Science topics: AnalysisFixed Point Theory

Science topic

# Fixed Point Theory - Science topic

In mathematics, a fixed-point theorem is a result saying that a function F will have at least one fixed point (a point x for which F(x) = x), under some conditions on F that can be stated in general terms. Results of this kind are amongst the most generally useful in mathematics.

Questions related to Fixed Point Theory

If possible, give an example of a continuous function defined on a convex subset of a Banach space $X$ satisfies Kannan contraction but does not satisfy Banach contraction.

Hi everyone

I want to start the discussion on a real-life application of metrical and Generalized Metrical(b-metric, partial metric, rectangular metric, complex-valued metric, C*-algebra valued metric, etc) Fixed Point Theory. I hope you can contribute to the discussion.

I am working on geometry of banach spces and applications in metric fixed point theory , especially my interesting is renorming of Banach spaces, Is anyone interested in collaboration

Actually proving a new metric-like space to be metrizable is an interesting study in fixed point theory. Though I don't have so much knowledge or idea about all the metrization theorems except for Urishon metrization theorem. So I want to know more about this area. Thank you.

**Dear researchers**

**As we know, recently a new type of derivatives have been introduced which depend two parameters such as fractional order and fractal dimension. These derivatives are called fractal-fractional derivatives and divided into three categories with respect to kernel: power-law type kernel, exponential decay-type kernel, generalized Mittag-Leffler type kernel.**

**The power and accuracy of these operators in simulations have motivated many researchers for using them in modeling of different diseases and processes.**

**Is there any researchers working on these operators for working on equilibrium points, sensitivity analysis and local and global stability?**

**If you would like to collaborate with me, please contact me by the following:**

**Thank you very much.**

**Best regards**

**Sina Etemad, PhD**

Hi everyone,

I want to start the discussion about open problems in the field of Fixed Point Theory. I hope you can contribute to the discussion.

This set of ODEs describes a dynamical system where a,b,c,d and e are positive real valued parameters of the system. We know at a fixed point all system dynamics are zero. Though in this special case, the set of nonlinear equations after setting all dynamics to zero, states that one of the system parameters (e) should be equal to zero wich is not the case. Does such a system (for particular this one) have a equilibrium point or this result states that it has not.

Dear Researchers

As you know, nowadays, the mathematical models of different phenomena and processes are designed by means of fractional operators in the context of various systems of boundary or initial value problems with boundary conditions. Some of such well-known mathematical models can be found in many papers like pantograph equations, Langevin equations, Jerk equations, Snap equations, etc. All of these models are practical examples of fractional boundary value problems.

Could you suggest other examples about practical applications in fractional boundary value problems? I am going to study the dynamical behaviors of these new models theoretically and numerically.

Thank you very much.

Best regards

As question stated , maybe can also include symplectic topology.

Please let me know if such function, which does not satisfy Banach contraction principle, but the fixed points exist for these functions.

How we can studying the existence and uniqueness of solutions of the functional equations by fixed point theory

As we know, the vastness of the subject is realized by the variety of interdisciplinary subjects that belong to several mathematical domains such as classical analysis, differential and integral equations, functional analysis, operator theory, topology and algebraic topology; as well as other subjects such as Economics, Commerce etc.

There are many generalizations about Banach's contraction principle in fixed point theory. Are there any applications these generalizations in any applied fields?

What is the stability of a fixed point (non-isolated), which has zero eigenvalues? Is there any analytical procedure for finding stability of these type of fixed points. If numerical analysis can do the job, then how to do that?

I read in many articles a statement that best proximity point theory has applications in the field of Economics, game theory, biological science. But I want to see some physical problem that was mathematically modeled and then solved by using best proximity point theory or fixed point theory.

I'm currently working on fixed point theorems on uniformly convex spaces and I will love if anyone can point my attention to spaces that are uniformly convex apart from the ones I have listed above.

i have trouble in solving a problem using an implicit algorithm. I am not able to get the initial approximation and also how will i proceed to the next iteration.

I would like to collect the applications of partition of unity theorem in math, for example manifold, topology, fixed point theory, differential forms, differential geometry, vector analysis, algebraic topology, differential topology , and any other related fields.

suggest me any good materilas on fixed point theory and dynamic programing,and fuzzy metric space

Please I would like your help on getting an e-copy of the book entitled "The theory of fixed point classes" by Tsai-Han Kiang.

Best regards,

M.S. Abdullahi

Can we use fixed point theory to study the inventory control problems? If yes then please share any literature.

How we can use Fixed point theory to find the fluid layer stability or instability?

Whenever we try to introduce Fixed Point Theory, we can use some real life examples. I want to know some of such examples. Like the map meets the floor in one and only one fixed point. If anybody can present more of such type?

Fixed point theory. Stochastic Analysis

It is said that fixed point theory has lot of applications not only in the field of mathematics but also in various disciplines. Which one is the most important?

How we can use Fixed point theory to find stability condition of some Flow problems?

I am trying to prove the existence of positive solutions to:

-y''=f(y), 0<x<1,

y(0)=y(1)=0.

where f(y)=k sin(y)-sin(2y) "k~ arbitrary constant". Any help with known result or useful technique is much appreciated.

For example, when we xerox a document, the printer takes the A4 page to the same. Are there other better examples?

What are the applications of implicit iterative algorithms? Moreover, is there any nonlinear nonexpansive mapping example satisfying some result (any research paper in literature with implicit iteration) having implicit iteration process?

i am looking for a software tools set that let me setup a multi-point to multi-point VPN which is called VPLS over IP (not MPLS) . does any one have any suggestion how can I get in to this?

MRI which uses NMR enjoy the resonance feature of hydrogen nucleus for imaging. this technique is completely different from reflection feature of objects used in radar scanning. i would like to know why this technique is not used for radar scanning to detect other material that used in aircraft or devices that have special materials .

Dear All,

Why most mathematicians choose kkm-mapping to solve the problems in variational inequality ? while the problems can been solve by another methods such as fixed point theorem, critical point theorems and so on.

best regards

We know that from Shukla's paper (Shukla, S: Partial b-metric spaces and fixed point theorems. Mediterr. J. Math. (to appear).doi:10.1007/s00009-013-0327-4)

If (X,p) be a partial metric space and q≥1, then (X,p_{b}) is a partial b-metric space with the coefficient s=2^{q-1} , where p_{b} is defined by p_{b}(x;y)=(p(x,y))^{q}. Whether this statement is true according to a modified definition of partial b-metric in the paper of Z. Mustafa and et al.(Z. Mustafa, J.R. Roshan, V. Parvaneh and Z. Kadelburg, Some common fixed point results in ordered partial b-metric spaces, Journal of Inequalities and Applications, 2013, 2013:562.)

Let X be a complete metric space (C*-algebra valued) and CB(X) be nonempty closed and bounded subset of X. Can we define a mapping T:X------->CB(X), i.e. Can we have a C*-algebra valued multi-valued mapping? If Yes, please can someone provide me with an example of such a mapping?

Because I know if X=R(set of real numbers), any interval I be it open, closed, half-open or half-closed then I is a subset of R and we can define such a mapping T by for instance Tx = [0, x/2), thus we can be able to get a fixed point depending on some conditions either on T, X or both.

I hope my question is well constructed and understandable.

when I studied some delay systems, the fixed points of these systems have zero eigenvalue. I don't how can study its stability?

Such as the differential equations or more generally, evolution equations are the fields where the Banach's Contraction Principle in Fixed Point Theory is recommended., Book of "A. Pazy, Semigroups of linear operators and Applications to Partial Differential Equations".

What are the additional conditions as needed in order to establish the

existence of a unique fixed point satisfying the condition for any α ∈ (0, 1] there exists

β ∈ (0, α) such that d

_{α}(x, z) ≤ s[d_{β}(x, y) + d_{β}(y, z)] in Gbq-family (X, d_{α}).Related information can be found in below paper.

Kumari, Panda S., and Dinesh Panthi. "Cyclic contractions and fixed point theorems on various generating spaces." Fixed Point Theory and Applications 2015.1 (2015): 153.

Distribution of nearest neighbors versus separation distance (r) is plotted for a point pattern. If the function exhibits three peaks at three different r, then what would be the interpretation of such a graph?

I can see the transform whose kernel is log function

Every group of prime order is cyclic.

Cyclic implies abelian.

Every subgroup of an abelian group is normal.

Every group of Prime order is simple.

Manifold concept was first introduced by Riemann.

Assume that M is a compact manifold with fixed point property. Let N be a compact submanifold of M x M, with dim (N)=dim (M). Assume that $\pi_{1}:N \to M$ is a surjective map, where $\pi_{1}$ is the projection on the first component.

Is it true that N has non empty intersection with the diagonal {(x,x)\in M x M}?

If there is no extranous fixed points for any iterative methods, what does mean?

Such methods, possible to diverge at any points in complex plane. ?

If there is many extranous fixed points, then what it means?

For example, one optimal fourth order modified newton's method gives 30 extranous fixed points for solving p(z)=z^3-1. for this results what say's.

Your valuable answer and comments lead me to good work

Thanks in advance

I have a function f

f: Z^2 -> Z^2

such that

(x', y') = f(x, y)

and

x'-y' <= x-y

I need a reference paper or book that shows (perhaps using a more general statement) that iterative applications of f converge to a fixed point (x_0, y_0) IN A FINITE NUMBER OF ITERATIONS.

I have implemented beamformer(MVDR/LCMV) for speech enhancement in matlab, now I am trying to convert it to fixed point implementation. during the weight calculation step correlation matrix inversion is required, but in fixed point implementation correlation matrix inversion is not giving correct results(may be due to very small values in correlation matrix).

I have always thought that fixed points and equilibria refer to the same thing until I started studying stability of fixed points where I noticed that to find an equilibrium of a function f we need to solve f(x)=0 and not f(x)=x as we do for fixed points !!!

Aren't they the same thing or am I just missing some points?

The definition of Jachymski function can be found in the paper

''C. Alegre, J. Marn and S. Romaguera, A ﬁxed point theorem in generalized contraction involving W-distances on complete quesi-metric spaces, Fixed theory and applications, 40,1-8,(2014).

I'm looking for optimizing multivalued vector valued function.

I am wondering if there are some theorems in nonlinear analysis that address the following properties of implicit function (set valued function) that the implicit function is f(x) : X-> P(Y) where X , Y \subset R^n , and P(Y) denotes the power set of Y. and y \in f(x) specified by F(x,y)=0. The properties are

1- Existence of y \in f(x) for any x \in Y

2- hemi-continuity ( or upper and lower hemi-continuity) of the set valued function

3- differentiability class of f(x) that is the maximum order of differentiability f(x) -( we can assume f(x) is single value if required)

4- f(x) is convex single valued or set valued function

5- f(x) is single valued

6- the set valued function f(x) is connected for any x \in X

any theorem that can address one of those properties is also useful

We have some important fixed point theorem likes the three celebrated fixed point

theorems: The Banach, Brouwer & Schauder theorems. My question is to use the method of

upper and lower solution and add some conditions to give new Theorem for the

existence of couple solution (u,v) for system.

i.e., Is a convex set in R^n with the fixed point property always compact ?

As you know fixed point theory has many applications in all sciences.

Fixed and floating point date type synthesizable HDL code what are the diff ways/tricks/new& diff ideas that a fixed or floating point algorithm can be implemented in FPGA using Verilog and the same for VHDL

For the betterment of student and professionals:SInce this info is not fully/widely available in book only engineers who were working in FPGA embedded system application development knows better ways and possibilities with current technical advancements.

Can anyone suggest new branches where we can apply fixed point theory? Is there any application of fixed point theory to medical sciences?