Search

By processing the problem through fixed point theory and propagator theory, we investigate the periodicity of solutions to a class of impulsive evolution equations in Hilbert spaces and establish some existence theorems for periodic solutions. Moreover, the asymptotic stability of periodic solutions is obtained under suitable conditions. As one will see, the concept of an impulsive propagator is introduced for the first time in the paper. [ABSTRACT FROM AUTHOR]

These remarks are based on a talk the writer gave at the 11th International Conference in Fixed Point Theory and Applications, held at Galatasaray University in Istanbul, Turkey, July 20-24, 2015. They represent selected thoughts on a career in research, largely devoted to metric fixed point theory, that has spanned over 50 years. [ABSTRACT FROM AUTHOR]

Let f be an holomorphic function which maps the unit disk into itself. In this paper, consider the zero of order k ( i.e., $f(z)-f(0)$ (or $f(z)$ ) has a zero of order k at $z=0$ ), we obtain the sharp estimates of the classical boundary Schwarz lemma involving the boundary fixed point. The results presented here would generalize the corresponding result obtained by Frolova et al. (Complex Anal. Oper. Theory 8:1129-1149, 2004). [ABSTRACT FROM AUTHOR]

In this paper, a new concept of the common property (E.A) for two hybrid pairs of mappings is introduced in Menger PM-spaces. Utilizing this concept, some common fixed point theorems, which shed some new light on the study of fixed point results for hybrid pairs in Menger PM-spaces, are obtained under strict contractive conditions. The corresponding results in metric spaces which generalize many known results are also obtained. Finally, an example is also given to exemplify our main results. [ABSTRACT FROM AUTHOR]

In this short note, we announce that all the presented fixed point results in the setting of multiplicative metric spaces can be derived from the corresponding existing results in the context of standard metric spaces in the literature. [ABSTRACT FROM AUTHOR]

The article presents a study on various problems regarding roots and coincidence points for maps into the Klein bottle. The authors show the possibility of constructing an infinite family of maps no two of which can be joined by a root free homotopy. They show that the root problem can be solved when both the domain and target are the Klein bottle and the end maps are not root free. They examine the relationship between the minimal coincidence problem and the restricted minimal problem.

The article focuses on the Anosov theorem for infranilmanifolds with an odd-order Abelian holonomy group. It recalls the notion of almost-crystallographic groups and infranilmanifolds. It describes a class of maps on infranilmanifolds, for which the Anosov theorem always holds. It shows that the Anosov theorem can be generalized to infranilmanifolds with an odd-order Abelian holonomy group F.

In this work, we discuss the concept of Banach operator pairs in modular vector spaces. We prove the existence of common fixed points for these type of operators which satisfy a modular continuity in modular compact sets. On the basis of our result, we are able to give an analog of DeMarr's common fixed point theorem for a family of symmetric Banach operator pairs in modular vector spaces. [ABSTRACT FROM AUTHOR]

We introduce a new concept of generalized metric spaces for which we extend some well-known fixed point results including Banach contraction principle, Ćirić's fixed point theorem, a fixed point result due to Ran and Reurings, and a fixed point result due to Nieto and Rodríguez-López. This new concept of generalized metric spaces recover various topological spaces including standard metric spaces, b-metric spaces, dislocated metric spaces, and modular spaces. [ABSTRACT FROM AUTHOR]

In recent literature concerning fixed point theory for self-mappings T : X → X in metric spaces (X, d), there are some new concepts which can be mutually related so that the inherent properties of each one might be combined for such self-mappings. Self-mappings T : X → X can be referred to, for instance, as Kannan-mappings, reasonable expansive mappings, and Picard T-stable mappings. Some relations between such concepts subject either to sufficient, necessary, or necessary and sufficient conditions are obtained so that in certain self-mappings can exhibit combined properties being inherent to each of its various characterizations. [ABSTRACT FROM AUTHOR]

We use a concept of abstract convexity to define the almost S-KKMc property, al-S-KKMc(X, Y) family, and almost Φ-spaces. We get some new approximate fixed point theorems and fixed point theorems in almost Φ-spaces. Our results extend some results of other authors. [ABSTRACT FROM AUTHOR]

We study generalized Levitin-Polyak well-posedness of vector equilibrium problems with functional constraints as well as an abstract set constraint. We will introduce several types of generalized Levitin-Polyak well-posedness of vector equilibrium problems and give various criteria and characterizations for these types of generalized Levitin-Polyak well-posedness. [ABSTRACT FROM AUTHOR]

We prove a general principle in Random Fixed Point Theory by introducing a condition named (ρ) which was inspired by some of Petryshyn's work, and then we apply our result to prove some random fixed points theorems, including generalizations of some Bharucha-Reid theorems. [ABSTRACT FROM AUTHOR]

We prove some results on the existence of fixed points for multivalued generalized w-contractive maps not involving the extended Hausdorff metric. Consequently, several known fixed point results are either generalized or improved. [ABSTRACT FROM AUTHOR]

We present generalized versions of Caristi's fixed point theorem for multivalued maps. Our results either improve or generalize the corresponding generalized Caristi's fixed point theorems due to Bae (2003), Suzuki (2005), Khamsi (2008), and others. [ABSTRACT FROM AUTHOR]

We define a weaker Meir-Keeler type function and establish the fixed point theorems for a weaker Meir-Keeler type ψ-set contraction in metric spaces. [ABSTRACT FROM AUTHOR]

Based on previous notions of expansive mapping, n times reasonable expansive mapping is defined. The existence of fixed point for n times reasonable expansive mapping is discussed and some new results are obtained. [ABSTRACT FROM AUTHOR]

The article examines the necessary and sufficient conditions for realizing Φ as the fixed point set of a map homotopic to f. The authors aim to show that the same conditions remain sufficient when Φ is only assumed to be a locally contractible subset of X. The authors solved the relative form of the realization problem for Φ a subpolyhedron of X. They extended the results to the case where Φ is a locally contractible subset.

The article defines a base-point-free version of the Lefschetz invariant using the fundamental groupoid. It describes the classical Lefschetz-Nielsen invariant and introduces the Hattori-Stallings trace that will replace the usual trace in the construction of the algebraic invariant. It discusses the general theory of groupoids and modules over ringoids. It presents the base-point-free refinements of the classical geometric and algebraic Lefschetz-Nielsen invariants.

The article introduces an ε - Nielsen number Nε(f) that is a lower bound for the number of fixed points of all self-maps of X that are ε - homotopic to f. It defines X as a compact, connected differentiable manifold, possibly with boundary. It proves that there is always a map g : X → X that is ε - homotopic to f such that g has exactly fixed points. It describes procedures for calculating Nε for maps of 1-manifolds.