Báo cáo hóa học: "Research Article T -Stability of Picard Iteration in Metric Spaces" pot

... Kirk, or any other iteration scheme since, if one obtains convergence to a fixed point for a map using Picard s iteration, there is no point in considering any other more complicated iteration procedure. Acknowledgment This ... 5 Then, Picard s iteration is T- stable. Proof. From 2, Theorem 11, T has a unique fixed point q. Also, T satisfies 1. It remains to show that 2 i...

Ngày tải lên: 21/06/2014, 22:20

... sufficient conditions that Picard s iteration is T- stable for an arbitrary self-map, and then demonstrate that a number of contractive conditions are Picard T- stable. We will need the following lemma ... is not bounded, then it cannot possibly converge. If these conditions hold for x n1  Tx n , that is, Picard s iteration, then we will say that Picard s iteration is T- stable...

Ngày tải lên: 22/06/2014, 00:20

... of the concept of altering distance function. It has also been extended in the context of multivalued 14 and fuzzy mappings 15. The concept of altering distance function has also been introduced ... equivalently dz 1 ,z 2 0, that is, z 1  z 2 . This proves the uniqueness of the fixed point. If we particularly take φ t 1 − kψ t t& gt;0 where 0 <k<1, then we obtain t...

Ngày tải lên: 21/06/2014, 23:20

... prove that ρ n p, x ≥ γ.Inviewofthefact that was mentioned at the beginning, we get ρ 2 p, xδα, t ≥ γ. Assuming the statement for n − 1 holds, we will prove it for n. 1 Let k ≤ 2. Putting ... hence, α · t  β /t  p p−1 −1 . Further, we obtain t  βp p−1 −1 − α −1 . It is obvious that we have a minimum at this point in the interval 0, 1. Then, we obtain 1/α · t...

Ngày tải lên: 21/06/2014, 07:20

... on the maximisation of joint entropy of the output and using correlation between output and input to recover the ICs for undercomplete situation. This technique is an iterative approach that minimises ... comparison of this approach with the rank, R,ofG indicates that R is not suitable for estimating N. The results also indicate that there is a significant improvement of quality of s...

Ngày tải lên: 21/06/2014, 19:20

... particular the fixed point set of f and the fixed point set of g intersect. The rest of the proof is similar to that of Esp ´ ınola and Kirk 24, Theorem 4.3 and so is omitted. In the next result, we ... convexity of the values of T but, this time, we ask the geodesic space M not to have bifurcating geodesics. That is, for any two segments starting at the same point and having...

Ngày tải lên: 21/06/2014, 20:20

... A t − B t T  t Q  t . It is easy to see that T t Q t G −1 t G  t  T t Q t G −1 t  A t − B t T  t Q  t   T t Q t P t − T t Q t G −1 t B t T  t Q  t  T t Q t T  t Q  t  T  t Q  t . ... 2.11. Finally, Q t G −1 t B t  Q t G −1 t B t P ρ t  Q t G −1 t B t T t Q t T −1 t Q ρ t  Q t G −1...

Ngày tải lên: 21/06/2014, 05:20

... all time, that is, whether there are resonances that might cause the amplitude of the oscillations to increase without bound. The first positive result of boundedness of solutions in the superlinear ... Problems 2. The Proof of Theorem The proof of Theorem 1.1 is based on Moser’s small twist theorem for reversible mapping. It mainly consists of two steps. The first one is to find a...

Ngày tải lên: 21/06/2014, 07:20

... exponentially. An example is give to illustrate that the result obtained can be applied to concrete partial differential equations. 1. Introduction Of concern is the exponential stability of two ...   T S    √ Av t βu t    2 dt. 2.28 Proof. Taking the inner product of both sides of 1.2 with v t and integrating over S, T , we see  T S   v  t   2 dt   T...

Ngày tải lên: 21/06/2014, 11:20

... properly cited. 1. Introduction The aim of this article is to extend the applications of the fixed point alternative method to provide a fuzzy version of Hyers-Ulam-Rassias stability for the functional ... Applications The uniqueness of T follows from the fact that T is the unique fixed point of J 1 with the property that there exists k ∈ 0, ∞ such that N  T  x  − f  x ...

Ngày tải lên: 21/06/2014, 20:20