İnci M Erhan

Fixed point theorems for operators on partial metric spaces

Fixed point theorems for operators of a certain type on partial metric spaces are given. Orbitally continuous operators on partial metric spaces and orbitally complete partial metric spaces are defined, and fixed point theorems for these operators are given.

Fixed point theorems on quasi-partial metric spaces

Abstract In this paper, the concept of a quasi-partial metric space is introduced, and some general fixed point theorems in quasi-partial metric spaces are proved.

Fixed points of ( ψ , ϕ ) contractions on rectangular metric spaces

Existence and uniqueness of fixed points of a general class of (ψ,ϕ) contractive mappings on complete rectangular metric spaces are discussed. One of the theorems is a generalization of a fixed point theorem recently introduced by Lakzian and Samet. Fixed points of (ψ,ϕ) contractions under conditions involving rational expressions are also investigated. Several particular cases and applications as well as an illustrative example are given.MSC:46T99, 47H10, 54H25.

Cyclic Contractions on -Metric Spaces

Conditions for existence and uniqueness of fixed points of two types of cyclic contractions defined on -metric spaces are established and some illustrative examples are given. In addition, cyclic maps satisfying integral type contractive conditions are presented as applications.

Coupled fixed point theorems on partially ordered G-metric spaces

The purpose of this paper is to extend some recent coupled fixed point theorems in the context of partially ordered G-metric spaces in a virtually different and more natural way.MSC:46N40, 47H10, 54H25, 46T99.

Fixed Point Theorems for a Class of α-Admissible Contractions and Applications to Boundary Value Problem

A class of α-admissible contractions defined via altering distance functions is introduced. The existence and uniqueness conditions for fixed points of such maps on complete metric spaces are investigated and related fixed point theorems are presented. The results are reconsidered in the context of partially ordered metric spaces and applied to boundary value problems for differential equations with periodic boundary conditions.

Remarks on ‘Coupled coincidence point results for a generalized compatible pair with applications’

AbstractVery recently, Hussain et al. (Fixed Point Theory Appl. 2014:62, 2014) announced the existence and uniqueness of some coupled coincidence point. In this short note we remark that the announced results can be derived from the coincidence point results in the literature. MSC: 47H10, 54H25.

Coupled Coincidence Point and Coupled Fixed Point Theorems via Generalized Meir-Keeler Type Contractions

We prove coupled coincidence point and coupled fixed point results of 𝐹∶𝑋×𝑋→𝑋 and 𝑔∶𝑋→𝑋 involving Meir-Keeler type contractions on the class of partially ordered metric spaces. Our results generalize some recent results in the literature. Also, we give some illustrative examples and application.

A note on 'Coupled fixed point theorems for mixed g-monotone mappings in partially ordered metric spaces'

AbstractRecently, some (common) coupled fixed theorems in various abstract spaces have appeared as a generalization of existing (usual) fixed point results. Unexpectedly, we noticed that most of such (common) coupled fixed theorems are either weaker or equivalent to existing fixed point results in the literature. In particular, we prove that the very recent paper of Turkoglu and Sangurlu ‘Coupled fixed point theorems for mixed g-monotone mappings in partially ordered metric spaces [Fixed Point Theory and Applications 2013, 2013:348]’ can be considered as a consequence of the existing fixed point theorems on the topic in the literature. Furthermore, we give an example to illustrate that the main results of Turkoglu and Sangurlu (Fixed Point Theory Appl. 2013:348, 2013) has limited applicability compared to the mentioned existing fixed point result. MSC:47H10, 54H25.

Best proximity points of generalized almost ψ-Geraghty contractive non-self-mappings

AbstractIn this paper, we introduce the new notion of almost ψ-Geraghty contractive mappings and investigate the existence of a best proximity point for such mappings in complete metric spaces via the weak P-property. We provide an example to validate our best proximity point theorem. The obtained results extend, generalize, and complement some known fixed and best proximity point results from the literature. MSC:47H10, 54H25, 46J10, 46J15.