Contractions In B-metric Spaces Research Articles

Ulam–Hyers Stability via Fixed Point Results for Special Contractions in b-Metric Spaces

In this paper, we present some fixed point results for Subrahmanyan contraction in the setting of a b-metric space. We consider the case of multivalued operators. We also deduce the Ulam–Hyers stability property of the fixed point inclusion. The notion of b-metric generalizes the one of a metric, as in the third condition, the right-hand side is multiplied by a real number greater than 1. We remark that the second axiom, i.e., the one which shows the symmetry of the b-metric, remains unchanged. The findings presented in this paper extend some recent results which were proved in the context of a metric space. Some open questions are presented at the end of the paper.

Fixed Point Results for Frum-Ketkov Type Contractions in b-Metric Spaces

The purpose of this paper is to present some fixed point results for Frum-Ketkov type operators in complete b-metric spaces.

Set-valued Contractions in b-Metric Spaces with Application

In this article, we present a (α, F)-set-valued mapping in setting b-metric space by characterizing the weak contraction condition with the C function and the α-set-valued function of type S. There are examples and implementations accessible that illustrate the validity of our findings.

On Convex F-Contraction in b-Metric Spaces

In this paper, we introduce a notion of convex F-contraction and establish some fixed point results for such contractions in b-metric spaces. Moreover, we give a supportive example to show that our convex F-contraction is quite different from the F-contraction used in the existing literature since our convex F-contraction does not necessarily contain the continuous mapping but the F-contraction contains such mapping. In addition, via some facts, we claim that our results indeed generalize and improve some previous results in the literature.

New Generalizations of Set Valued Interpolative Hardy-Rogers Type Contractions in b-Metric Spaces

Debnath and De La Sen introduced the notion of set valued interpolative Hardy-Rogers type contraction mappings on b-metric spaces and proved that on a complete b-metric space, whose all closed and bounded subsets are compact, the set valued interpolative Hardy-Rogers type contraction mapping has a fixed point. This article presents generalizations of above results by omitting the assumption that all closed and bounded subsets are compact.

The Existence and Uniqueness of the Solution of a Nonlinear Fredholm–Volterra Integral Equation with Modified Argument via Geraghty Contractions

Using some of the extended fixed point results for Geraghty contractions in b-metric spaces given by Faraji, Savić and Radenović and their idea to apply these results to nonlinear integral equations, in this paper we present some existence and uniqueness conditions for the solution of a nonlinear Fredholm–Volterra integral equation with a modified argument.

Fixed Points of g-Interpolative Ćirić–Reich–Rus-Type Contractions in b-Metric Spaces

We use interpolation to obtain a common fixed point result for a new type of Ćirić–Reich–Rus-type contraction mappings in metric space. We also introduce a new concept of g-interpolative Ćirić–Reich–Rus-type contractions in b-metric spaces, and we prove some fixed point results for such mappings. Our results extend and improve some results on the fixed point theory in the literature. We also give some examples to illustrate the given results.

On existence of fixed points for generalized Geraghty type almost cyclic contractions in b-metric spaces

In this paper, we estalibsh the existence and uniqueness of fixed point for generalized Geraghty type of almost cyclic contraction mappings in b-metric spaces. These results extend and generalize well-known results in [2], [4], [6], [7].

On Istrăţescu Type Contractions in b-Metric Spaces

In this paper, we introduce the notions of α -almost Istrăt̨escu contraction of type E and of type E ∗ in the setting of b-metric space. The existence of fixed points for such mappings is investigated and some examples to illustrate the validity of the main results are considered. In the last part of the paper, we list some immediate consequences.

Fixed-Points of Interpolative Ćirić-Reich–Rus-Type Contractions in b-Metric Spaces

The concept of symmetry is inherent in the study of metric spaces due to the presence of the symmetric property of the metric. Significant results, such as with the Borsuk–Ulam theorem, make use of fixed-point arguments in their proofs to deal with certain symmetry principles. As such, the study of fixed-point results in metric spaces is highly correlated with the symmetry concept. In the current paper, we first define a new and modified Ćirić-Reich–Rus-type contraction in a b-metric space by incorporating the constant s in its definition and establish the corresponding fixed-point result. Next, we adopt an interpolative approach to establish some more fixed-point theorems. Existence of fixed points for ω -interpolative Ćirić-Reich–Rus-type contractions are investigated in this context. We also illustrate the validity of our results with some examples.

Set-Valued Interpolative Hardy–Rogers and Set-Valued Reich–Rus–Ćirić-Type Contractions in b-Metric Spaces

In this paper, using an interpolative approach, we investigate two fixed point theorems in the framework of a b-metric space whose all closed and bounded subsets are compact. One of the theorems is for set-valued Hardy–Rogers-type and the other one is for set-valued Reich–Rus–Ćirić-type contractions. Examples are provided to validate the results.

Some new fixed point results for convex contractions in B-metric spaces

The purpose of this paper is to consider various results for convex contraction mappings in the context of B-metric spaces. We, among other things, generalize, extend, correct and enrich the recent published results from the context of convex contractions defined on an ordinary metric spaces to the ones on the so-called B-metric spaces. One example shows that this generalization is genuine. Let us note that this paper represents only the beginning of our investigation of the properties of convex contractions observed in any general metric space. In the papers that are to be published, our considerations are applied to cone metric spaces, partial metric spaces, G-metrics, GB-metrics, extended B-metric spaces and many others.

Fixed Point Results of Rational Type Contractions in b-Metric Spaces

The aim of this manuscript is to establish fixed point results satisfying contractive conditions of rational type in the setting of b-metric spaces. The results proved herein are the generalization and extension of some well known results in the existing literature. Example is also given in order to illustrate the validity of the presented results.

Some applications with new admissibility contractions in b-metric spaces

Some applications with new admissibility contractions in b-metric spaces

New fixed point theorems for set-valued contractions in b-metric spaces

In this paper, we indicate a way to generalize a series of fixed point results in the framework of b-metric spaces and we exemplify it by extending Nadler’s contraction principle for set-valued functions (see Nadler, Pac J Math 30:475–488, 1969) and a fixed point theorem for set-valued quasi-contraction functions due to Aydi et al. (see Fixed Point Theory Appl 2012:88, 2012).

Fixed point results for multivalued hardy-rogers contractions in b-metric spaces

The purpose of this paper is to present some fixed point results in b-metric spaces using a contractive condition of Hardy-Rogers type with respect to the functional H. The data dependence of the fixed point set, the well-posedness of the fixed point problem, as well as, the Ulam-Hyres stability are also studied.

Remarks on cyclic contractions in b-metric spaces and applications to integral equations

In this note we construct counterexamples to answer open questions on cyclic contractions posed by Radenovic in (Afr Mat 27(1):291–295, 2016) and Radenovic et al. (Appl Math Comput 273:155–164, 2016), and to show an error in the result of Nashine et al. (Publ Inst Math (Beograd) (N.S.) 93(107):69–93, 2013). We also show that many applications of fixed point results in b-metric spaces to integral equations in the literature may be replaced by that in metric spaces.

A note on some recent fixed point results for cyclic contractions in b-metric spaces and an application to integral equations

In this paper we obtain some equivalences between cyclic contractions and non-cyclic contractions in the framework of b-metric spaces. Our results improve and complement several recent fixed point results for cyclic contractions in b-metric spaces established by George et al. (2015) and Nashine et al. (2014). Moreover, all the results are with much shorter proofs. In addition, an application to integral equations is given to illustrate the usability of the obtained results.

The class of ( α , ψ ) $(\alpha,\psi)$ -type contractions in b-metric spaces and fixed point theorems

We study the existence and uniqueness of fixed points for self-operators defined in a b-metric space and belonging to the class of $(\alpha,\psi)$ -type contraction mappings. The obtained results generalize and unify several existing fixed point theorems in the literature.

A note on fixed point theorems for weakly T-Kannan and weakly T-Chatterjea contractions in b-metric spaces

In this paper, we consider fixed point results in the setup of $b$-metric spaces for weakly T-Kannan and weakly T-Chatterjea contractive mappings. Thus, we improve and complement recent results established by Z. Mustafa et al.\ [J.\ Inequal.\ Appl.\ 2014, 2014:46] and A. Razani, V. Parvaneh [Russ.\ Math.\ (Izv.\ VUZ), 57 (3), 38--45 (2013)], with much shorter proofs. Moreover, we show that the results of A.H. Ansari et al.\ [J. Inequal.\ Appl.\ 2014, 2014:429] are not generalizations of the known ones. An example is given illustrating our results.