共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper, the following facts are stated in the setting of b-metric spaces.
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- (1)The contraction constant in the Banach contraction principle fully extends to [0, 1), but the contraction constants in Reich’s fixed point theorem and many other fixed point theorems do not fully extend to [0, 1), which answers the early stated question on transforming fixed point theorems in metric spaces to fixed point theorems in b-metric spaces.
- (2) Caristi’s theorem does not fully extend to b-metric spaces, which is a negative answer to a recent Kirk–Shahzad’s question (Remark 12.6) [Fixed Point Theory in Distance Spaces. Springer, 2014].
2.
M. Almahalebi 《Acta Mathematica Hungarica》2018,154(1):187-198
Using the fixed point method, we investigate the stability of a generalization of Jensen functional equationwhere \({n \in \mathbb{N}_{2}}\), \({b_{k}=\exp(\frac{2i\pi k}{n})}\) for \({0\leq k \leq n-1}\), in Banach spaces. Also, we prove the hyperstability results of this equation by the fixed point method.
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$$ \sum_{k=0}^{n-1} f(x+ b_{k}y)=nf(x),$$
3.
In this paper, we will consider the following multipoint boundary value problem for the following second-order dynamic equations on time scales where :RR is an increasing homeomorphism and positive homomorphism and (0)=0. By using fixed point theorems, we obtain an existence theorem of positive solutions for the above boundary value problem, which includes and improve some related results in the relevant literature. As an application, an example to demonstrate our results is given. 相似文献
4.
Dehong Ji Yu Tian Weigao Ge 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(11):5406-5416
This paper deals with the existence of positive solutions for the one-dimensional p-Laplacian subject to the boundary value conditions: where p(s)=|s|p−2s,p>1. We show that it has at least one or two positive solutions under some assumptions by applying the fixed point theorem. The interesting points are that the nonlinear term f is involved with the first-order derivative explicitly and f may change sign. 相似文献
5.
With the notation
,we prove the following result.Theorem 1. Assume that p is a trigonometric polynomial of degree at most n with real coefficients that satisfiesThenwithWe also prove thatandfor every
, where
denotes the collection of all trigonometric polynomials of the form 相似文献
||p||L2(K)An1/2 and ||p′||L2(K)Bn3/2.
M4(p)−M2(p)M2(p)
M2(p)−M1(p)10−31M2(p)
6.
A. Bahraini G. Askari M. Eshaghi Gordji R. Gholami 《Journal of Fixed Point Theory and Applications》2018,20(2):89
Recently Eshaghi et al. introduced orthogonal sets and proved the real generalization of the Banach fixed point theorem on these sets. In this paper, we prove the real generalization of Diaz–Margolis fixed point theorem on orthogonal sets. By using this fixed point theorem, we study the stability of orthogonally \(*\)-m-homomorphisms on Lie \(C^*\)-algebras associated with the following functional equation: for each \(m=1,2,3,4.\). Moreover, we establish the hyperstability of these functional equations by suitable control functions.
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$$\begin{aligned} \begin{aligned}&f(2x+y)+f(2x-y)+(m-1)(m-2)(m-3)f(y)\\&\quad =2^{m-2}[f(x+y)+f(x-y)+6f(x)]. \end{aligned} \end{aligned}$$
7.
In this paper, we use Schauder and Banach fixed point theorem to study the existence, uniqueness and stability of periodic solutions of a class of iterative differential equation
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$$\begin{aligned} c_0x''(t)+c_1x'(t)+c_2x(t)=x(p(t)+bx(t))+h(t). \end{aligned}$$
8.
9.
Positive solutions of three-point boundary value problems for systems of nonlinear second order ordinary differential equations 总被引:1,自引:0,他引:1
In this paper, we study the three-point boundary value problems for systems of nonlinear second order ordinary differential equations of the form Under some conditions, we show the existence and multiplicity of positive solutions of the above problem by applying the fixed point index theory in cones. 相似文献
10.
Choonkil Park Dong Yun Shin Jung Rye Lee 《Journal of Fixed Point Theory and Applications》2016,18(3):569-586
In this paper, we solve the additive \({\rho}\)-functional equations where \({\rho}\) is a fixed non-Archimedean number or a fixed real or complex number with \({\rho \neq 1}\). Using the fixed point method, we prove the Hyers–Ulam stability of the above additive \({\rho}\)-functional equations in non-Archimedean Banach spaces and in Banach spaces.
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$$\begin{aligned} f(x+y)-f(x)-f(y)= & {} \rho(2f(\frac{x+y}{2})-f(x)-f(y)), \\ 2f(\frac{x+y}{2})-f(x)-f(y)= & {} \rho(f(x+y)-f(x)-f(y)), \end{aligned}$$
11.
Ri-An Yan Shu-Rong Sun Dian-Wu Yang 《Journal of Applied Mathematics and Computing》2015,48(1-2):187-203
In this paper, we study the existence of solutions for the boundary value problems of fractional perturbation differential equations or subject to where \(1<\alpha <2,\,D^{\alpha }\) is the standard Caputo fractional derivatives. Using some fixed point theorems, we prove the existence of solutions to the two types. For each type we give an example to illustrate our results.
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$$\begin{aligned} D^{\alpha }\left( \frac{x(t)}{f(t,x(t))}\right) =g(t,x(t)),\;\;a.e.\;t\in J=[0,1], \end{aligned}$$
$$\begin{aligned} D^{\alpha }\left( x(t)-f(t,x(t))\right) =g(t,x(t)),\;\;a.e.\;t\in J, \end{aligned}$$
$$\begin{aligned} x(0)=y(x),\;\;x(1)=m, \end{aligned}$$
12.
Prondanai Kaskasem Chakkrid Klin-eam Yeol Je Cho 《Journal of Fixed Point Theory and Applications》2018,20(2):76
In this paper, we prove the Hyers–Ulam–Rassias stability of the generalized Cauchy–Jensen set-valued functional equation defined by for all \(x,y,z \in X\) and \(\alpha \ge 2\) on a Banach space by using the fixed point alternative theorem.
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$$\begin{aligned} \alpha f\left( \frac{x+y}{\alpha } + z\right) = f(x) \oplus f(y)\oplus \alpha f(z) \end{aligned}$$
13.
Laura Ferracuti Cristina Marcelli Francesca Papalini 《Set-Valued and Variational Analysis》2011,19(1):1-21
Combining fixed point theorems with the method of lower and upper solutions, we get the existence of solutions to the following nonlinear differential inclusion:satisfying various nonlinear boundary conditions, covering Dirichlet, Neumann and periodic problems. Here Φ is a non-surjective homeomorphism and D is a generic positive continuous function.
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$ (D(x(t))\Phi(x'(t)))' \in G(t,x(t),x'(t)) \ \ \mbox{a.e. } t\in I=[0,T], $
14.
Using the fixed point method, we investigate the generalized Hyers–Ulam stability of the ternary homomorphisms and ternary derivations between fuzzy ternary Banach algebras for the additive functional equation of n-Apollonius type, namelywhere \({n \geq 2}\) is a fixed positive integer.
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$${\sum_{i=1}^{n} f(z-x_{i}) = -\frac{1}{n} \sum_{1 \leq i < j \leq n} f(x_{i}+x_{j}) + n f (z-\frac{1}{n^{2}} \sum_{i=1}^{n}x_{i}),}$$
15.
We first introduce basic concepts of \((2,\beta )\)-Banach spaces and we will reformulate the fixed point theorem [8, Theorem 1] in this space. After that, we achieve the general solution of the radical sextic functional equation for f a mapping from the set of all real numbers \({\mathbb {R}}\) into a vector space. In addition, we prove a new type of stability results for radical sextic functional equation in \((2,\beta )\)-Banach spaces. The method is based on a fixed point Theorem 3.1 in some functions spaces.
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$$\begin{aligned} f\left( \root 3 \of {x^3+y^3}\right) +f\left( \root 3 \of {x^3-y^3}\right) = 2f(x)+2f(y),\quad x,y\in {\mathbb {R}}, \end{aligned}$$
16.
17.
Blow-up analysis for a system of heat equations with nonlinear flux which obey different laws 总被引:1,自引:0,他引:1
We consider a system of heat equations ut=Δu and vt=Δv in Ω×(0,T) completely coupled by nonlinear boundary conditions We prove that the solutions always blow up in finite time for non-zero and non-negative initial values. Also, the blow-up only occurs on ∂Ω with for p,q>0, 0≤α<1 and 0≤β<p. 相似文献
18.
Let X be a metric space andμa finite Borel measure on X. Let pμq,t and pμq,t be the packing premeasure and the packing measure on X, respectively, defined by the gauge (μB(x,r))q(2r)t, where q, t∈R. For any compact set E of finite packing premeasure the authors prove: (1) if q≤0 then pμq,t(E)=pμq,t(E);(2)if q>0 andμis doubling on E then pμq,t(E) and pμq,t(E) are both zero or neither. 相似文献
19.
By using a fixed point theorem of strict-set-contraction, some new criteria are established for the existence of positive periodic solutions of the following periodic neutral Lotka–Volterra system with state dependent delays where (i,j=1,2,…,n) are ω-periodic functions and (i=1,2,…,n) are ω-periodic functions with respect to their first arguments, respectively. 相似文献
20.
We establish a stability result concerning the functional equation: in a large class of complete probabilistic normed spaces, via fixed point theory.
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$\sum\limits_{i = 1}^m {f\left( {mx_i + \sum\limits_{j = 1,j \ne i}^m {x_j } } \right) + f\left( {\sum\limits_{i = 1}^m {x_i } } \right) = 2f\left( {\sum\limits_{i = 1}^m {mx_i } } \right)} $