OK, these are the full definitions:
a = 1; b = 1; m = 2; A = 3; B = 1; a1 = {1 , 1, 1}; b1 = {1, 3, 4};
\[Lambda]1[a_, b_, m_, A_, B_] :=
a + b/(B - 2*b )*(a - A - Sqrt[(a - A)^2 - 4 *m*(B - 2*b)]) /;
2*b > B;
\[Lambda]1[a_, b_, m_, A_, B_] :=
a + B*m/(a - A) /; 2*b == B && a > A ;
\[Lambda]1[a_, b_, m_, A_, B_] :=
a + b/(B - 2*b )*(a - A - Sqrt[(a - A)^2 - 4 *m*(B - 2*b)]) /;
2 b < B && a >= A + 2 Sqrt[m (B - 2*b)];
\[Lambda]1[a_, b_, m_, A_, B_] := Infinity;
\[Lambda]2[a_, b_, m_, A_, B_] := Infinity /; 2 b > B;
\[Lambda]2[a_, b_, m_, A_, B_] := Infinity /; 2*b == B && a > A ;
\[Lambda]2[a_, b_, m_, A_, B_] :=
a + b/(B - 2*b )*(a - A + Sqrt[(a - A)^2 + -4 *m*(B - 2*b)]) /;
2 b < B && a >= A + 2 Sqrt[m (B - 2*b)];
\[Lambda]2[a_, b_, m_, A_, B_] := Infinity;
PosPart[x_] := x /; x >= 0;
PosPart[x_] := 0;
D1[a_, b_, m_, A_, B_, a1_, b1_] :=
Total[Map[PosPart, (\[Lambda]1[a, b, m, A, B] - a1)/(2*b1)]]
D2[a_, b_, m_, A_, B_, a1_, b1_] :=
Total[Map[PosPart, (\[Lambda]2[a, b, m, A, B] - a1)/(2*b1)]]
And I apologize, of course "?" is missing in the title. Thank you.