Sentence examples for mappings then the from inspiring English sources

In the following theorem, we prove that if, for any given mapping f, there exists a mapping F (near f) with some properties possessed by cubic-quadratic-additive mappings, then the mapping F must be uniquely determined.

In the following theorem, we prove that if, for any given mapping f, there exists a mapping F (near f) with some properties which are certainly satisfied by monomial mappings, then the mapping F is uniquely determined.

(v) If ( S i ), 1 ≤ i ≤ m, is a family of nonexpansive mappings, then the mapping S = ∏ i = 1 m S i is nonexpansive.

(vi) If ( T i ), 1 ≤ i ≤ m, is a family of averaged mappings, then the mapping T = ∏ i = 1 m T i is averaged.

If T 1, T 2 : H → H are univariate mappings, then the Algorithm 2.1 reduces to the following.

If T 1, T 2 : H → H are univariate mappings then the problem (SGMVI) reduced to the following.

(III) If A, B : H → H are single-valued mappings, then, from the problem (1.1), we have the following system of general nonlinear mixed variational inequalities problems:  .

If A, B : H → H are single-valued mappings, then, from the problem (1.1), we have the following system of general nonlinear mixed variational inequalities problems: Find x*, y* ∈ H, such that (1.4).

See, for example, [1 22] and the following examples: Example 1.1 If F : B 1 → B 1 and G : B 2 → B 2 are two single-valued mappings, then, from the problem (1.1), we have the following problem: Find ( x, y ) ∈ B 1 × B 2 such that { 0 ∈ N 1 ( x, G ( y ) ) + M 1 ( x, x ), 0 ∈ N 2 ( F ( x ), y ) + M 2 ( y, y ).

We prove that if F is a finite-dimensional Banach space and X has the super fixed point property for nonexpansive mappings, then F⊕X has the super fixed point property with respect to a large class of norms including all lp norms, 1⩽p<∞.

In this paper we first introduce the notion of proximally g-Meir-Keeler type mappings, then we study the existence and uniqueness of coupled best proximity points for these mappings.