Why not call your specific airline and ask? Or go to the specific airline site and look for the information.
This is for SWA.
These items are permitted onboard and DO NOT COUNT toward the carryon limit:
Purses of reasonable size
Coats and other outer garments
Small cameras
Food items for onboard consumption, in disposable packages
Approved child-restraint devices which have been ticketed or for which complimentary space is known to be available
Devices required to assist Customers with disabilities
These items are also permitted onboard, but DO count toward the carryon limit:
Briefcases; shopping bags; backpacks; computers or peripherals
Portfolio cases, if space is available onboard in a portfolio container
Delicate, stowable items (such as musical instruments) of reasonable size, provided space is available onboard
Papoose-like baby carriers with hard, non-folding frames, and unapproved child-restraint devices*, if space is available onboard
* Unapproved child-restraint devices may not be used during taxi, takeoff, and landing