But NNG's Tamas Kerecsen says those solutions are too generalized to be effective in vehicles.
1. f is said to be a generalized weak T-C-contraction if, for all x, y ∈ X, ψ ( d ( T f x, T f y ) ) ≤ ψ ( d ( T x, T f y ) + d ( T y, T f x ) 2 ) − φ ( d ( T x, T f y ), d ( T y, T f x ) ). 2.
A self-mapping T : X → X is said to be a generalized weak-contraction mappingif it satisfies the following condition: ψ ( Ω ( T x, T 2 x, T y ) ) ≤ ψ ( Ω ( x, T x, y ) ) − ϕ ( Ω ( x, T x, y ) ) for all x, y ∈ X, with x ≤ y, where ψ ∈ Ψ and ϕ ∈ Φ. Theorem 10Let ( X, G, ≤ ) be a partially ordered completeG-metric space, and let Ω be anΩ-distance onX.
Theorem 10 Let { A i } i = 1 k be nonempty closed subsets of a complete metric space (X, d), let φ : ℝ+ → ℝ+ be a φ-mapping in X, and let f : c u p i = 1 k A i → ∪ i = 1 k A i be a generalized cyclic weaker Meir-Keeler φ -contraction.
f is a generalized weak T-K-contraction. .
f is a generalized weak T-C-contraction, or.
Suppose that: 1. f is a generalized weak T-C-contraction, or 2.
Suppose that (T: X rightarrow X) is a generalized weak contraction mapping.
This shows that the function u ( x, t, ε ) is a generalized (weak) solution of problem (1 -(4).
