Moreover, if X has only rational singularities, then Y has only rational singularities by Theorem
Sadarangani, Fixed point theorems
for weakly contractive mappings in partially ordered sets, Nonlinear Anal.
In Section 2 of this paper we extend Theorem
2 by proving that a connected 4-regular multigraph G with [mu](G) [less than or equal to] 2 has a [P.
5] Chen Jianguo, A Simple Proof of the Four Color Theorem
and Its Significance, Journal of Foshan University (Social Science Edition), No.
On Tauberian theorems
for (A)(C,[alpha]) summability method.
Now by the above Lemma, we can obtain the following corollary, which includes [3, Theorem
In view of Theorem
1 the following theorem
can be carried out.
Kiran: Fixed point theorems
for multi-valued mappings obtained by altering distances, Math.
Their work called 'Formalization, Mechanization and Automation of Godel's Proof of God's Existence' state that his ontological proof of God has been analysed for the first time with an unprecedented degree of detail and formality with the help of higher-order theorem
Ruscheweyh, A subordination theorem
for [phi]-like functions, J.
If we use the Menelaus's theorem
in the h-triangles ADC and ABD for the h-lines BPE, and CPF respectively, then
Since Y1 is bounded, in order to prove our theorem
, it is sufficient, by Minkowski's inequality, to show that