Let (T:Xrightarrow X) and (G Xrightarrow X) be two mappings such that T is a G-isotone mapping and (T X subseteq G(X)).
Let f,T X→X be two mappings such that f(X)⊆T X), dominating map f is a weak annihilator of T. Suppose that for every three comparable elements x,y,z∈X, ψ G ( fx, fy, fz ) ≤ ψ M 4 ( x, y, z ) − φ M 4 ( x, y, z ), Open image in new window (59).
Assume f : X → X and γ : X × X → [ 0, ∞ ) be two mappings such that f is a non-decreasing γ-admissible mapping. Assume that there exist ψ ∈ Ψ, α ∈ Φ α, and β ∈ Φ β such that ψ ( t ) − α ( s ) + β ( s ) > 0 for all t > 0 and s = t or s = 0. (2.12).
Assume f : X → X and γ : X × X → [ 0, ∞ ) be two mappings such that f is a non-decreasing and γ-admissible mapping. Assume that there exist ψ ∈ Ψ, α ∈ Φ α, and β ∈ Φ β such that ψ ( t ) − α ( s ) + β ( s ) > 0 for all t > 0 and s = t or s = 0 (2.1).
Let F : X × X → X and g : X → X be two mappings such that (2.1).
Let be a complete metric space, and let be two mappings such that for all (1.11).
Let be a complete metric space, and let, be two mappings such that for each, (1.4).
Let f, T : X → X be two mappings such that the pair ( f, T ) is ( A, B ) -weakly increasing.
Let be a complete metric space and let and be two mappings such that for all, (4.1).
Let T, g : X → X be two mappings such that T X ⊆ g X and T is ( g, ≼ ) -nondecreasing.
Let ((X,D) ) be a complete metric space, and let (T,f Xrightarrow X ) be two mappings such that T is continuous, one-to-one, and sequentially convergent.
