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