Afrah A. N. Abdou

Fixed Points of Generalized Contractive Maps

We prove some results on the existence of fixed points for multivalued generalized -contractive maps not involving the extended Hausdorff metric. Consequently, several known fixed point results are either generalized or improved.

A New Approach to Fixed Point Results in Triangular Intuitionistic Fuzzy Metric Spaces

The aim of this paper is to propose some fixed point theorems in complete parametric metric spaces. Using these theorems, we deduce as corollaries the recent results of Ionescu et al. Moreover, we suggest some new contractions and prove certain fixed point theorems in triangular intuitionistic fuzzy metric spaces. We also discuss some illustrative examples to highlight the realized improvements.

Fixed point results of pointwise contractions in modular metric spaces

The notion of a modular metric on an arbitrary set and the corresponding modular spaces, generalizing classical modulars over linear spaces like Orlicz spaces, were recently introduced. In this paper we investigate the existence of fixed points of modular contractive mappings in modular metric spaces. These are related to the successive approximations of fixed points (via orbits) which converge to the fixed points in the modular sense, which is weaker than the metric convergence.MSC: 47H09, 46B20, 47H10, 47E10.

Fixed Point Results for Generalized Contractive Multimaps in Metric Spaces

The concept of generalized contractive multimaps in the setting of metric spaces is introduced, and the existence of fixed points for such maps is guaranteed under certain conditions. Consequently, our results either generalize or improve a number of fixed point results including the corresponding recent fixed point results of Ciric (2008), Latif-Albar (2008), Klim-Wardowski (2007), and Feng-Liu (2006). Examples are also given.

Fixed points of multivalued contraction mappings in modular metric spaces

AbstractThe purpose of this paper is to study the existence of fixed points for contractive-type multivalued maps in the setting of modular metric spaces. The notion of a modular metric on an arbitrary set and the corresponding modular spaces, generalizing classical modulars over linear spaces like Orlicz spaces, were recently introduced. In this paper we investigate the existence of fixed points of multivalued modular contractive mappings in modular metric spaces. Consequently, our results either generalize or improve fixed point results of Nadler (Pac. J. Math. 30:475-488, 1969) and Edelstein (Proc. Am. Math. Soc. 12:7-10, 1961). MSC:47H09, 46B20, 47H10, 47E10.

On Mann’s Method with Viscosity for Nonexpansive and Nonspreading Mappings in Hilbert Spaces

In the setting of Hilbert spaces, inspired by Iemoto and Takahashi (2009), we study a Mann’s method with viscosity to approximate strongly (common) fixed points of a nonexpansive mapping and a nonspreading mapping. A crucial tool in our results is the nonspreading-average type mapping.

On the fixed points of nonexpansive mappings in modular metric spaces

The notion of a modular metric on an arbitrary set and the corresponding modular spaces, generalizing classical modulars over linear spaces like Orlicz spaces, have been recently introduced. In this paper we investigate the existence of fixed points of modular nonexpansive mappings. We also discuss some compactness properties of the family of admissible sets in modular metric spaces with uniform normal structure property.MSC:47H09, 46B20, 47H10, 47E10.

Distance type and common fixed point theorems in Menger probabilistic metric type spaces

In this paper, we introduce the concept of rt-distance on a Menger probabilistic metric type space. Further we prove some fixed point theorems in a complete Menger probabilistic metric type space which generalizes some famous fixed point theorems.

Some New Weakly Contractive Type Multimaps and Fixed Point Results in Metric Spaces

Some new weakly contractive type multimaps in the setting of metric spaces are introduced, and we prove some results on the existence of fixed points for such maps under certain conditions. Our results extend and improve several known results including the corresponding recent fixed point results of Pathak and Shahzad (2009), Latif and Abdou (2009), Latif and Albar (2008), Cirić (2008), Feng and Liu (2006), and Klim and Wardowski (2007).

Common fixed point results for compatible-type mappings in multiplicative metric spaces

In this paper, we prove some common fixed point theorems for generalized contractive mappings satisfying some conditions, that is, compatible and compatible-type mappings in multiplicative metric spaces. Our results improve and generalize the corresponding results given in the literature. Moreover, we give some examples to illustrate our main results. c ©2016 All rights reserved.