Sentence examples for the general split from inspiring English sources

Under suitable conditions, we prove that the sequences generated by the proposed new algorithm converges strongly to a solution of the general split equality fixed point problem and the general split equality problem for quasi-nonexpansive mappings in Hilbert spaces.

Under suitable conditions, we prove that the sequence generated by the proposed new algorithm converges strongly to a solution of the general split variational inclusion problem.

That said, the general split between the growing area of affluence around the Loop and the Near North Side and the outlying neighborhoods is undeniably real.

and the general split equality problem: ( GSEP ) to find  x ∈ C y ∈ Q  such that  A x = B y. (1.8).

The purpose of this paper is first to introduce and study the general split equality variational inclusion problems and the general split equality optimization problems in the setting of infinite-dimensional Hilbert spaces and then propose a new simultaneous iterative algorithm.

The purpose of this paper is to introduce and study the general split equality problem and general split equality fixed point problem in the setting of infinite-dimensional Hilbert spaces.

Motivated by the above works, the purpose of this paper is to introduce the following general split equality fixed point problem: ( GSEFP ) to find  x ∈ C : = ⋂ i = 1 ∞ F ( S i ), y ∈ Q : = ⋂ i = 1 ∞ F ( T i )  such that  A x = B y, (1.7).

Motivated by the works in [14 17] and related literature, the purpose of this paper is to introduce and consider the following general split variational inclusion problem.

In 2011, Moudafi [3] presented the following general split variational inclusion problem: mbox{Find }bar{x}in H_{1}mbox{ such that }0in f( bar {x})+B_{1}(bar{x}) mbox{ and }0in g(Abar{x})+B_{2}(A bar{x}).

Therefore (GSEOP) (4.1) is equivalent to the following general split equality variational inclusion problem (GSEVIP): to find x ∗ ∈ H 1 and y ∗ ∈ H 2 such that 0 ∈ ⋂ i = 1 ∞ U i ( x ∗ ), 0 ∈ ⋂ i = 1 ∞ K i ( y ∗ ) and A x ∗ = B y ∗. (4.2).

Let H 1 and H 2 be two real Hilbert spaces, B i : H 1 → H 1 and K i : H 2 → H 2, i = 1, 2, … be two families of set-valued maximal monotone mappings, A : H 1 → H 2 be a linear and bounded operator, and A ∗ be the adjoint of A. The so-called general split variational inclusion problem is to find  x ∗ ∈ H 1  such that  0 ∈ ⋂ i = 1 ∞ B i ( x ∗ )  and  0 ∈ ⋂ i = 1 ∞ K i ( A x ∗ ).