Search

In this work, we analyse the class of strictly pseudocontractive mappings in general metric spaces by providing a comprehensive and appropriate definition of a strictly pseudocontractive mapping, which serves as a natural extension of the existing notion. Moreover, we establish its various characterizations and explore several significant properties of these mappings in relation to fixed point theory in CAT(0) spaces. Specifically, we establish that these mappings are Lipschitz continuous, satisfying the demiclosedness-type property, and possessing a closed convex fixed point set. Furthermore, we show that the fixed points of the mappings can be effectively approximated using an iterative scheme for fixed points of nonexpansive mappings. The results in this work contribute to a deeper understanding of strictly pseudocontractive mappings and their applicability in the context of fixed point theory in metric spaces. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present a common fixed point theory for a pair of multivalued operators in complete metric spaces. Existence and stability results for the common fixed point problem will be discussed. The approach is based on some fixed point results for multivalued graphical contractions and for multivalued operators of Feng-Liu type. Our results extend to the multivalued case some recent results in the literature. [ABSTRACT FROM AUTHOR]

In the present paper we study the relationships between different concepts of convex structures in metric spaces that that are related to the works of K. Menger [Menger, K. Untersuchungen über allgemeine Metrik. Math. Ann. 100 (1928), 75-163], H. Busemann [Busemann, H. The geometry of geodesics, Academic Press, 1955], I. N. Herstein; J. Milnor [Herstein, I. N.; Milnor, J. An axiomatic approach to measurable utility. Econometrica 21 (1953), 291-297], E. Michael [Michael, E. Convex structures and continuous selections. Canad. J. Math. 11 (1959), 556-575], A. Nijenhuis [Nijenhuis, A. A note on hyperconvexity in Riemannian manifolds. Canad. J. Math. 11 (1959), 576-582.], W. Takahashi; T. Shimizu [Shimizu, T.; Takahashi, W. Fixed points of multivalued mappings in certain metric spaces. Topol. Methods Nonlinear Anal. 8 (1996), no. 1, 197-203 and Takahashi, W. A convexity in metric space and nonexpansive mappings I. Kodai Math. Sem. Rep. 22 (1970), 142-149], M. Taskovi'c [Taskovi'c, M. General convex topological spaces and fixed points. Math. Moravica 1 (1997), 127-134], Yu. A. Aminov [Aminov, Yu. A. Two-Dimensional Surfaces in 3-Dimensional and 4-Dimensional Euclidean Spaces. Results and Unsolved Problems. Ukr. Math. J. 71 (2019), no. 1, 1-38.], H. V. Machado [Machado, H. V. A characterization of convex subsets of normed spaces. Kodai Math. Sem. Rep. 25 (1973), 307-320], and many other papers. Some well known examples of concrete convex structures are reexamined and the possibilities of different embeddings of metric spaces with convex structures are also studied. Corollary 6.1 states that the Bolyai-Lobachevskii plane and the Bolyai-Lobachevskii half-plane are not isometrically embedding in some strictly convex normed space. A characteristic of the invariant metric generated by a norm is presented (Proposition 4.6). [ABSTRACT FROM AUTHOR]

Let (M,d) be a metric space, X⊂ M be a nonempty closed subset and K⊂ M be a nonempty compact subset. By definition, an upper semi-continuous multivalued operator F:X→ P(X) is said to be a strong Frum-Ketkov type operator if there exists α ∈ ]0,1[ such that ed(F(x),K)\≤ α Dd(x,K), for every x→ X, where ed is the excess functional generated by d and Dd is the distance from a point to a set. In this paper, we will study the fixed points of strong Frum-Ketkov type multivalued operators. [ABSTRACT FROM AUTHOR]

In this manuscript, we introduce the notion of admissible hybrid Geraghty contraction and we investigate the existence of fixed points of such mappings in the setting of complete metric spaces. Our results not only extend and generalize several results in the fixed point theory literature, but also unify most of them. We give some corollaries to illustrate the novelty of the main result. [ABSTRACT FROM AUTHOR]

Let (M, d) be a metric space, .... In this paper, we will give sufficient conditions ensuring that a Frum-Ketkov operator is weakly Picard. Some generalized Frum-Ketkov operators are also studied. [ABSTRACT FROM AUTHOR]

Let (X, d) be a metric space, f, fn : X → X, with Ff = ..., n ∈ N. For the fixed point equation (1) x = f(x) we consider the following iterative algorithm, (2) x ∈ X; x0 = x; xn+1(x) = fn(xn(x)); n ∈ N. By definition, the algorithm (2) is convergent if, xn(x) → x*(x) ∈ Ff as n → ∞, ∀ x ∈ X. In this paper we give some conditions on fn and f which imply the convergence of algorithm (2). In this way we improve some results given in [Rus, I. A., An abstract point of view on iterative approximation of fixed points. impact on the theory of fixed point equations, Fixed Point Theory, 13 (2012), No. 1, 179-192]. In our results, in general we do not suppose that, Ff ≠ ∅. Some research directions are formulated. [ABSTRACT FROM AUTHOR]

The aim of this article is to improve the results of Piri et al. [Fixed Point Theory and Applications 2014, 2014:210] by introducing new types of contractions say Suzuki-Berinde type F-contractions and Suzuki type rational F-contractions. We also establish a common fixed point theorem for a sequence of multivalued mappings. An example is also given to support our main results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of operators, for which a fixed point theorem is proven. This class of mappings is very large and unifies several classes of contractive type operators from the literature, including Berinde mappings. Such fact is proven via a comparison with various metrical contractive type mappings. [ABSTRACT FROM AUTHOR]