Is it possible to use mutex in multiprocessing case on Linux/UNIX ?

Mutual exclusion locks (mutexes) prevent multiple threads from simultaneously executing critical sections of code that access shared data (that is, mutexes are used to serialize the execution of threads). All mutexes must be global. A successful call for a mutex lock by way of mutex_lock() will cause another thread that is also trying to lock the same mutex to block until the owner thread unlocks it by way of mutex_unlock(). Threads within the same process or within other processes can share mutexes.

Mutexes can synchronize threads within the same process or in other processes. Mutexes can be used to synchronize threads between processes if the mutexes are allocated in writable memory and shared among the cooperating processes (see mmap(2)), and have been initialized for this task.

Initialization

Mutexes are either intra-process or inter-process, depending upon the argument passed implicitly or explicitly to the initialization of that mutex. A statically allocated mutex does not need to be explicitly initialized; by default, a statically allocated mutex is initialized with all zeros and its scope is set to be within the calling process.

For inter-process synchronization, a mutex needs to be allo- cated in memory shared between these processes. Since the memory for such a mutex must be allocated dynamically, the mutex needs to be explicitly initialized using mutex_init().

It is quite possible to use a process-shared mutex.

In fact, modern applications prefer using a process shared mutex along with process shared condition variable over a semaphore because the latter is less flexible.

I remember using Red Hat Linux in 2004 and at that time it supported both process shared mutexes and condition variables.

Not quite. POSIX threads has a concept of a process-shared attribute which can be used to create mutexes that can be operated on by multiple processes.

You can put such a mutex in shared memory so that multiple processes can all get at it.

Whether LINUX implements this., I'm not sure, I've never had a need to use it since it seems unnecessarily complex.

For a useful precis of attributes, see my answer to this question.