Bhagavān Śrī Rāma is - सर्वलोकशरण्य sarvalōka-śaraṇya - the supreme shelter (आश्रय, शरण) and - रक्षिता जीवलोकस्य rakṣitā jīvalōkasya - the protector (रक्षक) of all Jivas and the world. Bhagavān is infinite (विभु), and Jiva is finite and tiny (अणु), therefore Jiva by its' nature (प्रकृति) is protectable (रक्ष्य) and ever dependent (आश्रित) on Bhagavān Śrī Rāma. So, How can Jiva, against his Svasvarup [own finite nature], say may the auspiciousness [mangalam] happen to (do Mangalashasana of) the Supreme Lord?
Maṅgalānuśāsana seems normal, when we wish may good happen to devotees, may safety betide to devotees, may devotees get all happiness, However how come a Vaishnava does the maṅgalāśāsana of the all powerful Sarvēśvar Bhagavān, against his own Svarūpa (of a finite soul being ever dependent on and रक्ष्य protectable by Bhagavān)?
Why Maṅgalāśāsana of Bhagavān? For simple understanding, There are two stages (conditions) in Bhakti (devotion) : (1) jñāna, and (2) Prema (overwhelming-love).
In jñāna a devotee thinks Sarvēśvar Bhagavān is our रक्षक (Rakṣak) Protector and आश्रय shelter, and we are रक्ष्य (Rakṣya) protectable; while in Prema (love), it is sometimes exactly opposite! Sometimes devotees in their - प्रेमाधिक्य prēmādhikya - abundance of love forget the real nature of Bhagavān being all powerful and do maṅgalāśāsana for Sarvēśvar Bhagavān. Still, there is no loss of SvaSvarūpa of devotee, as in Prēma (abundance of love) Bhagavān himself loves to get the auspicious wishes, care and love from his devotees.
In Śrīmad Vālmīki Rāmāyaṇa, We see the Maṅgalānuśāsana of Bhagavān Śrī Rāma done by many, while Śrī Rāma himself is the supreme lord of all the worlds सर्वलोकेश्वरः and their ultimate refuge परगतिः. Śrīmad Vālmīki Rāmāyaṇa makes us fall in love of the divine prince and princess, and the heart overwhelmed with love for them starts praying [wishing] may all good happen to our beloved Priyā-Priyatam Śrī Sītā-Rāma.
In Prema, a devotee is deeply in love of सौन्दर्य (all attractive beauty) - सौकुमार्य (tenderness)- लावण्य (loveliness)- माधुर्य (sweetness) of the prince-charming (Sarvēśvar Bhagavān Śrī Rāma) ... where his lotus feet are so delicate so tender that they are unable to bear the touch of even the most delicate palms of the most beautiful, most tender and sweetest princess Sītā jī ! And therefore in Prema (love), a devotee being enticed and spell-bound on the सौन्दर्य (all attractive beauty)- सौकुमार्य (tenderness)-लावण्य (loveliness)- माधुर्य (sweetness) of Bhagavān becomes concerned and anxious (व्याकुल) for the beloved’s happiness and does Maṅgalānuśāsana for Sarvēśvar Bhagavān, may all good (maṅgal) happen to our sweetest Lord Śrī Rāma, may sweetest prince get all happiness, may divine couple Śrī Sītā and Śrī Rāma enjoy together, etc.
In Prema (overwhelming love), we can see the examples of Śrī Sītā, Śrī Vishwāmitra, Śrī Hanumān, Śrī Jatāyu, Sakhi-s (& Gopis) of Śrī Sītā (Rāma), Maharāj Śrī Dasarath, Devī Kausalyā, all the people of Ayodhyā, the sages of Daṇdakāraṇya, Śrī Nanda-Gopa, Śrī Vasudeva, Śrī Devakī, Devī Yashodā, Gopi-s etc doing Maṅgalānuśāsana of Sarvēśvar Bhagavān.
(1) Śrī Sītā - She knows truly the real nature of Śrī Rāma, still She does Maṅgalānuśāsana for her beloved consort in her love forgetting his रक्षत्व rakṣatva (being the supreme protector of all the worls, including all the gods).
पूर्वां दिशं वज्रधरो दक्षिणां पातु ते यमः ।
वरुणः पश्चिमामाशां धनेशस्तूत्तरां दिशम् ॥ (श्री वाल्मीकि रामायण २.१६.२४)
pūrvāṃ diśaṃ vajradharō dakṣiṇāṃ pātu tē yamaḥ ।
varuṇaḥ paścimāmāśāṃ dhanēśastūttarāṃ diśam ॥ (Śrī Vālmīki Rāmāyaṇa 2.16.24)
“May Indra the god of rain in the east, Yama the god of death in the south, Varuṇa the regent of the ocean in the west and Kubera the god of riches and treasure in the north, protect you.”
(2) Śrī Vishwāmitra also knows Śrī Rāma is the supreme absolute one.
अहं वेद्मि महात्मानं रामं सत्यपराक्रमम् । (श्री वाल्मीकि रामायण १.१९.१४)
aham vēdmi mahātmānaṃ rāmaṃ satya parākramam । (Śrī Vālmīki Rāmāyaṇa 1.19.14)
“I (Vishwāmitra) have known (through my tapa) that Rāma is the supreme soul (veda aham etam puruSam mahaantam - Purusha Suktam), with invincible (true) valor (in all quarters of time).”
However, when the ogress Tāṭakā suddenly attacked the tender princes Śrī Rāma and Lakṣmaṇa, then Vishwāmitra forgot Śrī Rāma is the supreme person in reality whom he brought in forest to protect his Yajñas from demons, seeing his सौकुमार्य (tenderness, softness), Vishwāmitra became restless and immediately daunted Tāṭakā off through his huṃkāra (powerful sound) and uttered :
स्वस्ति राघवयोः अस्तु - (श्री वाल्मीकि रामायण १.२६.१४)
svasti rāghavayōḥ astu - (Śrī Vālmīki Rāmāyaṇa 1.26.14)
“May good happen to Rāma and Lakṣhmaṇa as well.”
(3) Devī Kausalyā - several shlokas were said by Devī Kausalyā as the Maṅgalāśāsana of Śrī Rāma, forgetting his real nature of being the supreme Lord. There is a whole chapter in Śrī Vālmīki Rāmāyaṇa dedicated to it, where She invokes auspicious wishes for the happiness and felicity of Śrī Rāma while giving him farewell very reluctantly:
श्रीराममङ्गलाशासनम् - श्रीकौसल्यादेवीकृतम्
(ŚrīRāmamaṅgalāśāsanam - ŚrīKausalyādevīkṛtam)
यन्मङ्गलं सहस्राक्षे सर्वदेवनमस्कृते ।
वृत्रनाशे समभवत् तत्ते भवतु मङ्गलम् ॥ (श्री वाल्मीकि रामायण २.२५.३२)
yanmaṅgalaṃ sahasrākṣē sarvadēvanamaskṛtē ।
vṛtranāśē samabhavat tattē bhavatu maṅgalam ॥ (Śrī Vālmīki Rāmāyaṇa 2.25.32)
Devī Kausalyā said -
“Which felicity occurred in the thousand-eyed God, the one who is honored by all the gods, at the time of destroying Vṛtra, May that same felicity occur to You. Oh’ my Rāma!”
यन्मङ्गलं सुपर्णस्य विनताऽकल्पयत्पुरा ।
अमृतं प्रार्थयानस्य तत्ते भवतु मङ्गलम् ॥ (श्री वाल्मीकि रामायण २.२५.३३)
yanmaṅgalaṃ suparṇasya vinatā'kalpayatpurā ।
amṛtaṃ prārthayānasya tattē bhavatu maṅgalam ॥ (Śrī Vālmīki Rāmāyaṇa 2.25.33)
“May the same good fortune be bestowed on you, that was bestowed by Vinatā on Garuda, when he was seeking Amṛta (ambrosia).”
अमृतोत्पादने दैत्यान् घ्नतो वज्रधरस्य यत् ।
अदितिर्मङ्गलं प्रादात् तत्ते भवतु मङ्गलम् ॥ (श्री वाल्मीकि रामायण २.२५.३४)
amṛtōtpādanē daityān ghnatō vajradharasya yat ।
aditirmaṅgalaṃ prādāt tattē bhavatu maṅgalam ॥ (Śrī Vālmīki Rāmāyaṇa 2.25.34)
“May the same good fortune be bestowed on you, that was bestowed by Aditi on Indra the wielder of the thunderbolt, killing the demons at the time of extracting Amṛta (nectar).”
त्रीन्विक्रमान्प्रक्रमतो विष्णोरमिततेजसः ।
यदासीन्मङ्गलं राम तत्ते भवतु मङ्गलम् ॥ (श्री वाल्मीकि रामायण २.२५.३५)
trīnvikramānprakramatō viṣṇōramitatējasaḥ ।
yadāsīnmaṅgalaṃ rāma tattē bhavatu maṅgalam ॥ (Śrī Vālmīki Rāmāyaṇa 2.25.35)
“Oh, Rāma! Which good auspicious fortune (felicity) occurred to Vishnu who was immensely glorious while making his three strides (in order to measure the three worlds), May that same good fortune happen to you.”
ऋतवस्सागरा द्वीपा वेदा लोका दिशश्च ते ।
मङ्गलानि महाबाहो दिशन्तु शुभमङ्गलाः ॥ (श्री वाल्मीकि रामायण २.२५.३६)
ṛtavassāgarā dvīpā vēdā lōkā diśaśca tē ।
maṅgalāni mahābāhō diśantu śubhamaṅgalāḥ ॥ (śrī vālmīki rāmāyaṇa 2.25.36)
Oh, Rama, the mighty armed! May the seasons, oceans, dvīpās (principal division of earth girdled by oceans), Vēdas, various worlds and all the [ten] directions, bestow good [auspicious] fortune on you!
(4) In Śrī Vālmīki Rāmāyaṇa, Sages of Dandakārayana who lost their heart and soul after being enticed (विस्मित) on the सौन्दर्य (Saundarya - beauty) of Śrī Rāma, forgot the true nature of Śrī Rāma, and they did Maṅgalāśāsana for Sarvēśvar Bhagavān Śrī Rāma.
(5) All teenager-girls (बालिका), Young-Youthful ladies (तरुणी) and old-ladies (वृद्ध) of Ayodhyā pray at dawn and dusk everyday for the sake of Śrī Rāma in Vālmīki Rāmāyaṇa.
Similarly in Prema (love), devaki, Yashoda and Gopis etc do Maṅgalāśāsana for Śrī Krishna. Gopis in love ask protection for Śrī Krishna.
श्रीराघवेन्द्रमङ्गलमाला - जगद्गुरुश्रीराघवानन्दाचार्यकृतम्
śrīrāghavēndra-maṅgalamālā - jagadguru-śrīrāghavānandācārya-kṛtam
The garland of auspicious wish invocations - composed by Jagadguru Śrī Rāghavānandācārya (the guru of Bhagavad Śrī Rāmānand)
राघवेन्द्रं नमस्कृत्य हर्यानन्दं गुरुं तथा ।
कुर्वे मङ्गलमालां श्रीराघवेन्द्रस्य तुष्टये ॥१॥
rāghavēndraṃ namaskṛtya haryānandaṃ guruṃ tathā ।
kurvē maṅgalamālāṃ śrīrāghavēndrasya tuṣṭayē ॥1॥
Bowing down to Bhagavān Śrī Rāghavēndra,
and to my guru Śrī Haryānanda,
I (Śrī Rāghavānanda*) am composing Śrī Rāghavēndra-Maṅgalamālāṃ (the garland of auspicious wish invocations)
for the pleasure of Śrī Rāghavēndra.
मङ्गलानां निवासाय जगन्मङ्गलकारिणे ।
मङ्गलैकस्वरूपाय राघवेन्द्राय मङ्गलम् ॥२॥
maṅgalānāṃ nivāsāya jaganmaṅgalakāriṇē ।
maṅgalaikasvarūpāya rāghavēndrāya maṅgalam ॥2॥
May good (fortune) happen to Śrī Rāghavēndra,
Who is the abode of all auspiciousness (Maṅgalam),
Who brings (does) Maṅgalam to (welfare of) all the worlds,
Whose form is verily all Maṅgalam (Ānandamayam).
श्रीजानकीनिवासाय श्रीसाकेतनिवासिने ।
निखिलान्तर्निवासाय राघवेन्द्राय मङ्गलम् ॥३॥
śrījānakīnivāsāya śrīsākētanivāsinē ।
nikhilāntarnivāsāya rāghavēndrāya maṅgalam ॥3॥
May good (fortune) happen to Śrī Rāghavēndra,
Who lives in the heart of Śrī Jānakī Sītā,
Who lives in Śrī Sāketa [the supreme abode],
Who lives in the Antaḥkaraṇa of entire existence.
सीताकान्ताय शान्तायनन्तपापान्तकारिणे ।
अनन्तरूपरूपाय राघवेन्द्राय मङ्गलम् ॥४॥
sītākāntāya śāntāyanantapāpāntakāriṇē ।
anantarūparūpāya rāghavēndrāya maṅgalam ॥4॥
May good (fortune) happen to Śrī Rāghavēndra,
Who is the beloved husband (kānt) of Śrī Sītā,
Who is calm and destroyer of infinite sins,
Whose form is infinite (of cosmic form).
प्रपन्नानन्ददात्रे च प्रपन्नार्तिविनाशिने ।
अविनाशीस्वरुपाय राघवेन्द्राय मङ्गलम् ॥५॥
prapannānandadātrē ca prapannārtivināśinē ।
avināśīsvarupāya rāghavēndrāya maṅgalam ॥5॥
May good (fortune) happen to Śrī Rāghavēndra,
Who gives Ānand (bliss) to those who seek refuge in him,
Who eradicates the sufferings of surrendered souls in every way,
Who is of unchanging immutable Svarupa (form, nature).
वाञ्छाकल्पलताराम लोकाभिराममूर्तये ।
सकलापद्विरामाय राघवेन्द्राय मङ्गलम् ॥६॥
vāñchākalpalatārāma lōkābhirāmamūrtayē ।
sakalāpadvirāmāya rāghavēndrāya maṅgalam ॥6॥
May the good happen to Śrī Rāghavēndra,
Who is the garden of the divine wish-fulfilling creepers (trees) [to his devotees],
Whose [incomparable] form delights (pleases) all in all the worlds,
Who makes a full stop on all afflictions and calamities.
सर्वविद्याधिराध्यायाविद्याशून्यपरात्मने ।
वेदवेद्यानवद्याय राघवेन्द्राय मङ्गलम् ॥७॥
sarvavidyādhirādhyāyāvidyāśūnyaparātmanē ।
vēdavēdyānavadyāya rāghavēndrāya maṅgalam ॥7॥
May good (fortune) happen to Śrī Rāghavēndra,
Who is worshiped by all prescribed rituals mentioned in the Vedas and Vedanta,
Who is the Ultimate Reality completely devoid of ignorance,
Who can be truly known through the Vedas (the first & ultimate source of right knowledge),
Who is completely without any blesmish.
चिदचिद्भ्यां विशिष्टाय शिष्टपक्षसुरक्षिणे ।
सच्चिदानन्दरूपाय राघवेन्द्राय मङ्गलम् ॥८॥
cidacidbhyāṃ viśiṣṭāya śiṣṭapakṣasurakṣiṇē ।
saccidānandarūpāya rāghavēndrāya maṅgalam ॥8॥
May good (fortune) happen to Śrī Rāghavēndra,
Who is distinct and distinguished from Chid (sentient souls) and Achid (insentient nature),
Who is protector of the virtuous path,
Who is verily of Sat (eternal, real, existence) - Chid (consiciosuness) - Ānand (bliss) Rupa (form).
ब्रह्मणे परिपूर्णाय कार्यकारणरूपिणे ।
शार्ङि्गणे पूर्णकामाय राघवेन्द्राय मङ्गलम् ॥९॥
brahmaṇē paripūrṇāya kāryakāraṇarūpiṇē ।
śārṅigaṇē pūrṇakāmāya rāghavēndrāya maṅgalam ॥9॥
May good (fortune) happen to Śrī Rāghavēndra,
Who is Paripurṇa (the most complete) Brahm,
Who is both the kārya (manifested) and the Kāraṇ (cause) Brahm,
Who is the wielder of the now name 'śārṅga',
Who is 'Purṇakāma' (of no unfulfilled desire).
भक्ततन्त्रस्वतन्त्राय भक्ताभिष्टार्थदायिने ।
भक्त्यामुक्तिप्रदात्रे च राघवेन्द्राय मङ्गलम् ॥१०॥
bhaktatantrasvatantrāya bhaktābhiṣṭārthadāyinē ।
bhaktyāmuktipradātrē ca rāghavēndrāya maṅgalam ॥10॥
May good (fortune) happen to Śrī Rāghavēndra,
Who is in control of his devotees yet eternally independent in his nature,
Who is bestower of the desired objects upon his devoted seekers,
Who grants liberation upon pleased by the devotion [of his seekers].
सर्वशक्तिमते सर्वशेषिणे सर्ववेदिने ।
सर्वसम्पद्विधात्रे च राघवेन्द्राय मङ्गलम् ॥११॥
sarvaśaktimatē sarvaśēṣiṇē sarvavēdinē ।
sarvasampadvidhātrē ca rāghavēndrāya maṅgalam ॥11॥
May the good happen to Śrī Rāghavēndra,
Who is the supreme Lord of all powers,
Who is the Śhēṣhin of the entire universe with its all animate and inanimate beings,
Who is knower of everything,
and Who is giver of all wealth and prosperity.
त्याज्यवर्ज्याय पूज्यायानन्त श्रेयोगुणाब्धये ।
सर्वेषां चित्तचौराय राघवेन्द्राय मङ्गलम् ॥१२॥
tyājyavarjyāya pūjyāyānanta śrēyōguṇābdhayē ।
sarvēṣāṃ cittacaurāya rāghavēndrāya maṅgalam ॥12॥
May the good happen to Śrī Rāghavēndra,
Who is ever free from ignoble qualities which should be rejected,
Who is worthy of adoration (worship) by all,
Who is an infinite ocean of sublime and auspicious virtues,
Who steals the minds (hearts) of everyone (even men).
संहर्त्रे चास्यविश्वस्य कर्त्रे भर्त्रे तथैव च ।
कीर्त्तनात्तारयित्रे च राघवेन्द्राय मङ्गलम् ॥१३॥
saṃhartrē cāsyaviśvasya kartrē bhartrē tathaiva ca ।
kīrttanāttārayitrē ca rāghavēndrāya maṅgalam ॥13॥
May the good happen to Śrī Rāghavēndra,
Who is the creator, sustainer, and ultimately the destroyer of the entire universe,
Who enables one to cross [the ocean of] the Saṃsāra who sing his divine name.
दिव्यदेहाय हृद्याय दिव्यालङ्कारधारिणे ।
दिव्यपरिकरायाथ राघवेन्द्राय मङ्गलम् ॥१४॥
divyadēhāya hṛdyāya divyālaṅkāradhāriṇē ।
divyaparikarāyātha rāghavēndrāya maṅgalam ॥14॥
May the good happen to Śrī Rāghavēndra,
Who has divine-body, which is adorned with the most exquisite and divine ornaments,
Whose form captivates the hearts of all beings,
Who is accompanied by divine attendants and servants.
व्यापिनेऽन्तर्बहिश्चास्य सर्वस्य जगतः सते ।
अद्वितीयस्वरूपाय राघवेन्द्राय मङ्गलम् ॥१५॥
vyāpinē'ntarbahiścāsya sarvasya jagataḥ satē ।
advitīyasvarūpāya rāghavēndrāya maṅgalam ॥15॥
May good (fortune) happen to Śrī Rāghavēndra,
Who by pervading entire universe, is present both internally and externally,
Who is the completely incomparable one without a second.
श्रीकौशल्यातनूजाय श्रीसरयूविहारिणे ।
चक्रवर्त्तिकुमाराय राघवेन्द्राय मङ्गलम् ॥१६॥
śrīkauśalyātanūjāya śrīsarayūvihāriṇē ।
cakravarttikumārāya rāghavēndrāya maṅgalam ॥16॥
May good (fortune) happen to Śrī Rāghavēndra,
the beloved son of Śrī Kauśalyā Devī and the prince of the mighty emperor Daśaratha,
Who disports on the banks of the sacred river Sarayu.
ताडकाघातिने विश्वामित्रस्य यज्ञरक्षिणे ।
अहल्योद्धारकाराय राघवेन्द्राय मङ्गलम् ॥१७॥
tāḍakāghātinē viśvāmitrasya yajñarakṣiṇē ।
ahalyōddhārakārāya rāghavēndrāya maṅgalam ॥17॥
May good (fortune) happen to Śrī Rāghavēndra,
Who is the eliminor of the ogress Tāḍakā,
Who is protector of the Yajña of the great sage Viśhvāmitra from demons like Māricha and Subāhu,
Who is the liberator of Ahalyā.
जनकाराधितायाथ शम्भुचापविभेदिने ।
जानकीपरिणेत्रे च राघवेन्द्राय मङ्गलम् ॥१८॥
janakārādhitāyātha śambhucāpavibhēdinē ।
jānakīpariṇētrē ca rāghavēndrāya maṅgalam ॥18॥
May good (fortune) happen to Śrī Rāghavēndra,
Who was honored by the great King Janaka of Mithila,
Who broke the divine bow of Lord Shambhu (Shiva) effortlessly,
Who entered into a blissful marital union with the beloved daughter of King Janaka, the princess Sita.
*Śrī Rāghavānanda was 21st in the lineage of the Āchāryas of Śrī-Sampradāya (Śrī-Rāmānanda-Sampradāya).
Read here complete Śrī Rāghavendra-maṅgal-mālā in Saṃskṛt with Hindī Translation.