Erdal Karapınar

Couple fixed point theorems for nonlinear contractions in cone metric spaces

The notion of coupled fixed point is introduced by Bhaskar and Lakshmikantham (2006) in [13]. In this manuscript, some results of Lakshmikantham and Ciric (2009) in [5] are extended to the class of cone metric spaces.

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.

Existence and uniqueness of a common fixed point on partial metric spaces

Abstract In this work, a general form of the weak ϕ -contraction is considered on partial metric spaces, to get a common fixed point. It is shown that self-mappings S , T on a complete partial metric space X have a common fixed point if it is a generalized weak ϕ -contraction.

Coupled fixed point results for ( ψ,φ )-weakly contractive condition in ordered partial metric spaces

In this paper, we prove some coupled fixed point theorems involving a (@j,@f)-weakly contractive condition for mapping having the mixed monotone property in ordered partial metric spaces. These results are analogous to theorems of Van Luong and Xuan Thuan (2011) [10] on the class of ordered partial metric spaces. Also, an application is given to support our results.

A fixed point theorem for set-valued quasi-contractions in b-metric spaces

In this article, we give a fixed point theorem for set-valued quasi-contraction maps in b-metric spaces. This theorem extends, unifies and generalizes several well known comparable results in the existing literature.

A generalized contraction principle with control functions on partial metric spaces

Partial metric spaces were introduced by Matthews in 1994 as a part of the study of denotational semantics of data flow networks. In this article, we prove a generalized contraction principle with control functions @f and @j on partial metric spaces. The theorems we prove generalize many previously obtained results. We also give some examples showing that our theorems are indeed proper extensions.

Common fixed points for single-valued and multi-valued maps satisfying a generalized contraction in G-metric spaces

In this article, we establish some common fixed point theorems for a hybrid pair {g, T} of single valued and multi-valued maps satisfying a generalized contractive condition defined on G-metric spaces. Our results unify, generalize and complement various known comparable results from the current literature.2000 MSC: 54H25; 47H10; 54E50.

Quadruple fixed point theorems for nonlinear contractions

The notion of coupled fixed point is introduced by Gnana-Bhaskar and Lakshmikantham. Very recently, the concept of tripled fixed point was introduced by Berinde and Borcut. In this manuscript, a quadruple fixed point is considered and some new related fixed point theorems are obtained. We also give some examples to illustrate our results.

Tripled coincidence point theorems for weak φ-contractions in partially ordered metric spaces

In this article, we present tripled coincidence point theorems for F: X3 → X and g: X → X satisfying weak φ-contractions in partially ordered metric spaces. We also provide nontrivial examples to illustrate our results and new concepts presented herein. Our results unify, generalize and complement various known comparable results from the current literature, Berinde and Borcut and Abbas et al.

Remarks on some coupled fixed point theorems in G-metric spaces

In this paper, we show that, unexpectedly, most of the coupled fixed point theorems in the context of (ordered) G-metric spaces are in fact immediate consequences of usual fixed point theorems that are either well known in the literature or can be obtained easily.MSC:47H10, 54H25.