for the case of [(ii -gH]-differentiability, converge unii -gH]-differentiabilityutii -gH]-differentiabilityt ) of (3.1), respeconverge on [ t 0, t 0 + r ] where r = min { p, ρ / M 1, ρ / M 2 }.
Then we shall prove the existence of two unique solutions ({widetilde{Y}},widehat{Y}in L([a,b],mathcal{K})) to the integral equations (8) and (9) on the interval ([a,t^{ast}]), respectively.
Consequently, we derive an equivalent integral form of FFDE which allows us to investigate the approximate solutions (for each type of fractional H-differentiability) convergence to the two unique solutions.
for the case of [(ii -gH]-differentiability (where d > 0 such that the sequence (3.9) ii -gH]-differentiabilitye foregoii -gH]-differentiabilitydo exist), converge uniformly to twhereique solutions x ˆ ( t ) and x ˜ ( t ) of (3.1), respectively, on [ t 0, t 0 + r ] where r = min { p, ρ / M 1, ρ / M 2, d }.
for the case of (ii -differentiability (where 0 < d ≤ p such that equatii -differentiabilityined, i.e., the foregoing Hukuhara differences do exist), converge uniformly to twhereique solutions X ˆ ( t ) and X ˜ ( t ) of (3.1), respectively, on [ a, a + r ] where r = min { p, d }.
Assume that F satisfies the Lipschitz condition (7) for all (tin[a,b]) and all (Y_{1},Y_{2}in L([a,b],mathcal{K})). Then there exist two unique solutions Ỹ, Ŷ to the interval-valued integral equation (4) in the space (mathcal {L}^{alpha}([a,t^{ast}],mathcal{K})).
The market for biometric transactions currently contains three unique solutions from Biopay, Pay-By-Touch, and TouchCredit.
Similarly, how can we be sure that there is always one unique solution, or are bargaining problems to some extent underdetermined?
As two collinearity equations can be written for one particular point, relating its imaging point (x, y) in the photo frame to its three coordinates (X P, Y P, Z P ) in the space frame, three different points with known (x, y) and (X P, Y P, Z P ) can define six equations, thus resulting in unique solutions of six unknowns (X C, Y C, Z C, ω, φ, κ) (Figure 1).
In fact, by using the classical matching technique to obtain a matching solution of a three-point boundary value problem, it needs usually four two-point boundary value problems and among them two two-point boundary value problems need to have unique solutions, the other two two-point boundary value problems need to have at most one solution.
Roman showed [21] that the unique solutions of two relative discrete problems textstylebegin{array}{c} mathcal{L}u=f, langle l_{k},urangle=widetilde{g}_{k},quad k=1,2, end{array}displaystyle qquad textstylebegin{array}{c} mathcal{L}v=f, langle L_{k},vrangle=g_{k},quad k=1,2, end{array} (18) where the functionals (l_{k}) and (L_{k}) may be different, are related as well.
