We note that [5, Theorem
1.1] strongly supports Conjecture 1.5.
The two-dimensional Pythagorean theorem
establishes a relationship between three squares.
By applying Theorem
2 to the polynomial p(z) = [z.sup.n]p(1/z), we easily get Theorem
In a similar manner, in proof of Theorem
9, we obtain the result (40).
(i) follows from Theorem
8.12.2 of , and (ii) follows from Theorems
8.10.5 and 8.13.2 of  applying to X = [C.sub.p](Y) and Y = [C.sub.p](X).
In view of Theorem
6, the numbers [c.sub.1], ..., [c.sub.n] in Theorem
4 can be replaced by functions analytic in D.
Also, we prove the following nonsymmetric theorem
for (H, G)-coincidences which is a version for manifolds of the main theorem
One of our main tools for the proofs given in Sections 3 and 4 is the time scales Holder inequality, see [11, Theorem
6.13], which says
In [, Theorem
10], it is explained that the space of solutions of a weakly delayed system (1), depending initially on 2([m.sub.n] + 1) parameters (i.e., on the initial data (3)) is reduced (as k [greater than or equal to] [m.sub.n] + 2) to a space of solutions depending either on [m.sub.n] + 1 or even only on 2 parameters.
By the dominated convergence theorem
5 we have the following theorem
Observe that if in Theorem
14 we have [alpha] = 1, the statement of Theorem
14 becomes the statement of Theorem
Postolache, Fixed point theorem
for weakly Chatterjea-type cyclic contractions, Fixed Point Theory Appl., Article ID 2013:28 (2013), 9 pages.