Bessem Samet

Generalized - Contractive Type Mappings and Related Fixed Point Theorems with Applications

We establish fixed point theorems for a new class of contractive mappings. As consequences of our main results, we obtain fixed point theorems on metric spaces endowed with a partial order and fixed point theorems for cyclic contractive mappings. Various examples are presented to illustrate our obtained results.

Coupled fixed point theorems for nonlinear contractions in partially ordered G-metric spaces

Abstract We prove coupled coincidence and coupled common fixed point theorems for a mixed g -monotone mapping satisfying nonlinear contractions in partially ordered G -metric spaces. Presented theorems are generalizations of the very recent results of Choudhury and Maity [B.S. Choudhury, P. Maity, Coupled fixed point results in generalized metric spaces, Math. Comput. Modelling 54 (1–2) (2011) 73–79].

Common fixed points of generalized contractions on partial metric spaces and an application

Abstract In this paper, common fixed point theorems for four mappings satisfying a generalized nonlinear contraction type condition on partial metric spaces are proved. Presented theorems extend the very recent results of I. Altun, F. Sola and H. Simsek [Generalized contractions on partial metric spaces, Topology and its applications 157 (18) (2010) 2778–2785]. As application, some homotopy results for operators on a set endowed with a partial metric are given.

Nonlinear coupled fixed point theorems in ordered generalized metric spaces with integral type

In this article, we study coupled coincidence and coupled common fixed point theorems in ordered generalized metric spaces for nonlinear contraction condition related to a pair of altering distance functions. Our results generalize and modify several comparable results in the literature.2000 MSC: 54H25; 47H10; 54E50.

Remarks on G-metric spaces and fixed point theorems

We discuss the introduced concept of G-metric spaces and the fixed point existing results of contractive mappings defined on such spaces. In particular, we show that the most obtained fixed point theorems on such spaces can be deduced immediately from fixed point theorems on metric or quasi-metric spaces.MSC:47H10, 11J83.

The topological asymptotic expansion for the Maxwell equations and some applications

The aim of the topological sensitivity analysis is to derive an asymptotic expansion of a design functional with respect to a topological perturbation of the domain. In this paper, such an expansion is obtained for the 3D Maxwell equations when we introduce a small dielectric object in the domain and when we insert a small metallic obstacle. Some numerical results are presented in the context of buried object detection and shape inversion of 3D objects in free space from time-domain scattered field data.

The Topological Asymptotic for the Helmholtz Equation

The aim of the topological sensitivity analysis is to obtain an asymptotic expansion of a functional with respect to the creation of a small hole in the domain. In this paper such an expansion is obtained for the Helmholtz equation with a Dirichlet condition on the boundary of a circular hole. Some applications of this work to waveguide optimization are presented.

Common fixed-point results for nonlinear contractions in ordered partial metric spaces

In this paper, a new class of a pair of generalized nonlinear contractions on partially ordered partial metric spaces is introduced, and some coincidence and common fixed-point theorems for these contractions are proved. Presented theorems are twofold generalizations of very recent fixed-point theorems of Altun and Erduran (Fixed Point Theory Appl 2011(Article ID 508730):10, 2011), Altun et al. (Topol Appl 157(18):2778-2785, 2010), Matthews (Proceedings of the 8th summer conference on general topology and applications, New York Academy of Sciences, New York, pp. 183-197, 1994) and many other known corresponding theorems.2000 Mathematics Subject Classifications: 54H25; 47H10.

An extension of coupled fixed point's concept in higher dimension and applications

We introduce the concept of fixed point of N-order for mappings F:X^N->X, where N>=2 and X is an ordered set endowed with a metric d. We establish fixed point results for such mappings satisfying a given contractive condition. Presented theorems extend and generalize the coupled fixed point results of Bhaskar and Lakshmikantham [T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (7) (2006) 1379-1393] and the tripled fixed point results of Berinde and Borcut [V. Berinde, M. Borcut, Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal. 74 (2011) 4889-4897]. Some applications to integral equations and to matrix equations are also presented in this work.

On ( Ψ,φ )-weakly contractive condition in partially ordered metric spaces

Recently, Heman Kumar Nashine and Bessem Samet [H.K. Nashine, B. Samet, Fixed point results for mappings satisfying (@j,@f)-weakly contractive condition in partially ordered metric spaces, Nonlinear Anal. 74 (2011) 2201-2209] studied some coincidence fixed point and common fixed point theorems for two mappings satisfying (@j,@f)-weakly contractive condition in an ordered complete metric space. In the present paper, we study some coincidence fixed point and common fixed point theorems for three mappings S,T and R satisfying (@j,@f)-weakly contractive condition in an ordered complete metric space, where the mappings S and T are assumed to be weakly increasing with respect to R. Our results generalize several well-known results in the literature.