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Recently, Jleli and Samet [J. Inequal. Appl. (2014), 2014:38] introduced and studied a new contraction to prove a generalization of the Banach contraction principle. In this paper, we introduce the concept of $${\alpha}$$ - $${H\Theta}$$ -contraction with respect to a general family of functions H and we establish Jleli-Samet-type fixed point results in metric and ordered metric spaces. As an application of our results we deduce Suzuki-type fixed point results for $${H\Theta}$$ -contractions. We also derive certain fixed and periodic point results for orbitally continuous generalized $${\Theta}$$ -contractions. Moreover, we present an illustrative example to highlight the obtained improvements. [ABSTRACT FROM AUTHOR]

In this paper, we establish certain new fixed point theorems for contractive inequalities using an auxiliary function which dominates the ordinary metric function. As application, we derive some recent known results as corollaries. Certain interesting consequences of our results are also presented. An example is given to illustrate the usability of the obtained results. [ABSTRACT FROM AUTHOR]

The aim of the paper is to introduce new Suzuki and convex type contractions and prove new best proximity results for these contractions in the setting of a metric space. As applications, we deduce similar results for such type of contractions in partially ordered metric spaces and derive new Suzuki type fixed point results. An illustrative example is provided here to highlight our findings. [ABSTRACT FROM AUTHOR]

We give a new type of contractive condition that ensures the existence and uniqueness of fixed points and best proximity points in complete metric spaces. We provide an example to validate our best proximity point theorem. This result extends and complements some known results from the literature. [ABSTRACT FROM AUTHOR]

In this paper, first we introduce certain new classes of Suzuki type contractions in triangular and non-Archimedean fuzzy metric spaces. Further we establish fixed point theorems for such kind of mappings in non-Archimedean and triangular fuzzy metric spaces. We also prove Suzuki type fixed point results in non-Archimedean and triangular ordered fuzzy metric spaces. The results presented here improve and generalize certain recent results from the literature. Two illustrative examples and an application to integral equations are given to support the usability of our results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce and study certain new concepts of α-ψ-proximal contractions in an intuitionistic fuzzy metric space. Then we establish certain best proximity point theorems for such proximal contractions in intuitionistic fuzzy metric spaces. As an application, we deduce best proximity and fixed point results in partially ordered intuitionistic fuzzy metric spaces. Several interesting consequences of our obtained results are presented in the form of new fixed point theorems which contain some recent fixed point theorems as special cases. Moreover, we discuss some illustrative examples to highlight the realized improvements. [ABSTRACT FROM AUTHOR]

In this paper, we introduce new notions of GP-metric space and GP (Λ;Θ)-contractive mapping and then prove some fixed point theorems for this class of mappings. Our results extend and generalized Banach contraction principle to GP-metric spaces. An example shows the usefulness of our results. c 2014 All rights reserved. [ABSTRACT FROM AUTHOR]

In 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. [ABSTRACT FROM AUTHOR]

We introduce the concept of triangular ηc-admissible mappings (pair of mappings) with respect to nc nonself-mappings and establish the existence of PPF dependent fixed (coincidence) point theorems for contraction mappings involving triangular αc-admissible mappings (pair of mappings) with respect to ηc nonself-mappings in Razumikhin class. Several interesting consequences of our theorems are also given [ABSTRACT FROM AUTHOR]

In this paper, we extend the p-metric space to an M-metric space, and we shall show that the definition we give is a real generalization of the p-metric by presenting some examples. In the sequel we prove some of the main theorems by generalized contractions for getting fixed points and common fixed points for mappings. [ABSTRACT FROM AUTHOR]

We consider the problem of finding a best proximity point which achieves the minimum distance between two nonempty sets in a non-Archimedean fuzzy metric space. First we prove the existence and uniqueness of the best proximity point by using different contractive conditions, then we present some examples to support our best proximity point theorems. [ABSTRACT FROM AUTHOR]

In this paper we obtain fixed and common fixed point theorems for self-mappings defined on a closed and convex subset C of a quasi-Banach space. We give also a constructive method for finding the common fixed points of the involved mappings. As an application we obtain a result of the existence of solutions of integral equations. [ABSTRACT FROM AUTHOR]

In this paper, first we introduce the notion of a Gm-Meir-Keeler contractive mapping and establish some fixed point theorems for the Gm-Meir-Keeler contractive mapping in the setting of G-metric spaces. Further, we introduce the notion of a Gcm-Meir-Keeler contractive mapping in the setting of G-cone metric spaces and obtain a fixed point result. Later, we introduce the notion of a G-(α,ψ)-Meir-Keeler contractive mapping and prove some fixed point theorems for this class of mappings in the setting of G-metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we prove some fixed point theorems in compact metric and compact cone metric spaces by using implicit relation. The presented theorems extend, generalize and improve many existing results in the literature such as a theorem by D. Dorić et al. [Dragan Dorić, Zoran Kadelburg and Stojan Radenović, Edelstein - Suzuki-type fixed point results in metric and abstract metric spaces, Nonlinear Anal. TMA 75 (2012) 1927 - 1932.] [ABSTRACT FROM AUTHOR]

Following a recent paper of Zand and Nezhad (2011), we establish some fixed point results in GP-metric spaces. The presented theorems generalize and improve several existing results in the literature. Also, some examples are presented. [ABSTRACT FROM AUTHOR]

We prove new fixed point theorems in the framework of partially ordered metric spaces. The main result is an extension and a generalization of many existing results in the literature. An example is also considered to illustrate the main result. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concepts of an α -admissible nonself-mapping, an α -F-contractive nonself-mapping, a weak α -F-contractive nonself-mapping, and a generalized α -F-contractive nonself-mapping and prove some P P F (past-present-future)-dependent fixed point theorems for the proposed contractive nonself-mappings in certain Razumikhin classes. By using our results, we derive some P P F -dependent fixed point theorems for an α -F-contractive nonself-mapping endowed with a graph or a partial order. Finally, we give some applications to illustrate the main results. [ABSTRACT FROM AUTHOR]