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This paper presents a novel concept of G -Hardy-Rogers functional operators on metric spaces endowed with a graph. It investigates sufficient circumstances under which such a mapping becomes a Picard operator. As applications of the principal idea discussed herein, a few important corresponding fixed point results in ordered metric spaces and cyclic operators are pointed out and analyzed. For upcoming research papers in this field, comparative graphical illustrations are created to highlight the pre-eminence of proposed notions with respect to the existing ones. [ABSTRACT FROM AUTHOR]

The aim of this paper is to improve some fixed point results given by I.A. Rus in (On a fixed point theorem of Maia, Studia Univ. Babes¸-Bolyai Math., 22(1977), 40-42), (Basic problem for Maia's theorem, Sem. on Fixed Point Theory, Preprint 3(1981), Babes¸-Bolyai Univ. Cluj- Napoca, 112-115) and (Data dependence of the fixed points in a set with two metrics, Fixed Point Theory, 8(2007), no. 1, 115-123), by applying, instead of contraction principle, some variants of Maia's fixed point theorem. 2010 Mathematics Subject Classification: 47H10, 47H09, 34K05, 34K12, 45D05, 45G10, [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of orthogonal relation on a soft set (F, A) and some related concepts. This notion allows us to consider fixed point theorem in SO-complete instead of complete soft metric spaces introduced by Yazar et.al. (Filomat 30:2 (2016), 269-279). Then, the existence and uniqueness of soft fixed points for a generalized soft contractive mapping are proved. Also, some examples are given to support that our main theorem is a real extension of Yazar et.al. [ABSTRACT FROM AUTHOR]

In this paper, we achieve some fixed point results for a newly furnished wider class of contraction mappings called (p, F, G)-contraction. Such a class is defined over a metric space where the concept of w-distance is used in place of a metric. Many previous results pertaining to G-contractions, Fw-contractions, F-G-contractions in the field of metric fixed point theory are subsumed in our main result. Various examples are constructed to justify the generality of our class of contraction mapping and extended results. [ABSTRACT FROM AUTHOR]

The main aim of this note is to investigate empirically the relationship between the spectral radius of the derivative of a function f : Rm→Rm and the spectral radius of the derivatives of its iterates, which is done by means of some numerical experiments for mappings of two and more variables. In this way we give a partial answer to an open problem raised in [Rus, I. A., Remark on a La Salle conjecture on global asymptotic stability, Fixed Point Theory, 17 (2016), No. 1, 159-172] and [Rus, I. A., A conjecture on global asymptotic stability, communicated at the Workshop "Iterative Approximation of Fixed Points", SYNASC2017, Timis¸oara, 21-24 September 2017] and also illustrate graphically the importance and difficulty of this problem in the general context. An open problem regarding the domains of convergence is also proposed. [ABSTRACT FROM AUTHOR]

In this paper, we present a new class of pseudo Picard operators in the setting of generalized metric spaces introduced recently in [M. JLELI AND B. SAMET: A generalized metric space and related fixed point theorems, Fixed Point Theory Appl., (2015) 2015:61]. An example is provided to illustrate the main result. [ABSTRACT FROM AUTHOR]

We give some fixed point results in the framework of the new generalization of metric space by the notion of orthogonal sets. We also provide some examples and applications to support our results. [ABSTRACT FROM AUTHOR]

In this paper we establish fixed point theorems to abridge the notion of α ψ contractions. We establish some fixed point theorems for α-type nonlinear contractions when underlying space is endowed with a graph. We also shed some light on some pre-existing results in literature that subsume the class of α-type contractions. Subsequently, several fixed point results for α-type contractions are rediscovered as important consequences. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to combine and extend some recent fixed point results of Suzuki, T., [A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 (2009), 5313-5317] and Secelean, N. A. & Wardowski, D., [ψF-contractions: not necessarily nonexpansive Picard operators, Results Math., 70 (2016), 415-431]. The continuity and the completeness conditions are replaced by orbitally continuity and orbitally completeness respectively. It is given an illustrative example of a Picard operator on a non complete metric space which is neither nonexpansive nor expansive and has a unique continuity point. [ABSTRACT FROM AUTHOR]

In this paper, we will develop a new method to study coupled fixed points of a mapping T : X x X → X, where (X, d) is a special class of b-metric spaces endowed with a graph. We will prove some general fixed point theorems which enable us to extend some old results in fixed point theory. Moreover, we will extend Edelstein's fixed point theorem for two variable mappings in ε-chainable b-metric spaces. [ABSTRACT FROM AUTHOR]

We introduce the notion of the orthogonal sets and give a real generalization of Banach' fixed point theorem. As an application, we find the existence of solution for a first-order ordinary differential equation. [ABSTRACT FROM AUTHOR]

In the present work, we introduce the concepts of (G ,φ, ψ)-contraction and (G,φ, ψ)-graphic contraction defined on metric spaces endowed with a graph G and we show that these two types of contractions generalize a large number of contractions. Subsequently, we investigate various results which assure the existence and uniqueness of fixed points for such mappings. According to the applications of our main results, we further obtain a fixed point theorem for cyclic operators and an existence theorem for the solution of a nonlinear integral equation. Moreover, some illustrative examples are provided to demonstrate our obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we consider, discuss, improve, and complement recent fixed points results for mappings satisfying cyclical contractive conditions established by Pacurar and Rus (Nonlinear Anal. 72:1181-1187, 2010) and Chandok and Postolache (Fixed Point Theory Appl. 2013:28, 2013). By using a new lemma we get much shorter and nicer proofs of some results with the new concept of mappings. [ABSTRACT FROM AUTHOR]

In this work we prove some extensions of the multivalued contraction principle and of Reich's fixed point theorem for multivalued operators in vector metric spaces. We also present a theory for the multivalued contraction principle in vector metric spaces in the spirit of the approach given by I. A. Rus and A. Petruşel. Some examples and open questions are pointed out. [ABSTRACT FROM AUTHOR]

In this paper we show that on complete metric spaces the class of weakly Picard operators contains some operators which are more general than the class of almost contractions. [ABSTRACT FROM AUTHOR]

We establish some fixed point results in cone metric space endowed with a graph. Our results include some results of Huang and Zhang, and Jachmski as special cases. Consequently, we obtain fixed point results for cyclic contraction in cone metric spaces. As an application we also obtain an existence theorem for the solution of integral equation. [ABSTRACT FROM AUTHOR]

We introduce a new type of contraction on a metric space endowed with a graph and prove fixed point theorems that generalize some of the results related with G-contraction for a directed graph G. Examples are given to justify that our contractions are more general than many others in this area. [ABSTRACT FROM PUBLISHER]

In 2008 Jachymski used the context of metric spaces endowed with a graph in theory of fixed points in some general structures and In 2012, Samet introduced a new concept of ψ-α-contractive type mappings and established fixed point theorems for such mappings in complete metric spaces. The purpose of this article is to compose this two contexts and present some new fixed point results for ψ-α-contraction on complete metric spaces endowed with a graph and in finally, as a consequence of our main result, we obtain fixed point theorems for cyclic contractive mappings. [ABSTRACT FROM AUTHOR]

The PPF dependent fixed point result in algebraically closed Razumikhin classes due to Agarwal et al [Fixed Point Theory Appl., 2013, 2013:280] is identical with its constant class counterpart; and this, in turn, is reducible to a fixed point principle involving SVV type contractions (over the subsequent metric space of initial Banach structure), without any regularity conditions about the Razumikhin classes. The conclusion rem [ABSTRACT FROM AUTHOR]

Abstract: Let be a metric space endowed with a graph such that the set of vertices of coincides with . We define the notion of -Reich type maps and obtain a fixed point theorem for such mappings. This extends and subsumes many recent results which were obtained for other contractive type mappings on ordered metric spaces and for cyclic operators. [Copyright &y& Elsevier]

Abstract: Following [W.A. Kirk, P.S. Srinivasan, P. Veeramany, Fixed points for mappings satisfying cyclical contractive conditions, Fixed Point Theory 4 (1) (2003) 79–89], we present a fixed point theorem for cyclic -contractions and following [I.A. Rus, The theory of a metrical fixed point theorem: Theoretical and applicative relevances, Fixed Point Theory 9 (2) (2008) 541–559] we construct a theory of this fixed point theorem. This theory is in connection with data dependence, well-posedness of the fixed point problem, limit shadowing property and sequences of operators and fixed points. A Maia type fixed point theorem for cyclic -contractions is also given. [Copyright &y& Elsevier]

In this paper, we prove some fixed point theorems for ψF-contractions in the framework of quasi-metric spaces generalizing and improving several similar results in metric spaces. At the same time, we consider iterated function systems consisting of ψF-contractions on quasi-metric spaces, and we give some sufficient conditions for the existence and uniqueness of their attractor which is, generally, a fractal. Some illustrative examples are provided. [ABSTRACT FROM AUTHOR]