Maryam A Alghamdi

Fixed point theory for cyclic generalized contractions in partial metric spaces

In this article, we give some fixed point theorems for mappings satisfying cyclical generalized contractive conditions in complete partial metric spaces.

On fixed point theory in partial metric spaces

In this paper, we continue the study of contractive conditions for mappings in complete partial metric spaces. Concretely, we present fixed point results for weakly contractive and weakly Kannan mappings in such a way that the classical metric counterpart results are retrieved as a particular case. Special attention to the cyclical case is paid. Moreover, the well-posedness of the fixed point problem associated to weakly (cyclic) contractive and weakly (cyclic) Kannan mappings is discussed, and it is shown that these contractive mappings are both good Picard operators and special good Picard operators.

G-β-ψ contractive-type mappings and related fixed point theorems

In this paper, we introduce the notion of generalized G-β-ψ contractive mappings which is inspired by the concept of α-ψ contractive mappings. We showed the existence and uniqueness of a fixed point for such mappings in the setting of complete G-metric spaces. The main results of this paper extend, generalize and improve some well-known results on the topic in the literature. We state some examples to illustrate our results. We consider also some applications to show the validity of our results.

The implicit midpoint rule for nonexpansive mappings

AbstractThe implicit midpoint rule (IMR) for nonexpansive mappings is established. The IMR generates a sequence by an implicit algorithm. Weak convergence of this algorithm is proved in a Hilbert space. Applications to the periodic solution of a nonlinear time-dependent evolution equation and to a Fredholm integral equation are included. MSC:47J25, 47N20, 34G20, 65J15.

A primal-dual method of partial inverses for composite inclusions

Spingarn’s method of partial inverses has found many applications in nonlinear analysis and in optimization. We show that it can be employed to solve composite monotone inclusions in duality, thus opening a new range of applications for the partial inverse formalism. The versatility of the resulting primal-dual splitting algorithm is illustrated through applications to structured monotone inclusions and optimization.

Best Proximity Points for Some Classes of Proximal Contractions

Given a self-mapping and a non-self-mapping , the aim of this work is to provide sufficient conditions for the existence of a unique point , called g-best proximity point, which satisfies . In so doing, we provide a useful answer for the resolution of the nonlinear programming problem of globally minimizing the real valued function , thereby getting an optimal approximate solution to the equation . An iterative algorithm is also presented to compute a solution of such problems. Our results generalize a result due to Rhoades (2001) and hence such results provide an extension of Banachs contraction principle to the case of non-self-mappings.

Fixed Points of Multivalued Nonself Almost Contractions

We consider multivalued nonself-weak contractions on convex metric spaces and establish the existence of a fixed point of such mappings. Presented theorem generalizes results of M. Berinde and V. Berinde (2007), Assad and Kirk (1972), and many others existing in the literature.

G-β-ψ-contractive type mappings in G-metric spaces

In this paper, we introduce G-β-ψ-contractive mappings which are generalizations of α-ψ-contractive mappings in the context of G-metric spaces. Additionally, we prove existence and uniqueness of fixed points of such contractive mappings. Our results generalize, extend and improve the existing results in the literature. We state some examples to illustrate our results.

Best proximity point results in geodesic metric spaces

In this paper, the existence of a best proximity point for relatively u-continuous mappings is proved in geodesic metric spaces. As an application, we discuss the existence of common best proximity points for a family of not necessarily commuting relatively u-continuous mappings.

Fixed point theorems in generalized metric spaces with applications to computer science

In 1994, Matthews introduced the notion of a partial metric space in order to obtain a suitable mathematical tool for program verification (Matthews in Ann. N.Y. Acad. Sci. 728:183-197, 1994). He gave an application of this new structure to formulate a suitable test for lazy data flow deadlock in Kahn’s model of parallel computation by means of a partial metric version of the celebrated Banach fixed point theorem (Matthews in Theor. Comput. Sci. 151:195-205, 1995). In this paper, motivated by the utility of partial metrics in computer science, we discuss whether they are a suitable tool for asymptotic complexity analysis of algorithms. Concretely, we show that the Matthews fixed point theorem does not constitute, in principle, an appropriate implement for the aforementioned purpose. Inspired by the preceding fact, we prove two fixed point theorems which provide the mathematical basis for a new technique to carry out asymptotic complexity analysis of algorithms via partial metrics. Furthermore, in order to illustrate and to validate the developed theory, we apply our results to analyze the asymptotic complexity of two celebrated recursive algorithms.MSC:47H10, 54E50, 54F05, 68Q25, 68W40.