This is the 12164th most frequent Turkish word.
gülümseyerek
"Smilingly."
Here, 'gülümseyerek' describes the manner of the child's approach, emphasizing the way the action was performed.
Çocuk gülümseyerek babasına yaklaştı.
The child approached his father while smiling.
In this case, 'gülümseyerek' together with 'konuşarak' denotes accompanying actions describing the engagement of the guests.
Misafirler, gülümseyerek konuşarak grup oluştu.
The guests formed a group while smiling and talking.
Here, 'gülümseyerek' introduces the adjective derivation indicating the manner of giving the greeting.