Marwan Amin Kutbi

Best Proximity Point Results for Modified --Proximal Rational Contractions

We first introduce certain new concepts of --proximal admissible and ---rational proximal contractions of the first and second kinds. Then we establish certain best proximity point theorems for such rational proximal contractions in metric spaces. As an application, we deduce best proximity and fixed point results in partially ordered metric spaces. The presented results generalize and improve various known results from best proximity point theory. Several interesting consequences of our obtained results are presented in the form of new fixed point theorems which contain famous Banachs contraction principle and some of its generalizations as special cases. Moreover, some examples are given to illustrate the usability of the obtained results.

Fixed Point Theory in -Complete Metric Spaces with Applications

The aim of this paper is to introduce new concepts of --complete metric space and --continuous function and establish fixed point results for modified ---rational contraction mappings in --complete metric spaces. As an application, we derive some Suzuki type fixed point theorems and new fixed point theorems for -graphic-rational contractions. Moreover, some examples and an application to integral equations are given here to illustrate the usability of the obtained results.

Coupled Coincidence Point Theorems for Nonlinear Contractions in Partially Ordered Quasi-Metric Spaces with a Q-Function

Using the concept of a mixed g-monotone mapping, we prove some coupled coincidence and coupled common fixed point theorems for nonlinear contractive mappings in partially ordered complete quasi-metric spaces with a Q-function q. The presented theorems are generalizations of the recent coupled fixed point theorems due to Bhaskar and Lakshmikantham (2006), Lakshmikantham and Ćirić (2009) and many others.

Some Common Coupled Fixed Point Results for Generalized Contraction in Complex-Valued Metric Spaces

We introduce and study the notion of common coupled fixed points for a pair of mappings in complex valued metric space and demonstrate the existence and uniqueness of the common coupled fixed points in a complete complex-valued metric space in view of diverse contractive conditions. In addition, our investigations are well supported by nontrivial examples.

F-closed sets and coupled fixed point theorems without the mixed monotone property

In this paper we present the notion of F-closed set (which is weaker than the concept of F-invariant set introduced in Samet and Vetro (Ann. Funct. Anal. 1:46-56, 2010), and we prove some coupled fixed point theorems without the condition of mixed monotone property. Furthermore, we interpret the transitive property as a partial preorder and, then, some results in that paper and in Sintunavarat et al. (Fixed Point Theory Appl. 2012:170, 2012) can be reduced to the unidimensional case.MSC:46T99, 47H10, 47H09, 54H25.

The Existence of Fixed Point Theorems via -Distance and -Admissible Mappings and Applications

We introduce the concept of the generalized -contraction mappings and establish the existence of fixed point theorem for such mappings by using the properties of -distance and -admissible mappings. We also apply our result to coincidence point and common fixed point theorems in metric spaces. Further, the fixed point theorems endowed with an arbitrary binary relation are also derived from our results. Our results generalize the result of Kutbi, 2013, and several results in the literature.

Some fixed point results for multi-valued mappings in b-metric spaces

The aim of this paper is to establish some fixed point theorems for set-valued mappings in the context of b-metric spaces. The proposed theorems expand and generalize several well-known comparable results in the literature. An example is also given to support our main result.MSC: 46S40, 47H10, 54H25.

Discussions on Recent Results for --Contractive Mappings

We establish certain fixed point results for -generalized convex contractions, -weakly Zamfirescu mappings, and -Ciric strong almost contractions. As an application, we derive some Suzuki type fixed point theorems and certain new fixed point theorems in metric spaces endowed with a graph and a partial order. Moreover, we discuss some illustrative examples to highlight the realized improvements.

On Rate of Convergence of Jungck-Type Iterative Schemes

We introduce a new iterative scheme called Jungck-CR iterative scheme and study the stability and strong convergence of this iterative scheme for a pair of nonself-mappings using a certain contractive condition. Also, convergence speed comparison and applications of Jungck-type iterative schemes will be shown through examples.

On new fixed point results for -contractive multi-valued mappings onα-complete metric spaces and their consequences

The purpose of this paper is to establish new fixed point results formulti-valued mappings satisfying an -contractive condition, and viaBianchini-Grandolfi gauge functions, on α-complete metric spaces.Our results unify, generalize, and complement various results from theliterature. We also give examples which support our main result while previousresults in the literature are not applicable. Some of the fixed point results inmetric spaces endowed with an arbitrary binary relation and endowed with a graphare given here to illustrate the usability of the obtained results.MSC: 47H10, 54H25.