B.G 4.11
ये यथा मां प्रपद्यन्ते तांस्तथैव भजाम्यहम्। मम वर्त्मानुवर्तन्ते मनुष्याः पार्थ सर्वशः ॥११॥
As they worship Me, accordingly I reciprocate to them. O Arjuna, humans are subsurvient to my ways in all aspects.
Gīta Bhāshya 4.11
The word "bhajāmi" is used in the current context to mean - "I partake by giving fruits". The names of multiple deities refer to one supreme lord only.
न च मद्भजनमात्रेण मुक्तिः भवति अन्यदेवतादिरूपेण। तथापि सर्वेषाम् अनुरूप्येण फलं ददामि इत्याह - ये यथा इति॥
By merely partaking Me in any other god forms, liberation is not obtained. Hence, it is conveyed through "yē yathā" verse, "I grant everyone the results according to their respective deeds".
भजामि सेवयामि फलदानेन। न तु गुणभावेन। कथमयं विशेष इत्यत आह - मम वर्त्मेति॥
The word "bhajāmi" is used here in the context to mean - "I partake by giving fruits". It certainly is not meant to praise the qualities (of the beings). How is this special?, is explained by stating - "being subservient to My ways".
अन्यदेवताः यजन्तोऽपि मम वर्त्मैव अनुवर्तन्ते। सर्वकर्मकर्तृत्वात् भोक्तृत्वाच्च मम।
Even those who worship other deities follow my path only. As I am the doer of all actions and also their enjoyer.
"योऽप्यन्यदेवता भक्ताः।"
इति वक्ष्यति।
"Even those who worship other deities"
- same is stated at B.Gita 9.23 as well.
"यो देवानां नामधा एक एव"
इति हि श्रुतिः।
"Those deities possessing multiple names are one person only."
- thus asserts, with certainty, Vedic testimonial.
भगवानेव च तत्र अभिधीयते।
The understanding of the lord only is established in this context, by statements such as
"अजस्य नाभौ अध्येक मर्पितम्"
इत्यादि तल्लिङ्गात् ॥११॥
"Is offered to the unborn, the one with the navel, the foremost one..."
- addressed to that distinguished personality (showing the referred god as none other than lord Vishnu, in Padmanabha form).
Gīta Tātparya 4.11
"tathaiva bhajāmi" = I give results accordingly. Even the worship of other deities must ultimately be dedicated to Lord Vishnu in order to yield results.
तथैव भजामि तदनुसारिफलदानरूपेण। अन्यदेवतायाजिनामपि मत्समर्पणेन वैष्णवमार्गानुवर्तनेनैव सम्यक् फलं भवति।
The words "tathaiva bhajāmi" mean "I give results accordingly". Even the worshippers of other deities dedicate to me only, but following directly Vaishnavism produces better results.
अन्यदैवतपूजाऽपि यस्मिन्नन्ते समर्पिता। स्वर्गादिफलहेतुः स्यात् नान्यथा तं भजेद्धरिम्॥
इत्याग्नेये ॥११-१२॥
"Even the worship of other deities becomes the cause of heaven and other rewards, only when they are dedicated to lord Vishnu in the end, not otherwise."
-states Agni Purana.
