Saud M. Alsulami

Ideal convergence of double sequences in random 2-normed spaces

Quite recently, Alotaibi and Mohiuddine (Adv. Differ. Equ. 2012:39, 2012) studied the idea of a random 2-normed space to determine some stability results concerning the cubic functional equation. In this paper, we define and study the concepts of I-convergence and I∗-convergence for double sequences in random 2-normed spaces and establish the relationship between these types of convergence, i.e., we show that I∗-convergence implies I-convergence in random 2-normed spaces. Furthermore, we have also demonstrated through an example that, in general, I-convergence does not imply I∗-convergence in random 2-normed spaces.MSC:40A05, 46A70.

Existence of weighted pseudo anti-periodic solutions to some non-autonomous differential equations

Abstract In this paper we first introduce two new concepts called respectively weighted pseudo periodicity and weighted pseudo anti-periodicity, which generalize respectively the well-known notions of periodicity and that of anti-periodicity. Basic properties of these new functions are discussed. Furthermore, the existence of weighted pseudo anti-periodic solutions to some damped non-autonomous second-order differential equations will be investigated. To illustrate our abstract results, the existence of weighted pseudo anti-periodic solutions to a plate-like equation is discussed.

Coupled coincidence points for monotone operators in partially ordered metric spaces

Using the notion of compatible mappings in the setting of a partially ordered metric space, we prove the existence and uniqueness of coupled coincidence points involving a (ϕ, ψ)-contractive condition for a mappings having the mixed g-monotone property. We illustrate our results with the help of an example.

Coupled fixed and coincidence points for monotone operators in partial metric spaces

In this paper, we prove some coupled fixed point results for (ϕ,φ)-weakly contractive mappings in ordered partial metric spaces. As an application, we establish coupled coincidence results without any type of commutativity of the concerned maps. Consequently, the results of Luong and Thuan (Nonlinear Anal. 74:983-992, 2011), Alotaibi and Alsulami (Fixed Point Theory Appl. 2011:44, 2011) and many others are extended to the class of ordered partial metric spaces.

PPF Dependent Fixed Point Results for Triangular αc-Admissible Mappings

We introduce the concept of triangular α c-admissible mappings (pair of mappings) with respect to η c nonself-mappings and establish the existence of PPF dependent fixed (coincidence) point theorems for contraction mappings involving triangular α c-admissible mappings (pair of mappings) with respect to η c nonself-mappings in Razumikhin class. Several interesting consequences of our theorems are also given.

Coupled point results in partially ordered metric spaces without compatibility

AbstractThe existence of fixed points, coupled fixed points, and coupled coincidence points without the assumption of compatibility is established. The results presented in this paper extend, improve, and generalize some well-known results in the literature. Also, an example is given to show that our results are real generalizations of known ones in coupled coincidence fixed point theory. MSC:54H25, 47H10.

Common fixed point theorems for nonlinear contractive mappings in fuzzy metric spaces

In this paper, we prove several common fixed point theorems for nonlinear mappings with a function ϕ in fuzzy metric spaces. In these fixed point theorems, very simple conditions are imposed on the function ϕ. Our results improve some recent ones in the literature. Finally, an example is presented to illustrate the main result of this paper.MSC:54E70, 47H25.

Generalized probabilistic metric spaces and fixed point theorems

AbstractIn this paper, we introduce a new concept of probabilistic metric space, which is a generalization of the Menger probabilistic metric space, and we investigate some topological properties of this space and related examples. Also, we prove some fixed point theorems, which are the probabilistic versions of Banach’s contraction principle. Finally, we present an example to illustrate the main theorems. MSC:54E70, 47H25.

Weakly isotone increasing mappings and endpoints in partially ordered metric spaces

The aim of this work is to extend the notion of weakly isotone increasing mappings to multivalued and present common endpoint theorems for T-weakly isotone increasing multivalued mappings satisfying generalized (ψ,φ)-weak contractive as well as almost contractive inequalities in complete partially ordered metric spaces. Examples are given in support of the new results obtained.MSC:47H10, 54H25, 54H10.

A family of nonlinear difference equations

We study solutions ( x n ) n ? N of nonhomogeneous nonlinear second order difference equations of the type ? n = x n ( ? n , 1 x n + 1 + ? n , 0 x n + ? n , - 1 x n - 1 ) + ? n x n , n ? N , with?given?initial?data? { x 0 ? R & x 1 ? R + } where ( ? n ) n ? N ? R + & ( ? n , 0 ) n ? N ? R + & ( ? n ) n ? N ? R , and the left and right ? -coefficients satisfy either ( ? n , 1 ) n ? N ? R + & ( ? n , - 1 ) n ? N ? R + or ( ? n , 1 ) n ? N ? R 0 + & ( ? n , - 1 ) n ? N ? R 0 + . Depending on ones standpoint, such equations originate either from orthogonal polynomials associated with certain Shohat-Freud-type exponential weight functions or from Painleves discrete equation #1, that is, ? .