Mappings In Geodesic Spaces Research Articles

Enriched multi-valued nonexpansive mappings in geodesic spaces

Enriched multi-valued nonexpansive mappings in geodesic spaces

Partially Nonexpansive Mappings in Geodesic Spaces

Partially Nonexpansive Mappings in Geodesic Spaces

Some fixed-point theorems of convex orbital (alpha, beta )-contraction mappings in geodesic spaces

The aim of this paper is to broaden the applicability of convex orbital (alpha, beta )-contraction mappings to geodesic spaces. This class of mappings is a natural extension of iterated contraction mappings. The paper derives fixed-point theorems both with and without assuming continuity. Furthermore, the paper investigates monotone convex orbital (alpha, beta )-contraction mappings and establishes a fixed-point theorem for this class of mappings.

Convex (α, β)-Generalized Contraction and Its Applications in Matrix Equations

This paper investigates the existence and convergence of solutions for linear and nonlinear matrix equations. This study explores the potential of convex (α,β)-generalized contraction mappings in geodesic spaces, ensuring the existence of solutions for both linear and nonlinear matrix equations. This paper extends the concept to partially ordered geodesic spaces and establishes new existence and convergence results. Illustrative examples are provided to demonstrate the practical relevance of the findings. Overall, this research contributes a novel approach to the field of matrix equations.

Theorems of Wolff–Denjoy type for semigroups of nonexpansive mappings in geodesic spaces

AbstractWe show that if is a one‐parameter continuous semigroup of nonexpansive mappings acting on a complete locally compact geodesic space that satisfies some geometric properties, then there exists such that S converge uniformly on bounded sets of Y to ξ. In particular, our result applies to strictly convex bounded domains in or with respect to a large class of metrics including Hilbert's and Kobayashi's metrics.

Some new fixed point theorems for nonexpansive-type mappings in geodesic spaces

Abstract In this article, we present some new fixed point existence results for nonexpansive-type mappings in geodesic spaces. We also give a number of illustrative examples to settle our claims. We study the asymptotic behavior of Picard iterates generated by these class of mappings under different conditions. Finally, we approximate the solutions of the constrained minimization problem in the setting of Cartan, Alexandrov, and Toponogov (CAT(0)) spaces.

Approximating Fixed Points of Enriched Nonexpansive Mappings in Geodesic Spaces

In this paper, we consider the class of enriched nonexpansive mappings in the setting of geodesic spaces. We obtain a number of fixed point theorems for these mappings in geodesic spaces. Further, we employ the SP iterative method and present some new convergence theorems for the class of enriched nonexpansive mappings under different assumptions. We present some results concerning Δ and strong convergence.

Some Results on Fixed Points for Monotone Inward Mappings in Geodesic Spaces

In this article, the partially ordered relation is constructed in geodesic spaces by betweeness property, A monotone sequence is generated in the domain of monotone inward mapping, a monotone inward contraction mapping is a monotone Caristi inward mapping is proved, the general fixed points for such mapping is discussed and A mutlivalued version of these results is also introduced.

Approximation of endpoints for multivalued nonexpansive mappings in geodesic spaces

Let [Formula: see text] be a complete CAT(0) space, [Formula: see text] be a closed and convex subset of [Formula: see text] and [Formula: see text] be a multivalued nonexpansive mapping. We prove that the sequence of Ishikawa iteration converges to an endpoint of [Formula: see text]. This improves, extends and unifies some recently announced results of the current literature.

Conformal and Geodesic Mappings onto Some Special Spaces

In this paper, we consider conformal mappings of Riemannian spaces onto Ricci-2-symmetric Riemannian spaces and geodesic mappings of spaces with affine connections onto Ricci-2-symmetric spaces. The main equations for the mappings are obtained as a closed system of Cauchy-type differential equations in covariant derivatives. We find the number of essential parameters which the solution of the system depends on. A similar approach was applied for the case of conformal mappings of Riemannian spaces onto Ricci-m-symmetric Riemannian spaces, as well as geodesic mappings of spaces with affine connections onto Ricci-m-symmetric spaces.

Geodesic mappings of spaces with affine connnection onto generalized Ricci symmetric spaces

The presented work is devoted to study of the geodesic mappings of spaces with affine connection onto generalized Ricci symmetric spaces. We obtained a fundamental system for this problem in a form of a system of Cauchy type equations in covariant derivatives depending on no more than 1/2 n2(n+1)+n real parameters. Analogous results are obtained for geodesic mappings of manifolds with affine connection onto equiaffine generalized Ricci symmetric spaces.

Geodesic Mappings of Spaces with Affine Connection Onto Symmetric Manifolds

In this paper we study fundamental equations of geodesic mappings of manifolds with affine connection onto symmetric manifolds. We obtain fundamental equations of this problem. At the end of our paper we demonstrate example of studied mappings.

Fixed points of locally nonexpansive mappings in geodesic spaces

This is an examination of the structure of fixed point sets of locally nonexpansive mappings in various geodesic spaces. Among other things, it is shown that if G is a bounded connected open subset of a complete CAT(0) space X and if T:G‾→X is continuous on G‾ and locally nonexpansive on G, then the condition d(u,T(u))<d(x,T(x)) for all u∈G and x∈∂G implies that the fixed point set of T is a nonempty closed convex subset of G. The following theorem is also consequence of one of our main results. Theorem. Let (X,d) be a complete CAT(0) space which has the geodesic extension property and whose Alexandrov curvature is bounded below. Suppose G is a connected open subset of X, and suppose T:G→G is a locally nonexpansive mapping for which Fix(T)‾⊂G and for which int(Fix(T))≠∅. Then Fix(T) is a closed convex subset of G, and moreover the sequence {Tn(x)} converges to a point of Fix(T) for each x∈G.

Viscosity Approximation Methods for Implicit Midpoint Rule of Nonexpansive Mappings in Geodesic Spaces

In this paper, we study the convergence theorem of the viscosity technique for the implicit midpoint rule of a nonexpansive mapping T in CAT(0) spaces. Under certain appropriate conditions on \( \{\alpha _n\} \), we prove \( \{x_n\} \) converges strongly to a fixed point of T which solves some variational inequality. Moreover, we give an application to the minimization problem.

Remarks on endpoints of multivalued mappings in geodesic spaces

AbstractWe discuss Panayanak’s results on the existence of an endpoint of a multivalued nonexpansive mapping. We show that all of his results can be extended and some can be established in a wider class of mappings. Out of his three open questions, two of them are solved in affirmative.

Viscosity approximation methods for multivalued nonexpansive mappings in geodesic spaces

AbstractWe prove strong convergence of the viscosity approximation method for multivalued nonexpansive mappings in $\operatorname{CAT}(0)$ CAT ( 0 ) spaces. Our results generalize the results of Dhompongsa et al. (2012), Wangkeeree and Preechasilp (2013) and many others. Some related results in $\mathbb{R}$ R -trees are also given.

Almost Geodesic Mappings of Spaces with Affine Connection

This paper is devoted to the further development of the theory of almost geodesic mappings of spaces with affine connection.

Best Proximity Pair Results for Relatively Nonexpansive Mappings in Geodesic Spaces

Given A and B two nonempty subsets in a metric space, a mapping T: A ∪ B → A ∪ B is relatively nonexpansive if d(Tx, Ty) ≤ d(x, y) for every x ∈ A, y ∈ B. A best proximity point for such a mapping is a point x ∈ A ∪ B such that d(x, Tx) = dist(A, B). In this work, we extend the results given in Eldred et al. (2005) [A.A. Eldred, W.A. Kirk, P. Veeramani, Proximal normal structure and relatively nonexpansive mappings, Studia Math. 171, 283–293] for relatively nonexpansive mappings in Banach spaces to more general metric spaces. Namely, we give existence results of best proximity points for cyclic and noncyclic relatively nonexpansive mappings in the context of Busemann convex reflexive metric spaces. Moreover, particular results are proved in the setting of CAT(0) and uniformly convex geodesic spaces. Finally, we show that proximal normal structure is a sufficient but not necessary condition for the existence in A × B of a pair of best proximity points.

Asymptotic behavior of averaged and firmly nonexpansive mappings in geodesic spaces

We further study averaged and firmly nonexpansive mappings in the setting of geodesic spaces with a main focus on the asymptotic behavior of their Picard iterates. We use methods of proof mining to obtain an explicit quantitative version of a generalization to geodesic spaces of a result on the asymptotic behavior of Picard iterates for firmly nonexpansive mappings proved by Reich and Shafrir. From this result we obtain effective uniform bounds on the asymptotic regularity for firmly nonexpansive mappings. Besides this, we derive effective rates of asymptotic regularity for sequences generated by two algorithms used in the study of the convex feasibility problem in a nonlinear setting.

Averaged alternating reflections in geodesic spaces

We study the nonexpansivity of reflection mappings in geodesic spaces and apply our findings to the averaged alternating reflection algorithm employed in solving the convex feasibility problem for two sets in a nonlinear context. We show that weak convergence results from Hilbert spaces find natural counterparts in spaces of constant curvature. Moreover, in this particular setting, one obtains strong convergence.