linked list in c code
Naming

You should consider renaming or removing Your memory_map() function, all functions from Your linkedlist library does have a prefix list_, and this one does not. Also, it's kind a misleading. For user of Your library it might look like something related to mmap().

What does p, k, x mean? Please, consider using proper names for Your variables.

Verbosity

Just returning false in case of error usually is not verbose enough. I'd suggest considering proper error codes and/or proper error logger, for example something like this:

#ifndef LLIST_LOG
#define LLIST_LOG(format, ...) \
    fprintf(stderr, "LLIST_LOG: %s(): " format "\n", \
          __FUNCTION__, ##__VA_ARGS__)
#endif /* LLIST_LOG */


Consistency

Spacing and indentation is inconsistent. You should decide, how many spaces do You put between functions, how and when You separate if() {}, while() {}, arithmetical operations, etc blocks from each other or other logical parts of Your code. Or even better, use already defined C coding style, for example Linux kernel one.

Input verification

Rule of thumb, user of Your library is going to be dumb. And/or it will get messy debugging bigger project with Your library included. So, really, verify ALL the inputs. For example, Your list_delete(NULL, 1) segfaults.

Generic practices

Back to memory_map(), in general it's quite common to provide iterator function which calls some callback with every single element of the structure as a parameter instead. It's way more versatile.

It's common to suffix include guards by some randomly generated gibberish or hash, especially for such a common names as LINKED_LIST. Also, for compatibility with some compilers it usually defines it to some specific value. For example:

#ifndef LINKED_LIST_H_093e74eeda79fcc4c29e9d2986f5b701
#define LINKED_LIST_H_093e74eeda79fcc4c29e9d2986f5b701 1


Also, You should consider adding function list_create() and list_destroy() for Your library user not to mess with malloc() and free() directly and handle errors properly there.

Generic rant

There is a memory leak in Your example ;)