Saturday, February 24, 2007

Nike Shop Mercurial R9

local version of the fixed point theorem of Banach (modular)

In modular spaces, the following result,

proposes a generalization of the local version of the principle of

contraction in Banach spaces.


Execice

Let (E, rho) a complete modular space, or modular rho

checks the Fatou property.
Let the ball B = B (y, r) = {x: rho (xy) is strictly less than r}.
T is an application of B in E sharp contraction, ie d,

there are two constants p, k, with k in] 0,1 [and p> 1

such as


rho ( p (Tx-Ty)) \\ leq k rho (xy) on ExE

Assume that rho (q (Ty-y)
Proof

is followed the same steps if the metric.

Let r 'in] 0, r [such that rho (q (Ty-y)) \\ leq (1 -k) r '

Consider the ball D = {x: rho (xy) \\ leq r'}. Let us show that D is stable by T;

Indeed, for x in D, we have:

rho (Tx-y) = rho ((p / p) (Tx-Ty) + (q / q) (Ty-y))

\\ leq rho (p (Tx-Ty)) + rho (q (Ty-y))

\\ leq kr '+ (1-k) r' = r '


As rho checks the Fatou property, D is rho-closed (check).

By

théorème2.1 in [Hanebaly (2005)], T has a fixed point.

< (1-k) r,ou q est le conjugué de p,

Tuesday, February 20, 2007

Mİlena Velba Pİcs

Local version of the fixed point theorem Banach

Exercise

<(1-k) r.

Let (E, d) a metric space complet.B = B (y, r) is the open ball

center y and radius r in ET is an application of B E

contractante.Si strictly k-d (Ty, y)

a fixed point.


(Hint: try to find a closed ball of center y, stable T)

Proof: Choose 0

Show that the closed ball D = {x: d (x, y) \\ leq r '} is stable T.


Indeed, if x is in D, then:

d (Tx, y) \\ leq d (Tx, Ty) + d (Ty, y) \\ leq kd (x, y) + (1-k) r '\\ leq r'.

Since D is complete, the existence of the fixed point of T follows the principle

Tuesday, February 13, 2007

Wwe Gif Images Of Breast

open problem in the theory of fixed point (Modular Spaces) (2) References

following problem is implicit in earlier work:

Let (E, \\ rho) a complete modular space, D is a subset of E

\\ rho-T ferme.Soit an application from D to D \\ rho-strictly <(1-k)r,montrer que T admet

contracting, ie,:

exists k in] 0,1 [such as \\ rho (Tx-Ty) \\ leq k \\ rho (xy) on DXD

Then T possesses Does a point Fixed?

Note: If < r'< r tel que d(Ty,y)\leq (1-k)r'<(1-k)r.

B \\ rho-terminal, the answer is positive and the proof is almost

immediate.Si satisfies the condition delta2 rho and rho (xy) is

finite for all x, y in D The theoreme3.1 [Hanebaly (2005)] provides a result.

. See also Ait Taleb-Hanebaly (Post-References)

Friday, February 2, 2007

Marriage Invitation Kavithaigal



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