāna) is a major branch of Buddhism focusing on the path of a Bodhisattva (spiritual aspirants/ enlightened beings). Extant literature is vast and primarely composed in the Sanskrit language. There are many sūtras of which some of the earliest are the various Prajñāpāramitā sūtras.
See also (Relevant definitions)
Full-text: Samsprish, Nabhastala, Kshiti, Abhinaya, Majj.
Relevant text
Search found 3 books and stories containing Avatirya, Avatīrya; (plurals include: Avatiryas, Avatīryas). You can also click to the full overview containing English textual excerpts. Below are direct links for the most relevant articles:
Garga Samhita (English) (by Danavir Goswami)
Verse 2.8.16 < [Chapter 8 - Description of Seeing Lord Kṛṣṇa]
Verse 2.8.48 < [Chapter 8 - Description of Seeing Lord Kṛṣṇa]
Vedic influence on the Sun-worship in the Puranas (by Goswami Mitali)
Part 7 - The Depiction of Sūrya in the Anthropomorphic Form < [Chapter 4 - Vedic Influence on the Sun-Worship in the Purāṇas]
Maha Prajnaparamita Sastra (by Gelongma Karma Migme Chödrön)
Appendix 2 - The location of Suvarṇabhūmi or Suvarṇadvīpa < [Chapter XVI - The Story of Śāriputra]