"Shivoham" (I am Shiva) is well known conventional term which represent the Self is Shiva. But I have not yet found similar for Vishnu as well like "Vishnuraham" (I am Vishnu). It might be because almost all Vaishnava sects are either dual, semi -dual or qualified dual. Does any acharya or scripture used such (or similar) term?
Note that I want a phrase like Shivoham not a sentence to demonstrate the Self is Vishnu.
The Brahmanuchintanam which is attributed to Adi Shankaracharya mentions the term "Vishnuraham":
ahaM viShNurahaM viShNurahaM viShNurahaM hariH |
kartR^ibhoktrAdikaM sarvaM tadavidyotthameva cha || 13||
English Translation: I am Vishnu, I am Vishnu, I am Vishnu, I am Hari. I am bliss, I am full, unborn, and immortal.
Prahlada, in the Yoga Vashista too, mentions the term "Vishnuraham":
avishnuh puujayavishnum
na puuja phalabhagbhavet |
vishnurbhuutvaa yajjedvishnum
ayam vishnuraham sthitah || (Yoga Vashistha, Sarga 31, Sloka 40)
English Translation: The prayer of a Non-Vishnu to Vishnu will not yield any result. Therefore, a seeker has to become Vishnu and then worship Him to achieve emancipation.
There are multiple places in Gopala Tapani Upanishad, Uttara Tapani where phrase gopalo'ham and so'ham occurs.
2.38-40:
tasmād eva paro rajaseti so’ham ity avadhāryātmānaṁ gopālo’ham iti bhāvayet, sa mokṣam aśnute | sa brahmatvam adhigacchati | sa brahma-vid bhavati yo gopān jīvān vai ātmatvenāsṛṣṭi-paryantam ālāti hy oṁ tat sad gopālo bhavati, yat so’haṁ || paraṁ brahma kṛṣṇātmako nityānandaika-rūpaḥ so’ham || etad gopāla eva paraṁ satyam abādhitam so’ham ity ātmānam ādāya manasaikyaṁ kuryāt || ātmānaṁ gopālo’ham iti bhāvayet | sa evāvyakto’nanto nityo gopālaḥ ||
Therefore, in the consciousness that “I am the divine Lord beyond the mode of passion,” one should meditate on the self, [thinking], “I am Gopåla.” Such a person enjoys the liberated state. He attains the status of Brahman. He becomes a knower of Brahman. He who from the very beginning of creation takes the living entities, known as the gopas, as his very self is verily Gopåla. One should think: The truth is identical with the sacred syllable Om, and I am he. I am he who is the Supreme Brahman, the essence of whom is Krishna, whose only form is one of eternal bliss. That Gopåla is the unobstructed Supreme Truth. Thinking, “I am he,” one should take control of the self and concentrate the mind. One should then meditate on the self, thinking, “I am Gopåla.” Verily Gopåla is unmanifest, infinite, and eternal.
2.46:
gopālo’ham ajo nityaḥ pradyumno’haṁ sanātanaḥ | rāmo’ham aniruddho’ham ātmānam arcayed budhaḥ
I am Gopåla, unborn and eternal. I am the everlasting Pradyumna. I am Råma and I am Aniruddha. The wise man thus worships the åtmå.
However these phrases are just one type of devotion and a state in which devotee identifies himself with object of devotion.
Baladeva Vidyabhusana explains these phrases in Govinda Bhasya, commentary on Brahma Sutras at Sutras 3.3.46 & 3.3.47. Explanation here.
In Bhagavata Purana too a similar phrase krsno'ham is seen:
gati-smita-prekṣaṇa-bhāṣaṇādiṣu priyāḥ priyasya pratirūḍha-mūrtayaḥ asāv ahaṁ tv ity abalās tad-ātmikā nyavediṣuḥ kṛṣṇa-vihāra-vibhramāḥ
SB 10.30.3 — Because the beloved gopīs were absorbed in thoughts of their beloved Kṛṣṇa, their bodies imitated His way of moving and smiling, His way of beholding them, His speech and His other distinctive features. Deeply immersed in thinking of Him and maddened by remembering His pastimes, they declared to one another, “I am Kṛṣṇa!”
kasyāñcit sva-bhujaṁ nyasya calanty āhāparā nanu kṛṣṇo ’haṁ paśyata gatiṁ lalitām iti tan-manāḥ
SB 10.30.19 — Another gopī, her mind fixed on Kṛṣṇa, walked about with her arm resting on the shoulder of a friend and declared, “I am Kṛṣṇa! Just see how gracefully I move!”
This chapter of Vishnu Purana also has the words krsno'ham(5.13.25&26)
kṛṣṇe nibaddhahṛdayā idam ūcuḥ parasparam kṛṣṇo 'ham etat lalitaṃ vrajāmy ālokyatāṃ gatiḥ anyā bravīti kṛṣṇasya mama gītir niśamyatām duṣṭa kāliya tiṣṭhātra kṛṣṇo 'ham iti cāparā bāhum āsphoṭya kṛṣṇasya līlāsarvasvam ādade
Many of the Gopīs imitated the different actions of Kṛṣṇa, and in his absence wandered through Vrindavan, representing his person. “I am Kṛṣṇa,” cries one; “behold the elegance of my movements.” “I am Kṛṣṇa,” exclaims another; “listen to my song.” “Vile Kālīya, stay! for I am Kṛṣṇa,” is repeated by a third, slapping her arms in defiance. A fourth calls out, “Herdsmen, fear nothing; be steady; the danger of the storm is over, for, lo, I lift up Govarddhana for your shelter.” And a fifth proclaims, “Now let the herds graze where they will, for I have destroyed Dhenuka.”
Adi Shankaracharya mentions Narayanoham in Vivekachudamani,
नारायणोऽहं नरकान्तकोऽहं पुरान्तकोऽहं पुरुषोऽहमीशः । अखण्डबोधोऽहमशेषसाक्षी निरीश्वरोऽहं निरहं च निर्ममः ॥ ४९४ ॥
nārāyaṇo'haṃ narakāntako'haṃ purāntako'haṃ puruṣo'hamīśaḥ | akhaṇḍabodho'hamaśeṣasākṣī nirīśvaro'haṃ nirahaṃ ca nirmamaḥ || 494 ||
- I am Nārāyaṇa, the slayer of Nāraka; I am the destroyer of Tripura, the Supreme Being, the Ruler; I am knowledge Absolute, the Witness of everything; I have no other Ruler but myself, I am devoid of the ideas of "I’ and "mine"
Plenty of such references exist.
Garuda Purana mentions 'Vasudevo'ham' (I am Vasudeva).
Garuda Purana I.92
Kundika Upanishad mentions Narayano'ham
आकाशवत्कल्पविदूरगोह मादित्यवद्भास्यविलक्षणोऽहम् । अहार्यवन्नित्यविनिश्चलोऽह मम्बोधिवत्पारविवर्जितोऽहम् ॥ १६॥
नारायणोऽहं नरकान्तकोऽहं पुरान्तकोऽहं पुरुषोऽहमीशः । अखण्डबोधोऽहमशेषसाक्षी निरीश्वरोऽहं निरहं च निर्ममः ॥ १७॥
I am always far beyond imagination like ether; I am different from it (the body) as the sun is from the objects of illumination; I am ever changeless just like the unchangeable (i.e. the Meru mountain) and, like the ocean am I limitless.
I am Nārāyaṇa, I am the destroyer of the (demon) Nāraka, I am (Śiva), the destroyer of the three (aerial) cities, I am the Purusha, I am the supreme Lord; I am the indivisible consciousness, the witness of all; I am without a superior, I am devoid of 'I-ness' (egotism) and 'mine-ness' (possessiveness).
The Rama-uttara Tapaniya Upanishad has the expression 'Ramo'hasmi' (I am Rama)
सदा रामोऽहमस्मीति तत्त्वतः प्रवदन्ति ये । न ते संसारिणो नूनं राम एव न संशयः ॥ इत्युपनिषत् ॥ य एवं वेद स मुक्तो भवतीति याज्ञवल्क्यः ॥ १९ ॥ इति द्वितीयः खण्डः ॥
Translation-
The Narada Purana voices a similar expression 'Ahameva Para Vishnu'-
अहमेव परो विष्णुर्मयि सर्वमिदं जगत् ।। इति यः सततं पश्येत्तं विद्यादुत्तमोत्तमम् ।। १५-५० ।।
'I am that supreme Vishnu, the whole world resides in Me', He who sees/realizes thus should be known as the Uttamottama Bhakta (foremost devotee).
~ Narada Purana - PurvAdha - Chapter 15
The Vaishnava Agama Agastya Samhita too contains the expression 'Ramo'ham', The contemplation of which is said to lead to liberation , moksha.
Another Vaisnavagama , Gautamiya Tantra too voices the expression as 'Krishna eva asmi'
A rough translation of some of the verses are as follows-
78: If the jiva is distinct from Brahman, it becomes an effect (of Brahman, the cause). This makes a scholar, the jiva, no different from an inert (achityam is the word here), just like a pot.
79: It is subject to destruction and also fear since the Shruti (Brihadaranyaka) says: there is fear from the second: dviteeyaad vai bhayam bhavati. But the Atman is nitya, sarvagata (all pervading), Immutable (nirvikari kutastha), free of any defect.
80: The One becomes many, bheda, due to bhranti, mAyA. Therefore there is nothing
called duality, dvaitam, there is no world, no assemblage (of various parts to make up the body mind complex).81: Huge/infinite space is spoken of as the house-space, pot space. So too those who are deluded, bhrAntAH, One Atma is spoken of as jiva and Ishwara.
81: Huge/infinite space is spoken of as the house-space, pot space. So too those who are deluded, bhrAntAH, One Atma is spoken of as jiva and Ishwara.
82: I am not the body, not the prANa, not the sense/motor organs, not the manas, buddhi, chitta and ahankara.
83: I am not the elements, earth, water, fire, air and space. I am not the shabda, sparsha, rupa and rasa.
84: I am not gandha and rupa (these five are the gunas/properties of the five elements). I am not mAyA, not samsara. Since I am always of the nature of witness, sAkshi, I am verily Krishna.
85: This contemplation is called samadhi.
Apart from all the other excellent answers given, here is one more instance.
This is from Taittiriya Aranyaka, Narayana Suktam.
nārāyaṇaḥ paraṁ brahma tattvaṁ nārāyaṇaḥ paraḥ| nārāyaṇaḥ paro jyotirātmā nārāyaṇaḥ paraḥ| nārāyaṇaḥ paro dhyātā dhyānam nārāyaṇaḥ paraḥ|
The Lord Narayana is the Supreme Absolute; Narayana is the Supreme Reality; Narayana is the Supreme Light; Narayana is the Supreme Self; Narayana is the Supreme Meditator; Narayana is the Supreme Meditation.
Here, Narayana is brahman and Narayana is also the (highest) person who meditates on brahman. The idea is that the highest form of meditation is one where the meditator thinks of himself or herself as identical to Narayana/brahman. Such a meditator is indeed identical to Narayana. In Mundaka Upanishad 3.2.9, it is mentioned that a knower of brahman becomes brahman.
sa yo ha vai tat paramaṃ brahma veda brahmaiva bhavati
He who knows that highest Brahman becomes even Brahman
In the Garuda purana we have:
श्रीगरुडमहापुराणम् २३५ सूत उवाच
वेदान्तसाङ्ख्यसिद्धान्तब्रह्मज्ञानं वदाम्यहम् । अहं ब्रह्म परं ज्योतिर्विष्णुरित्येव चिन्तयन् ॥ १,२३५.१ ॥
I am Brahman, Vishnu...thus one should contemplate.
