Φ-contraction Mappings Research Articles

A φ-Contractivity Fixed Point Theory and Associated φ-Invariant Self-Similar Sets

In this paper, we apply a generalized variant of the concept of fixed point theory due to contraction mappings on metric spaces to construct a general class of iterated function systems relative to the so-called φ-contraction mappings on a metric space. In particular, we give a general framework to the Hutchinson method of constructing self-similar sets as fixed points of suitable mappings issued from the φ-contractions on the metric space. The results may open a new axis in the generalization of self-similar sets and associated self-similar functions. Moreover, our results may be extended to general metric spaces with suitable assumptions. The theoretical results are applied for the computation of the fractal dimension of a concrete example of the new self-similar sets.

Common Best Proximity Point Results for T-GKT Cyclic ϕ-Contraction Mappings in Partial Metric Spaces with Some Applications

The aim of this paper is to derive some common best proximity point results in partial metric spaces defining a new class of symmetric mappings, which is a generalization of cyclic ϕ-contraction mappings. With the help of these symmetric mappings, the characterization of completeness of metric spaces given by Cobzas (2016) is extended here for partial metric spaces. The existence of a solution to the Fredholm integral equation is also obtained here via a fixed-point formulation for such mappings.

The Convergence of Ishikawa Iteration for Generalized Φ-contractive Mappings

Charles[1] proved the convergence of Picard-type iterative for generalized Φ− accretive non-self maps in a real uniformly smooth Banach space. Based on the theorems of the zeros of strongly Φ− quasi- accretive and fixed points of strongly Φ− hemi-contractions, we extend the results to Ishikawa iterative and Ishikawa iteration process with er- rors for generalized Φ− hemi-contractive maps .

Fixed point theorems for ϕ-contraction mappings in probabilistic generalized Menger space

In this paper, we define the concepts of ϕ-contraction in probabilistic generalized Menger space. We prove that ϕ-contraction mappings in probabilistic generalized Menger space have a unique fixed point. Also we prove some fixed point theorems related this concept. Some examples are given to support the obtained results.

A General Fixed Point Theorem for Two Pairs of Absorbing Mappings in Gp -Metric Spaces

Abstract A general fixed point theorem for two pairs of absorbing mappings satisfying a new type of implicit relation ([37]), without weak compatibility in Gp -metric spaces is proved. As applications, new results for mappings satisfying contractive conditions of integral type and for ϕ-contractive mappings are obtained.

A general fixed point theorem for two pairs of mappings satisfying a mixed implicit relation

Abstract In this paper a general fixed point theorem for mappings with a new type of common limit range property satisfying a mixed implicit relation is proved. In the last part of the paper, as application, some fixed point results for mappings satisfying contractive conditions of integral type and for φ-contractive mappings are obtained.

Some fixed point theorems for φ-contractive mappings in fuzzy normed linear spaces

Some fixed point theorems for φ-contractive mappings in fuzzy normed linear spaces

ϕ-contractive multivalued mappings in complex valued metric spaces and remarks on some recent papers

The purpose of this paper is twofold. Firstly, certain common fixed point theorems are established via ϕ-contractive multivalued mappings involving point-dependent control functions as coefficients in the framework of complex valued metric spaces. Our results improve and extend several results in the existing literature. Moreover, this section is equipped by some illustrative examples in support of our results. Secondly, we point out some slip-ups in the examples of some recent papers Ahmad, Klin-Eam, and Azam (2013) and Kutbi, Ahmad, Azam, and Al-Rawashdeh (2014) based on multivalued contractive mappings in complex valued metric spaces. Our observations are also authenticated with the aid of some appropriate examples. Some rectifications to correct the erratic examples are also suggested.

Common Best Proximity Point for Non-Self Mappings in Metric Type Spaces Under Contraction Condition

Lo'lo’ et al. (Fixed Point Theory App. 2015: 47, 2015) introduced common best proximity points theorem for four mappings in metric type spaces. In this paper, we introduce φ-contraction mappings and show the common best proximity points on such conditions in metric-type spaces.

Coupled g-coincidence point theorems for a generalized compatible pair in complete metric spaces

In this work, we give the notions of coupled g-coincidence point and -increasing property of F for mappings and and prove the existence and uniqueness of a coupled g-coincidence point theorem for mappings and with φ-contraction mappings in complete metric spaces without the -increasing property of F and the mixed monotone property of G. Further, we apply our results to the existence and uniqueness of a coupled g-coincidence point of the given mappings with the -increasing property of F and the mixed monotone property of H in partially ordered metric spaces.

( H , F ) -Closed set and coupled coincidence point theorems for a generalized compatible in partially G-metric spaces

In this work, we present a notion of an -closed set and prove the existence of a coupled coincidence point theorem for a pair of mappings with φ-contraction mappings in partially ordered metric spaces without H-increasing property of F and mixed monotone property of H. We give some examples of a nonlinear contraction mapping, which is not applied to the existence of coupled coincidence point by H using the mixed monotone property and H-increasing property of F. We also show the uniqueness of a coupled coincidence point of the given mappings. Further, we apply our results to the existence and uniqueness of a coupled coincidence point of the given mappings in partially ordered G-metric spaces with H-increasing property of F and mixed monotone property of H. These results generalize some recent results in the literature.

( G , F ) -Closed set and tripled point of coincidence theorems for generalized compatibility in partially metric spaces

In this work, we prove the existence of a tripled point of coincidence theorem for a pair {F,G} of mappings F,G:X×X×X→X with φ-contraction mappings in partially ordered metric spaces without G-increasing property of F and mixed monotone property of G, using the concept of a (G,F)-closed set. We give some examples of a nonlinear contraction mapping, which is not applied to the existence of tripled coincidence point by G using the mixed monotone property. We also show the uniqueness of a tripled point of coincidence of the given mapping. Further, we apply our results to the existence and uniqueness of a tripled point of coincidence of the given mapping with G-increasing property of F and mixed monotone property of G in partially ordered metric spaces.

Discussion of coupled and tripled coincidence point theorems for φ-contractive mappings without the mixed g-monotone property

Abstract After the appearance of Ran and Reuring’s theorem and Nieto and Rodríguez-López’s theorem, the field of fixed point theory applied to partially ordered metric spaces has attracted much attention. Coupled, tripled, quadrupled and multidimensional fixed point results has been presented in recent times. One of the most important hypotheses of these theorems was the mixed monotone property. The notion of invariant set was introduced in order to avoid the condition of mixed monotone property, and many statements have been proved using these hypotheses. In this paper we show that the invariant condition, together with transitivity, lets us to prove in many occasions similar theorems to which were introduced using the mixed monotone property. MSC:46T99, 47H10, 47H09, 54H25.

The equivalence of convergence theorems of Ishikawa-Mann iterations with errors for Φ-contractive mappings in uniformly smooth Banach spaces

Let E be an arbitrary uniformly smooth real Banach space, D be a nonempty closed convex subset of E ,a ndT : D → D a generalized Lipschitz Φ-contractive mapping with q ∈ F(T) � /

Coupled coincidence point theorems for \phi-contractive under (F,g)-invariant set in complete metric space

In this paper, we prove existence of a coupled coincidence point theorem and coupled common fixed point theorem for φ-contractive mappings in partially ordered complete metric space without the mixed g-monotone property by using the concept of an (F, g)-invariant set. We prove some coupled fixed point theorems for such nonlinear contractive mappings in a complete metric space.Our results are generalization of the results of Wutiphol Sintunavarat, Poom Kumam and Yeol Je Cho (Coupled fixed point theorems for nonlinear contractions without mixed monotone property, Fixed Point Theory and Applications 2012,2012:170.).

Generalized cyclic contractions in partially ordered metric spaces

Abkar and Gabeleh in (J. Optim. Theory. Appl. doi: 10.1007/s10957-011-9818-2) proved some theorems which ensure the existence and convergence of fixed points, as well as best proximity points for cyclic mappings in ordered metric spaces. In this paper we extend these results to generalized cyclic contractions and obtain some new results on the existence and convergence of fixed points for weakly contractive mappings, as well as on best proximity points for cyclic φ-contraction mappings in partially ordered metric spaces.