On (α,p)-convex contraction and asymptotic regularity (original) (raw)
Some fixed point theorems via asymptotic regularity
Filomat, 2020
In this article, we introduce some generalized contractive mappings over a metric space as extensions of various contractive mappings given by Kannan, Ćirić, Proinov and Górnicki. Some fixed point theorems have been proved for such new contractive type mappings via asymptotic regularity and some weaker versions of continuity. Supporting examples have been given in strengthening the hypothesis of our established theorems. As a by-product we explore some new answers to the open question posed by Rhoades.
In this paper, we introduce the new concept called partial generalized convex contractions and partial generalized convex contractions of order 2. Also, we establish some approximate fixed point theorems for such mappings in αcomplete metric spaces. Our results extend and unify the results of Miandaragh et al. [M. A. Miandaragh, M. Postolache, S. Rezapour, Approximate fixed points of generalized convex contractions, Fixed Point Theory and Applications 2013, 2013:255] and several well-known results in literature. We give some examples of a nonlinear contraction mapping, which is not applied to the existence of approximate fixed point and fixed point by using the results of Miandaragh et al. We also consider approximate fixed point results in metric space endowed with an arbitrary binary relation and approximate fixed point results in metric space endowed with graph.
Nonlinear contractions in metrically convex space
Publicationes Mathematicae Debrecen, 1994
In this paper we prove among other things the following fixed point theorem. Let T be a selfmapping of a complete Menger convex metric space (X, d) and Suppose that ψ is continuous at 0 and that there exists a positive sequence t n , (n ∈ N), such that lim n→∞ t n = 0 and ψ(t n ) < t n , (n ∈ N). Then T has a unique fixed point. Moreover T is γ-contractive for an increasing concave function γ and such that γ(t) < t for all t > 0. An application to a functional equation is also given.
A FIXED POINT THEOREM FOR -GENERALIZED CONTRACTION OF METRIC SPACES
In this paper we prove a fixed point theorem for -generalized contractions and obtain its consequences. KEYWORDS: D*-metric space,K-contraction, − í µí±í µí±í µí±í µí±í µí±í µí±í µí±í µí±í µí± §í µí±í µí± í µí±í µí±í µí±í µí±¡í µí±í µí±í µí±í µí±¡í µí±í µí±í µí± .
Some common fixed point theorems for a family of mappings in metrically convex spaces
Nonlinear Analysis: Theory, Methods & Applications, 2007
In the present paper some common fixed point theorems for a sequence and a pair of nonself-mappings in complete metrically convex metric spaces are proved which generalize such results due to Khan et al. Some fixed point theorems in metrically convex spaces, Georgian Math. J. 7 (3) (2000) 523-530], Assad [N.A. Assad, On a fixed point theorem of Kannan in Banach spaces, Tamkang J. Math. 7 (1976) 91-94], Chatterjea [S.K. Chatterjea, Fixed point theorems, C. R. Acad. Bulgare Sci. 25 (1972) 727-730] and several others. Some related results are also discussed.
Note on asymptotic contractions
Applicable Analysis and Discrete Mathematics, 2007
In 2003 W. A. Kirk introduced the notion of asymptotic contractions. In this paper we present one fixed point theorem of Kirk's type unifying and generalizing recent results of W.
New extension of p-metric spaces with some fixed-point results on M-metric spaces
Journal of Inequalities and Applications, 2014
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.
Journal of fixed point theory and its applications, 2024
A mapping T of a metric space (X, d) into a metric space (Y, ρ) is called restrictive Lipschitz if there exist: a positive decreasing to zero sequence (tn : n ∈ N) and a nonnegative sequence (Ln : Using a basis property of the sequence (tn : n ∈ N) (Lemma 1), we prove that if T is a continuous and restrictive Lipschitz mapping of a complete metrically convex space (X, d) into a metric space (Y, ρ) , then T is Lipschitz continuous with the constant L, that is and, in the case when the set {n ∈ N : Ln < L} is infinite, even essentially more, namely where the function α : [0, ∞) → [0, ∞) is continuous, increasing, concave (so subadditive) and such that α (t) < t for all t > 0. This result leads to the following fixed-point principle: Every continuous selfmapping T of a nonempty metrically convex complete metric space (X, d) that is restrictive Lipschitz with a sequence (Ln : n ∈ N) , such that 0 ≤ Ln < 1 (n ∈ N) and lim infn→∞ Ln ≤ 1, has a unique fixed point, and either it is a Banach contraction, or there is an increasing concave function α : [0, ∞) → [0, ∞), such that α (t) < t for t > 0 and d (T x, T y) ≤ α (d (x, y)) , x,y ∈ X. Some applications of these results to the theory of iterative functional equations are proposed.