Coincidence Point Research Articles

Coincidence and fixed points for multivalued mappings in incomplete metric spaces with applications

In the present paper, firstly, we review the notion of R-complete metric spaces, where R is a binary relation (not necessarily a partial order). This notion lets us to consider some fixed point theorems for multivalued mappings in incomplete metric spaces. Secondly, as motivated by the recent work of Wei-Shih Du (On coincidence point and fixed point theorems for nonlinear multivalued maps, Topology and its Applications 159 (2012) 49-56), we prove the existence of coincidence points and fixed points of a general class of multivalued mappings satisfying a new generalized contractive condition in R-complete metric spaces which extends some well-known results in the literature. In addition, this article consists of several non-trivial examples which signify the motivation of such investigations. Finally, we give an application to the nonlinear fractional boundary value equations.

On coincidence point and fixed point theorems for a general class of multivalued mappings in incomplete metric spaces with an application

In this paper, weprove existence of fixed and coincidence points for a general class of multivalued mappings satisfying a new generalized contractive condition in incomplete metric spaces which generalize a number of published results in the last decades. In addition, this article not only brings a new approaches on the subject and but also involves several non-trivial examples which demonstrate the significance of the motivation. Finally, the obtained results of this paper provide a result on the convergence of successive approximations for certain operators (not necessarily linear) on a norm space (not necessarily a Banach space). In particular, we conclude that the renowned Kelisky-Rivlin theorem works on iterates of the Bernstein operators on an incomplete subspace of C[0,1].

Coincidence point theorems for cyclic multi-valued and hybrid contractive mappings

In this paper, we consider the existence theorem of coincidence point for a pair of single-valued and multivalued mapping that are concerned with the concepts of cyclic contraction type mapping. Some illustrative examples and remarks are also discussed.

О распространении теоремы Чаплыгина на дифференциальные уравнения нейтрального типа

We consider functional-differential equation x ̇((g(t) )= f(t; x(h(t) ) ),t ∈ [0; 1], where function f satisfies the Caratheodory conditions, but not necessarily guarantee the boundedness of the respective superposition operator from the space of the essentially bounded functions into the space of integrable functions. As a result, we cannot apply the standard analysis methods (in particular the fixed point theorems) to the integral equivalent of the respective Cauchy problem. Instead, to study the solvability of such integral equation we use the approach based not on the fixed point theorems but on the results received in [A.V. Arutyunov, E.S. Zhukovskiy, S.E. Zhukovskiy. Coincidence points principle for mappings in partially ordered spaces // Topology and its Applications, 2015, v. 179, № 1, 13–33] on the coincidence points of mappings in partially ordered spaces. As a result, we receive the conditions on the existence and estimates of the solutions of the Cauchy problem for the corresponding functional-differential equation similar to the well-known Chaplygin theorem. The main assumptions in the proof of this result are the non-decreasing function f(t; •) and the existence of two absolutely continuous functions v,w, that for almost each t ∈ [0; 1] satisfy the inequalities v ̇(g(t) )≥f(t; v(h(t) ) ),w ̇(g(t) )≤f(t;w(h(t) ) ). The main result is illustrated by an example.

Kantorovich’s Fixed Point Theorem in Metric Spaces and Coincidence Points

Existence and uniqueness theorems are obtained for a fixed point of a mapping from a complete metric space to itself. These theorems generalize the theorems of L. V. Kantorovich for smooth mappings of Banach spaces. The results are extended to the coincidence points of both ordinary and set-valued mappings acting in metric spaces.

Rheokinetics and Characteristics of Resulted Gels during Isothermal Gelation Process for Lower Concentrated PAN/DMSO/H2O Solutions

Isothermal gelation processes for relatively low concentration PAN/DMSO/H2O solutions are studied by rheology. Winter–Chambon criterion is unitedly used to investigate the rheological kinetics and the structural and mechanical characteristics of the resulted gels are evaluated. It is found that during the isothermal gelation procedure, two coincident points appear sequentially, where loss tangent tan δ is independent of frequency. The occurrence of two coincident points suggests that the critical gel forms first, then it evolves into the second self-similar structure, and the average distance between crosslinks of network becomes shorter. The results also show that decreasing temperature, increase of PAN concentration or H2O content will lead to faster gelation kinetics and formation of more elastic and compact critical gel and the second self-similar structure. At the same temperature, the later formed second self-similar structure is always more elastic and compact than the critical gel, and the corresponding gel stiffness is stronger.

Вопросы возрастной и педагогической психологии: Л.С. Выготский и Д.Н. Узнадзе

The article analyzes the interrelation between L.S. Vygotsky’s and Uznadze’s views on some important issues of developmental and pedagogical psychology. This, in particular, refers to the problem of concept formation, periodisation of child development, relation between development and teaching, motive forces of development. Special attention is paid to “coincidence theory” and the principle of solving “empirical postulate” which is a methodological basis for the whole system of D.N. Uznadze’s psychological conception including issues of development and education. It is pointed out that in spite of not being very well acquainted with each other’s works, the difference between viewpoints of L.S. Vygotsky and D.N. Uznadze is considerably less than the things they have in common. As for the principal questions, their approaches are often consistent and, in some cases, identical. Also, a lot of interesting outcomes can be expected from a deeper analysis of the general psychological views of the author of the cultural-historical concept and the author of the theory of set.

THE NEED FOR IMPLANT DENTISTS TO KNOW ABOUT THE METHOD OF FORENSIC HUMAN IDENTIFICATION USING DENTAL IMPLANTS

The aim of this study is to present two cases in which dental implants greatly enhanced the forensic human identification and to show the important role of the implant dentist in this process. The skeletonized remains of two victims with dental implants were sent for exams. The morphological features (qualitative) and linear measurements (quantitative) of the implants were analyzed in the ante-mortem and postmortem radiographs. The points of coincidence observed in both the implants and teeth showed compatibility of findings that led the experts to determine the positive identification. The implants found in the bodies were decisive in the process of identification. This identification was only possible because the implant dentists presented complete documentation with good technical quality, enabling an efficient expert approach to comparison of the data. Therefore, it is important to make implant dentists aware of this significant role because they may be asked by the authorities or family members of the deceased to present a complete record chart.

A generalization of divided differences and applications

In this paper, we introduce a generalization of divided differences and apply it for constructing a new class of interpolation formulae. By studying the existence and uniqueness of the introduced class, we also consider some special cases of it and investigate the interpolating function corresponding to this class at coincident points leading to an extension of Taylor interpolation. Some numerical examples are also included.

Coincidence point theorems for KC-contraction mappings in JS-metric spaces endowed with a directed graph

We introduce the class of KC-contraction mappings and prove some coincidence point theorems for these contractions in JS-metric spaces endowed with a directed graph. An illustrative example as well as an application to integral equations are also given in order to support our main theoretical results.

N-tupled Coincidence Point Results for Nonlinear Contraction in Partially Ordered Complete Metric Spaces

n-tupled Coincidence Point Results for Nonlinear Contraction in Partially Ordered Complete Metric Spaces

Analytical and numerical aspect of coincidence point problem of quasi-contractive operators

We propose a new Jungck-S iteration method for a class of quasi-contractive operators on a convex metric space and study its strong convergence, rate of convergence and stability. We also provide conditions under which convergence of this method is equivalent to Jungck-Ishikawa iteration method. Some numerical examples are provided to validate the theoretical findings obtained herein. Our results are refinement and extension of the corresponding ones existing in the current literature.

Review of Deformable Image Registration for Clinical Application

One of the characteristics of deformable image registration (DIR) is to detect anatomical coincidence points between two different images. The advantages of using DIR with radiotherapy are as follows. (1) to support the determination of the target using images of modality and series different from the treatment plan image, and (2) to evaluate the dose administered to the target and risk organs by summing the multiple dose distributions. Although DIR has been widely used in the field of external irradiation, application in the field of brachytherapy has been widespread in recent years. Also, the use of DIR is tried for quantitative assessment of anatomical changes over time during the treatment period and determination of the treatment effect after completion of treatment.In this article, we describe the outline of the technique and the evidence of the current status about the application of DIR in clinical practice.

Preservation of the Coincidence Point Existence Property under Some Discrete Transformations of a Pair of Mappings of Metric Spaces

In topology, there are known results on preservation of the fixed point existence property under any homotopy of self-mappings on some spaces in the event that the initial mapping has a nonzero Lefschetz number. For contracting mappings of metric spaces and some of their generalizations, there are known results by M. Frigon on preservation of the contraction property and, consequently, the fixed point existence property under some special homotopies. In 1984, J.W.Walker introduced a discrete counterpart of homotopy for self-mappings of an ordered set, which he called an order isotone homotopy. The naturalness of this notion and its relation to the usual continuous homotopy follow from the work by R. E. Stong (1966). Recently, the author and D. A.Podoprikhin have extended Walker’s notion of an order isotone homotopy and suggested sufficient conditions for preservation of the fixed point (coincidence point) existence property under such discrete homotopy (a pair of homotopies) of a mapping (a pair of mappings) of ordered sets. This paper contains metric counterparts of the obtained results and some corollaries. The method of ordering a metric space proposed by A. Brondsted in 1974 is used.

Using Varignon’s Theorem to show concurrency of coplanar forces in equilibrium

If a body is in equilibrium under the action of three non-parallel coplanar forces, the forces must be concurrent (Muncaster 1993 A Level Physics 4th edn (Cheltenham: Nelson Thornes) p 44, 45, 49; Goh 2018 Phys. Teach. 56 384). It is easy to show that they are concurrent when the forces meet at a point in the body (Muncaster 1993 A Level Physics 4th edn (Cheltenham: Nelson Thornes) p 44, 45, 49). However, in a situation that is easily found in common physics problems, the point of coincidence of the three lines of forces lie outside the object. It is our intention in this paper to illustrate to students how Varignon’s Theorem could be used to show that the forces must meet at a point even if the point lies outside the object when the three forces are in equilibrium.

FREE ACTIONS OF SOME COMPACT GROUPS ON MILNOR MANIFOLDS

AbstractIn this paper, we investigate free actions of some compact groups on cohomology real and complex Milnor manifolds. More precisely, we compute the mod 2 cohomology algebra of the orbit space of an arbitrary free ℤ2 and $\mathbb{S}^1$-action on a compact Hausdorff space with mod 2 cohomology algebra of a real or a complex Milnor manifold. As applications, we deduce some Borsuk–Ulam type results for equivariant maps between spheres and these spaces. For the complex case, we obtain a lower bound on the Schwarz genus, which further establishes the existence of coincidence points for maps to the Euclidean plane.

Existence of common coincidence point of intuitionistic fuzzy maps

The aim of this paper is mainly to find the existence of a common coincidence point for three intuitionistic fuzzy set-valued maps in the context of (α, β) - level sets of an intuitionistic fuzzy set. The main result has been applied to derive the solution of a system of nonlinear integral equation s. Moreover, an interesting example is put forth to demonstrate the applicability of the method.

Coincidence theory for set-valued maps via compactness principles

A variety of coincidence type results are presented for set-valued maps on Hausdorff topological spaces. Our theory is based on coincidence results (in fact fixed point results) for compact maps.

Caristi-Like Condition and the Existence of Minima of Mappings in Partially Ordered Spaces

In this paper, we study mappings acting in partially ordered spaces. For these mappings, we introduce a condition, analogous to the Caristi-like condition, used for functions defined on metric spaces. A proposition on the achievement of a minimal point by a mapping of partially ordered spaces is proved. It is shown that a known result on the existence of the minimum of a lower semicontinuous function defined on a complete metric space follows from the obtained proposition. New results on coincidence points of mappings of partially ordered spaces are obtained.

Approximating coupled coincidence points by \alpha-dense curves

Approximating coupled coincidence points by \alpha-dense curves