theorems


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Related to theorems: Sylow theorems
See: premises
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Letting [lambda] = [[gamma].sup.-2] in the theorems of this section, where [gamma] > 0, we can obtain the change of scales for E[[F.sub.Z]([gamma], y) | [Z.sub.n]([gamma])] and E[[F.sub.Z]([gamma] * / [square root of 2], y/ [square root of 2])[G.sub.Z](-y * / [square root of 2], y/ [square root of 2]) | [Z.sub.n]([gamma] *)] ; that is, the scale y in the functions [F.sub.Z]([gamma]*, y), [G.sub.Z](-[gamma]* / [square root of 2], y/ [square root of 2]), and [Z.sub.n]([gamma]*) is moved to [K.sub.1], [K.sub.2], [[PSI].sub.1], and [H.sub.m] in evaluating the conditional expectations as above.
Then [M.sup.1/2.sub.h] and [mathematical expression not reproducible] can be replaced by [B.sub.1] and [B.sub.2], respectively, in each expression of the theorems.
Simsek, Some fixed point theorems on ordered metric spaces and application, Fixed Point Theory Appl., (2010), Article ID 621492, 17 pages.
This follows from Theorems 1.1 and 2.8 (see also [7, Theorem 6.3.5 (ii)]).
Using the above theorems, Dalal and Govil [15] also gave the following.
In this section, we consider two generalized fractional integral operators involving the Fox's H-function as the kernels and derived the following theorems.
(i) follows from Theorem 8.12.2 of [11], and (ii) follows from Theorems 8.10.5 and 8.13.2 of [11] applying to X = [C.sub.p](Y) and Y = [C.sub.p](X).
In this section, we present more general universality results which will be applied for the proof of Theorems 1-8.
A kind of Borsuk-Ulam type theorems consists in estimating the cohomological dimension of the set A(f,H, G).
In our previous work [43], we reviewed applications of our fixed point theorems for the multimap class of compact compositions of acyclic maps and, in [48], we collected most of fixed point theorems related to the KKM theory due to the author.
In the paper (in Section 2), we are concerned with conditional stability of (1) with the results formulated in Theorems 11-18.
Discovering the implications of a theorem takes time.