Sentence examples for mappings with respect from inspiring English sources

Let be two weakly inward and asymptotically nonexpansive mappings with respect to with sequences,, respectively.

Nashine and Samet [25] introduced weakly increasing mappings with respect to another map as follows.

Nashine et al. [26] proved some new coincidence point and common fixed point theorems for a pair of weakly increasing mappings with respect to another map.

Very recently, Shatanawi and Samet [33] proved some coincidence point theorems for a pair of weakly increasing mappings with respect to another map.

((mathcal G,F )) is a pair of asymptotically regular mappings with respect to (mathcal R ); orbital continuity of one of the involved maps; ((mathcal G,F )) is a pair of weakly increasing mappings with respect to (mathcal R ); ((mathcal G,F )) is a pair of dominating maps; ((mathcal G,F )) is a pair of compatible maps, and. the basic space is an ordered orbitally complete metric space.

Therefore, f and g are weakly increasing mappings with respect to ⪯.

Since T has a continuous selection t and T x, μ) is weakly (η, ϕ, C x -pseudo-mapping with respeC x -pseudo-mappingment on X × ∨, we know that t(x, μ) is also weakly (η, ϕ, C x -pseudo-mapping with respect to the first argument on X × ∨.

In Theorems 3.1 and 3.3, if the condition (d) is replaced by the condition that T x, μ) is (strictly) (η, ϕ, C x -pseudo-mapping with respeC x -pseudo-mappingment and B-u.s.C x -pseudo-mappings on X × ∨, then Theorems 3.1 and 3.3 still hold.

Assume that the conditions (a -(c) and (f) in Theorem 3.1 and the following conditions are satisfied: (d)' T x, μ) is weakly (η, ϕ, C x -pseudo-mapping with respeC x -pseudo-mappingment and B-u.s.C x -pseudo-mappings on X × {μ0}; (e)' there is a continuous selection t of T on X × {μ0}.

If are two set-valued mappings such that for any,, then is called a generalized mapping with respect to.

In this work, emphasis is given on univalent and sense-preserving logharmonic mappings in U with respect to a ∈ B 0. These mappings are of the form f ( z ) = z h ( z ) g ( z ) ¯, (2).