Then, if f is a solution of the common type of problem Df = cf, in which c is a constant, the perturbed problem is that of determining a function g such that (D + εP g = cg.
The negative sites on a cation exchanger are first neutralized with sodium ions by exposure to a strong solution of common salt (sodium chloride); when the hard water is passed through the resin, the undesirable ions in the water are replaced by sodium ions.
When the zeolite or resin becomes exhausted (when most of its exchangeable sodium is replaced with calcium and magnesium), it can be regenerated by washing with a strong solution of common salt, which removes the calcium and magnesium and replaces them once again by sodium.
Then the column must be regenerated by passing a concentrated solution of common salt slowly through the column; the excess sodium ions displace the ions that produce the hardness so that, after flushing with water, the bed of exchanger is ready to be used again.
He established the weak convergence of the sequence generated by his scheme to a solution of the split common fixed point problem.
Next, using the shrinking projection method introduced by Takahashi et al. [13], we prove a strong convergence theorem for finding a solution of the split common null point problem in Banach spaces.
In this section, using the hybrid method in mathematical programming, we first prove a strong convergence theorem for finding a solution of the split common null point problem in Banach spaces.
Then using the hybrid method and the shrinking projection method in mathematical programming, we prove two strong convergence theorems for finding a solution of the split common null point problem in Banach spaces.
Then using the hybrid method and the shrinking projection method in mathematical programming, we prove strong convergence theorems for finding a solution of the split common null point problem in Banach spaces.
Brine, salt water, particularly a highly concentrated water solution of common salt (sodium chloride).
