Fixed Point Theory and Applications - Latest Articles

Common fixed point theorems for weakly increasing mappings on ordered orbitally complete metric spaces

Hui-Sheng Ding — 2012-05-19T00:00:00Z

In this article, we prove existence results for common fixed points of two or three relatively asymptotically regular mappings satisfying the orbital continuity of one of the involved maps on ordered orbitally completemetric spaces. We furnish suitable examples to demonstrate the validity of the hypotheses of our results.

The hybrid algorithm for the system of mixed equilibrium problems, the general system of infinite variational inequalities and common fixed points for nonexpansive semigroups and strictly pseudo-contractive mappings

Poom Kumam — 2012-05-18T00:00:00Z

No description available

A general inexact iterative method for monotone operators, equilibrium problems and fixed point problems of semigroups in Hilbert spaces

Vittorio Colao — 2012-05-15T00:00:00Z

Let H be a real Hilbert space. Consider on H a nonexpansive family \mathcal{T}=\{T(t):0\leq t<\infty\} with a common fixed point, a contraction f with the coefficient 0<\alpha<1, and a strongly positive linear bounded self-adjoint operator A with the coefficient \bar{\gamma}>0. Assume that 0<\gamma<\bar{\gamma}/\alpha and that \mathcal{S}\{S(t):0\leq t<\infty\} is a family of nonexpansive self-mappings on H such that F(\mathcal{T})\subseteq F(\mathcal{S}) and \mathcal{T} has property (\mathscr{A}) with respect to the family \mathcal{\mathcal{S}}. It is proved that the following schemes (one implicit and one inexact explicit):x_t=b_t\gamma f(x_t)+(I-b_tA)S(t)x_tandx_0\in H,\quad x_{n+1}=\alpha_n\gamma f(x_n)+\beta_nx_n+((1-\beta_n)I-\alpha_nA)S(t_n)x_n + e_n,\quad n\geq 0converge strongly to a common fixed point x^*\in F(\mathcal{T}), where F(\mathcal{T}) denotes the set of common fixed point of the nonexpansive semigroup. The point x^* solves the variational inequality \langle(\gamma f -A)x^*,x-x^*\rangle\leq 0 for all x\in F(\mathcal{T}). Various applications to zeros of monotone operators, solutions of equilibrium problems, common fixed point problems of nonexpansive semigroup are also presented. The results presented in this paper mainly improve the corresponding ones announced by many others.

The extragradient-Armijo method for pseudomonotone equilibrium problems and strict pseudocontractions

Pham Ngoc Anh — 2012-05-10T00:00:00Z

In this article, we present a new iteration method for finding a common element of the set of fixed points of p strict pseudocontractions and the set of solutions of equilibrium problems for pseudomonotone bifunctions without Lipschitz-type continuous conditions. The iterative process is based on the extragradient method and Armijo-type linesearch techniques. We obtain weak convergence theorems for the sequences generated by this process in a real Hilbert space.

On the stability of set-valued functional equations with the fixed point alternative

Hassan Azadi Kenary — 2012-05-10T00:00:00Z

Using the fixed point method, we prove the Hyers-Ulam stability of a Cauchy-Jensen type additive set-valued functional equation, a Jensen type additive-quadratic set-valued functional equation, a generalized quadratic set-valued functional equation and a Jensen type cubic set-valued functional equation.

Common fixed points of almost generalized (\ps,\phi)-contractive mappings in ordered metric spaces

Wasfi Shatanawi — 2012-05-09T00:00:00Z

In this article, we introduce the notion of almost generalized (psi, phi)-contractive mappings in ordered metric spaces and we establish some fixed and common fixed point results in ordered complete metric spaces. Our results generalize several well-known comparable results in the literature. Finally, an example and an application are given in order to support the useability of our results.

Periodic points for the weak contraction mappings in complete generalized metric spaces

Chi-Ming Chen — 2012-05-09T00:00:00Z

In this article, we introduce the notions of the (\phi,\varphi)-weak and (\psi,\varphi)-weak contraction mappings in complete generalized metric spaces and prove two theorems which assure the existence of a periodic point for these two types of weak contraction.

Some Newton-like methods with sharper error estimates for solving operator equations in Banach spaces

D. r. Sahu — 2012-05-09T00:00:00Z

No description available

Coupled and tripled coincidence point results without compatibility

Nawab Hussain — 2012-05-09T00:00:00Z

In this article, we introduce a new and simple approach to coupled and tripled coincidence point theory. By using our method, we establish coupled coincidence point results of Lakshmikantham and 'Ciri'c, Binayak et al., Alotaibi and Alsulami without any type of commutativity condition on F and g. We also use our technique to prove tripled coincidence point results of Borcut and Berinde without commutativity of maps. Also, we give a supporting example of non-commuting, non-compatible mappings where the above mentioned results can not be applied.

Common fixed point and approximation results for generalized (f,g) weak contractions

F. Akbar — 2012-05-08T00:00:00Z

The existence of common fixed points is established for three mappings where T is generalized (f, g)-weakly contractive mapping on a nonempty subset of aBanach space. As applications, the invariant approximation results are proved. Our results unify and improve several recent results in the literature.