Nawab Hussain

Common fixed points of almost generalized contractive mappings in ordered metric spaces

The existence theorems of common fixed points for two weakly increasing mappings satisfying an almost generalized contractive condition in ordered metric spaces are proved. Some comparative example are constructed which illustrate the values of the obtained results in comparison to some of the existing ones in literature.

Suzuki-type fixed point results in metric type spaces

Suzuki’s fixed point results from (Suzuki, Proc. Am. Math. Soc. 136:1861-1869, 2008) and (Suzuki, Nonlinear Anal. 71:5313-5317, 2009) are extended to the case of metric type spaces and cone metric type spaces. Examples are given to distinguish our results from the known ones.MSC:47H10, 54H25.

KKM mappings in cone b-metric spaces

Abstract In this paper we establish some topological properties of the cone b -metric spaces and then improve some recent results about KKM mappings in the setting of a cone b -metric space. We also prove some fixed point existence results for multivalued mappings defined on such spaces.

Modified α-ψ-contractive mappings with applications

The aim of this work is to modify the notions of α-admissible and α-ψ-contractive mappings and establish new fixed point theorems for such mappings in complete metric spaces. Presented theorems provide main results of Karapinar and Samet (Abstr. Appl. Anal. 2012:793486, 2012) and Samet et al. (Nonlinear Anal. 75:2154-2165, 2012) as direct corollaries. Moreover, some examples and applications to integral equations are given here to illustrate the usability of the obtained results.MSC:46N40, 47H10, 54H25, 46T99.

Fixed Point Theorems in Ordered Banach Spaces and Applications to Nonlinear Integral Equations

We present some new common fixed point theorems for a pair of nonlinear mappings defined on an ordered Banach space. Our results extend several earlier works. An application is given to show the usefulness and the applicability of the obtained results.

Fixed points of cyclic weakly (ψ,φ,L,A,B)-contractive mappings in ordered b-metric spaces with applications

We introduce the notion of ordered cyclic weakly (ψ,φ,L,A,B)-contractive mappings, and we establish some fixed and common fixed point results for this class of mappings in complete ordered b-metric spaces. Our results extend several known results from the context of ordered metric spaces to the setting of ordered b-metric spaces. They are also cyclic variants of some very recent results in ordered b-metric spaces with even weaker contractive conditions. Some examples support our results and show that the obtained extensions are proper. Moreover, an application to integral equations is given here to illustrate the usability of the obtained results.MSC:47H10, 54H25.

α-admissible mappings and related fixed point theorems

In this paper, we prove the existence and uniqueness of a fixed point for certain α-admissible contraction mappings. Our results generalize and extend some well-known results on the topic in the literature. We consider some examples to illustrate the usability of our results.MSC:46N40, 47H10, 54H25, 46T99.

Fixed point results for single and set-valued α-η-ψ-contractive mappings

Samet et al. (Nonlinear Anal. 75:2154-2165, 2012) introduced α-ψ-contractive mappings and proved some fixed point results for these mappings. More recently Salimi et al. (Fixed Point Theory Appl. 2013:151, 2013) modified the notion of α-ψ-contractive mappings and established certain fixed point theorems. Here, we continue to utilize these modified notions for single-valued Geraghty and Meir-Keeler-type contractions, as well as multi-valued contractive mappings. Presented theorems provide main results of Hussain et al. (J. Inequal. Appl. 2013:114, 2013), Karapinar et al. (Fixed Point Theory Appl. 2013:34, 2013) and Asl et al. (Fixed Point Theory Appl. 2012:212, 2012) as corollaries. Moreover, some examples are given here to illustrate the usability of the obtained results.MSC:46N40, 47H10, 54H25, 46T99.

Fixed point and coupled fixed point theorems on b-metric-like spaces

We first introduce the concept of b-metric-like space which generalizes the notions of partial metric space, metric-like space and b-metric space. Then we establish the existence and uniqueness of fixed points in a b-metric-like space as well as in a partially ordered b-metric-like space. As an application, we derive some new fixed point and coupled fixed point results in partial metric spaces, metric-like spaces and b-metric spaces. Moreover, some examples and an application to integral equations are provided to illustrate the usability of the obtained results.MSC:47H10, 54H25, 55M20.

Coupled fixed points of weakly F-contractive mappings in topological spaces

Abstract In this work, we introduce a modified notion of weakly F -contractive mappings and prove new coupled fixed point theorems for the mappings which are weakly F -contractive. Also, we give an example to validate the main results in this work.