Function Theorem Research Articles

On compactness and fixed point theorems in partial metric spaces

In this paper we examine two basic topological properties of partial metric spaces, namely compactness and completeness. Our main result claims that in these spaces compactness is equivalent to sequential compactness. We also show that Hausdorff compact partial metric spaces are metrizable. In the second part of this article we discuss the significance of bottom sets of partial metric spaces in fixed point theorems for mappings acting in these spaces.

Second main theorem for meromorphic mappings intersecting moving targets on parabolic manifolds

In this paper, we establish a new second main theorem for meromorphic mappings from $M$ into $\mathbb{P}(V)$ intersecting moving targets $g_{j}:M\rightarrow\mathbb{P}(V^{\ast}),\ 1\leq j\leq q,$ where $M$ is a parabolic manifold and $V$ is a Hermitian vector space. As an application, we prove the algebraic dependence problem for meromorphic mappings with moving targets in general position.

Some New Fixed Point Theorems in Weak Partial Metric Spaces

The main objective of this work is to introduce and investigate fixed point (F. p) theorems for maps that satisfy contractive conditions in weak partial metric spaces (W.P.M.S), and give some new generalization of the fixed point theorems of Mathews and Heckmann. Our results extend, and unify a multitude of (F. p) theorems and generalize some results in (W.P.M.S). An example is given as an illustration of our results.

Ergodic and fixed point theorems for Bregman nonexpansive sequences and mappings in Banach spaces

Ergodic and fixed point theorems for Bregman nonexpansive sequences and mappings in Banach spaces

Common fixed point theorem for C-class functions in complete metric spaces with application

In this paper, we establish the existence and uniqueness of common fixed point theorem for self mappings satisfying contractive condition of integral type via the concept of C-class functions in complete metric spaces. Further, we furnish an example to validate our result. Our result improves various results in the current literature. Towards the end, the existence and uniqueness of common solutions for system of functional equations arising in dynamic programming are discussed as an application of our main result.

Some common fixed point results of multivalued mappings on fuzzy metric space

The aim of this paper is to establish new fixed point theorems for single-valued and multivalued maps which satisfy α-ψ-contraction conditions in the complete fuzzy metric space. In this paper, we extend the results of Hussain et al. and Samet et al. Some comparative examples are also given which demonstrate the superiority of our results from the exiting results in the literature.

Perov-fixed point theorems on a metric space equipped with ordered theoretic relation

<abstract><p>In this paper, we introduce a few new generalizations of the classical Perov-fixed point theorem for single-valued and multi-valued mappings in a complete generalized metric space endowed with a binary relation. We have furnished our work with examples to show that several metrical-fixed point theorems can be obtained from an arbitrary binary relation.</p></abstract>

On extended interpolative single and multivalued $F$-contractions

The main objective of this paper is to study an extended interpolative single and multivalued Hardy-Rogers type $F$-contractions in complete metric spaces. We prove some fixed point theorems for such mappings. Further, we give an application to integral equations to verify our main results. The results presented in this paper improve the recent works of Karapinar et al. [12] and Mohammadi et al. [16].

A fixed point theorem for twist maps

<p style='text-indent:20px;'>Poincaré's last geometric theorem (Poincaré-Birkhoff Theorem [<xref ref-type="bibr" rid="b2">2</xref>]) states that any area-preserving twist map of annulus has at least two fixed points. We replace the area-preserving condition with a weaker intersection property, which states that any essential simple closed curve intersects its image under <inline-formula><tex-math id="M1">\begin{document}$ f $\end{document}</tex-math></inline-formula> at least at one point. The conclusion is that any such map has at least one fixed point. Besides providing a new proof to Poincaré's geometric theorem, our result also has some applications to reversible systems.</p>

Interpolative contractions and intuitionistic fuzzy set-valued maps with applications

<abstract><p>Over time, the interpolative approach in fixed point theory (FPT) has been investigated only in the setting of crisp mathematics, thereby dropping-off a significant amount of useful results. As an attempt to fill up the aforementioned gaps, this paper initiates certain hybrid concepts under the names of interpolative Hardy-Rogers-type (IHRT) and interpolative Reich-Rus-Ciric type (IRRCT) intuitionistic fuzzy contractions in the frame of metric space (MS). Adequate criteria for the existence of intuitionistic fuzzy fixed point (FP) for such contractions are examined. On the basis that FP of a single-valued mapping obeying interpolative type contractive inequality is not always unique, and thereby making the ideas more suitable for FP theorems of multi-valued mappings, a few special cases regarding point-to-point and non-fuzzy set-valued mappings which include the conclusions of some well-known results in the corresponding literature are highlighted and discussed. In addition, comparative examples which dwell on the generality of our obtained results are constructed.</p></abstract>

On univalent log-harmonic mappings

We consider the class of univalent log-harmonic mappings on the unit disk. Firstly, we present general idea of constructing log-harmonic Koebe mappings, log-harmonic right half-plane mappings and log-harmonic two-slits mappings and then we show precise ranges of these mappings. Moreover, coefficient estimates for univalent log-harmonic starlike mappings are obtained. Growth and distortion theorems for certain special subclasses of log-harmonic mappings are studied. Finally, we propose two conjectures, namely, log-harmonic coefficient and log-harmonic covering conjectures.

PAIR OF NON-SELF-MAPPINGS AND COMMON FIXED POINTS IN PARTIAL METRIC SPACES

Gajić and Rakočević proved a common fixed point theorem for non-self mappings on a Takahashi convex metric space. In this paper, we prove a common fixed point theorem on a pair of non-self mappings obeying specified conditions on a convex partial metric space. We also provide an illustrative example on the use of the theorem.

Compatible self maps of type (A) in a cone metric spaces

In this paper the concept of compatibility for a pair of self maps in a cone metric space without assuming its normality was discussed, various types of compatibility, some definitions and theorems were studied. The purpose of this research is to obtain common fixed point theorems for compatible self maps of type (A), some results generalize some of the results in the literature.

Fixed Point Theorems for Upper Semicontinuous Set-Valued Mappings in p-Vector Spaces

Fixed Point Theorems for Upper Semicontinuous Set-Valued Mappings in p-Vector Spaces

Coincidence of Fixed Points with Mixed Monotone Property

The purpose of this paper is to introduce and prove some coupled coincidence fixed point theorems for self mappings satisfying -contractive condition with rational expressions on complete partially ordered metric spaces involving altering distance functions with mixed monotone property of the mapping. Our results improve and unify a multitude of coupled fixed point theorems and generalize some recent results in partially ordered metric space. An example is given to show the validity of our main result.

Upper semicontinuous selections for fuzzy mappings in noncompact $ WPH $-spaces with applications

<abstract><p>In this paper, we introduce the concept of a $ WPH $-space without linear structure and proceed to establish a new upper semicontinuous selection theorem for fuzzy mappings in the framework of noncompact $ WPH $-spaces as well as a special form of this selection theorem in crisp settings. As applications, fuzzy collective coincidence point theorems, fuzzy collectively fixed point theorems, and existence theorems of equilibria for the generalized fuzzy games with three constraint set-valued mappings and generalized fuzzy qualitative games in $ WPH $-spaces are obtained. As their special cases in crisp settings, we derive existence theorems of equilibria for generalized games and generalized qualitative games. Finally, we construct a multiobjective game model for water resource allocation and prove the existence of Pareto equilibria for this multiobjective game based on the existence theorem of equilibria for qualitative games.</p></abstract>

A Moser theorem for multiscale mappings

<p style='text-indent:20px;'>In this paper, we study the persistence of invariant tori in nearly integrable multiscale twist mappings with intersection property and high degeneracy in the integrable part. Such results are also presented for the mappings with distinct number of angles and actions, which affirms the existence of lower-dimensional invariant tori in such mappings. Hence we establish a Moser's theorem in multiscales.</p>

A KAM theorem for quasi-periodic non-twist mappings and its application

<p style='text-indent:20px;'>In this paper we consider quasi-periodic non-twist mappings with self-intersection property, which depend on a small parameter. Without assuming any twist condition, we prove that for many sufficiently small parameters the mapping admits an invariant curve. As application, we use this result to study Lagrange stability of second order systems.</p>

Feng-Liu type fixed point theorems for w-distance spaces and applications

In this article, we study Feng-Liu [Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings, J. Math. Anal. Appl. 317 (2006), 103-112.] type fixed point theorems and present some new results for multi-valued mappings in metric spaces using the concept of ?-distance. We also discuss, some non-trivial examples to illustrate facts. Finally, we present applications of our results to integral inclusions and non-linear matrix equations. An example is given, together with convergence and error analysis, as well as average CPU time analysis and visualization of solution in surface plot.

On a Fixed Point Theorem for General Multivalued Mappings on Finite Sets with Applications in Game Theory

We propose a new fixed point theorem that completely characterizes the existence of fixed points for multivalued maps on finite sets. Our result can be seen as a generalization of Abian’s fixed point theorem. In the context of finite games, our result can be used to characterize the existence of a Nash equilibrium in pure strategies and can therefore distinguish pure strategy equilibria from mixed strategy equilibria in the celebrated Nash theorem.