Point Theorems For Nonlinear Contractions Research Articles

Some multidimensional fixed point theorems for nonlinear contractions in C-distance spaces with applications

In this manuscript, we use the concept of multidimensional fixed point in a generalized space, namely, C-distance space with some nonlinear contraction conditions, such as Jaggi- and Dass-Gupta-type contractions. We provide results with a Jaggi-type hybrid contraction for the mentioned space. Moreover, we use control functions to get the desired results. After each theorem, we compare our results with previous ones to show that they are generalized. We provide examples to support our results. An application is also performed to solve the system of integral equations.

Fixed point results for nonlinear contractions of Perov type in abstract metric spaces with applications

<abstract><p>In this paper, we present some common fixed point results for $ g $-quasi-contractions of Perov type in cone $ b $-metric spaces without the assumption of continuity. Besides, by constructing a non-expansive mapping from a real Banach algebra $ \mathcal{A} $ to $ \mathcal{B}(\mathcal{A}) $, the space of all of its bounded linear operators, we explore the relationship between the results for the mappings of Perov type on cone metric (cone $ b $-metric) spaces and that for the corresponding mappings on cone metric (cone $ b $-metric) spaces over Banach algebras. As consequences, without the assumption of normality, we obtain common fixed point theorems for generalized $ g $-quasi-contractions with the spectral radius $ r(\lambda) $ of the $ g $-quasi-contractive constant vector $ \lambda $ satisfying $ r(\lambda)\in [0, \frac{1}{s}) $ (where $ s\ge 1 $) in the setting of cone $ b $-metric spaces over Banach algebras. In addition, we also get some fixed point theorems for nonlinear contractions of Perov type in the setting of cone normed spaces. The main results generalize, extend and unify several well-known comparable results in the literature. Finally, we apply our main results to some nonlinear equations.</p></abstract>

Coupled common best proximity point theorems for nonlinear contractions in partially ordered metric spaces

In this paper, we first introduce the concept of mixed γ-proximally monotone property type mappings and investigate the existence of the coupled proximally coincidence point for such mappings in partially ordered complete metric spaces. Furthermore, we prove the existence and uniqueness of coupled common best proximity points. Our results extend, improve and generalize several known results in the literature.

Fixed point theorems for nonlinear contractions with applications to iterated function systems

We introduce a new type of nonlinear contraction and present some fixed point results without using continuity or semi-continuity. Our result complement, extend and generalize a number of fixed point theorems including the the well-known Boyd and Wong theorem [On nonlinear contractions, Proc. Amer. Math. Soc. 20(1969)]. Also we discuss an application to iterated function systems.

Erratum to: Generalized n-tupled fixed point theorems for nonlinear contractions

Erratum to: Generalized n-tupled fixed point theorems for nonlinear contractions

Coupled fixed point theorems for monotone mappings in partially ordered metric spaces

In this paper, by reducing of coincidence and coupled fixed point results in ordered metric spaces to the respective results for mappings with one variable, some recent results established by T. G. Bhaskar and V. Lakshmikantham [T. G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Analysis 65 (2006) 1379-1393], V. Lakshmikantham and L. Ćirić [V. Lakshmikantham, L. Ćirić, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Analysis 70 (2009) 4341-4349] are extended, generalized, unified and improved by using mappings with monotonicity instead of with mixed monotone property. Moreover, two examples are given to support these improvements.

Coupled coincidence point theorems for nonlinear contractions in partially ordered quasi-metric spaces with a Q-function without mixed g-monotone property

Coupled coincidence point theorems for nonlinear contractions in partially ordered quasi-metric spaces with a Q-function without mixed g-monotone property

Generalized n-tupled fixed point theorems for nonlinear contractions

The notion of \(n\)-tupled fixed point is introduced by Imdad et al. (J Oper, Article ID 532867, 2013). In this continuation, we prove some \(n\)-tupled fixed point theorems for mappings having mixed monotone property in partially ordered complete metric spaces which are the generalizations of certain results contained in Karapinar and Luong (Comput Math Appl 64:1839–1848, 2012).

A note on ‘N-fixed point theorems for nonlinear contractions in partially ordered metric spaces’

In this note we prove that a kind of mappings depending on k arguments introduced in (Paknazar et al. in Fixed Point Theory Appl. 2013:111, 2013) only depend on their first argument. Therefore, results in that paper reduce to the unidimensional case. We also include some commentaries about the different notions of multidimensional fixed point.MSC:46T99, 47H10, 47H09, 54H25.

Results on n-tupled fixed points in complete asymptotically regular metric spaces

Abstract The notion of n-tupled fixed point is introduced by Imdad, Soliman, Choudhury and Das, Jour. of Operators, Vol. 2013, Article ID 532867. In this manuscript, we prove some n-tupled fixed point theorems (for even n) for mappings having mixed monotone property in partially ordered complete asymptotically regular metric spaces. Our main theorem improves the corresponding results of Imdad, Sharma and Rao (M. Imdad, A. Sharma, K.P.R. Rao, Generalized n-tupled fixed point theorems for nonlinear contractions, preprint).

Common fixed point theorems for nonlinear contractions in a Menger space

The main purpose of this paper is to introduce a new class of Jungck-type contraction and to present some common fixed point theorems for this mapping. Several examples are given to show that our result is a proper extension of many known results.

Coupled coincidence point theorems for nonlinear contractions under (F,g) -invariant set in cone metric spaces

Coupled coincidence point theorems for nonlinear contractions under (F,g) -invariant set in cone metric spaces

N-fixed point theorems for nonlinear contractions in partially ordered metric spaces

In present paper we introduce the concept of a new g-monotone mapping and define the notions of n-fixed point and n-coincidence point and prove some related theorems for nonlinear contractive mappings in partially ordered complete metric spaces. Our results are generalization of the main results of Lakshmikantham and Ćirić (Nonlinear Anal. 70:4341-4349, 2009) and include several recent developments. Moreover, we give an example to support our results.MSC:Primary 47H10; secondary 54H25; 34B15.

Coupled coincidence point theorems for nonlinear contractions under c-distance in cone metric‎ ‎spaces

In this paper, among others, we prove the following results: (1) Let (X;d) be a complete cone metric space partially ordered byv and q be a c-distance on X. Suppose F : X X ! X and g : X ! X be two continuous and commuting functions with F (X X) g(X). Let F satisfy mixed g-monotone property and q(F (x;y);F (u;v)) k (q(gx;gu) +q(gy;gv)) for some k 2 (0; 1) and all x;y;u;v 2 X with (gx v gu) and (gy w gv) or (gxw gu) and (gyv gv). If there exist x0;y02 X satisfying gx0v F (x0;y0) andF (y0;x0)v gy0, then there existx ;y 2 X such thatF (x ;y ) = gx and F (y ;x ) = gy , that is, F and g have a coupled coincidence point (x ;y ). (2) If, in (1), we replace completeness of (X;d) by completeness of (g(X);d) and commutativity, continuity of mappings F and g by the condition: (i) for any nondecreasing sequencefxng in X converging to x we have xnv x for all n. (ii) for any nonincreasing sequencefyng in Y converging to y we have yv yn for all n, then F and g have a coupled coincidence point (x ;y ).

Quadruple fixed point theorems for nonlinear contractions in partially ordered $G$-metric spaces

The purpose of this paper is to prove the quadruple coincidence point theorems for a mixed $g$-monotone mapping satisfying nonlinear contractions in partially ordered $G$-metric spaces. Our results generalize some results on the topics in the literature.

Fixed point theorems in probabilistic metric spaces using property (E.A)

In this paper, we prove a common fixed point theorem for even number of self mappings in Menger space by using an implicit relation with property (E.A). We also extend our main result to four finite families of mappings employing the notion of pairwise commuting due to Imdad et al. [Coincidence and common fixed point theorems for nonlinear contractions in Menger PM spaces, Chaos, Solitons & Fractals 42(5) (2009), 3121-3129]. Our results generalize and extend several well known comparable results existing in literature.

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.).

Coupled fixed point theorems for nonlinear contractions without mixed monotone property

Abstract In this paper, we show the existence of a coupled fixed point theorem of nonlinear contraction mappings in complete metric spaces without the mixed monotone property and give some examples of a nonlinear contraction mapping, which is not applied to the existence of coupled fixed point by using the mixed monotone property. We also study the necessary condition for the uniqueness of a coupled fixed point of the given mapping. Further, we apply our results to the existence of a coupled fixed point of the given mapping in partially ordered metric spaces. Moreover, some applications to integral equations are presented. MSC:47H10, 54H25.

Quadruple fixed point theorems for nonlinear contractions

The notion of coupled fixed point is introduced by Gnana-Bhaskar and Lakshmikantham. Very recently, the concept of tripled fixed point was introduced by Berinde and Borcut. In this manuscript, a quadruple fixed point is considered and some new related fixed point theorems are obtained. We also give some examples to illustrate our results.

Coupled coincidence point theorems for mixed monotone nonlinear operators

We obtain coupled coincidence and coupled common fixed point theorems for mixed g-monotone nonlinear operators F:X×X→X in partially ordered metric spaces. Our results are generalizations of recent coincidence point theorems due to Lakshmikantham and Ćirić [V. Lakshmikantham, L. Ćirić, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. 70 (2009) 4341–4349], of coupled fixed point theorems established by Bhaskar and Lakshmikantham [T.G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (7) (2006) 1379–1393] and also include as particular cases several related results in very recent literature.