Coincidence Theorems Research Articles

Fixed-point and coincidence theorems in ordered sets

The paper is devoted to the problem of the existence of common fixed points and coincidence points of a family of set-valued maps of ordered sets. Fixed-point and coincidence theorems for families of set-values maps are presented, which generalize some of the known results. The presented theorems, unlike previous ones, do not assume the maps to be isotone or coverable. They require only the existence of special chains having lower bounds with certain properties in the ordered set.

Common fixed points and coincidences of mapping families on partially ordered sets

New coincidence and common fixed point theorems are proved for families of multivalued mappings on partially ordered sets. The obtained results generalize some recent authors' fixed point theorems for one isotone multivalued mapping, and some recent coincidence theorems for two multivalued mappings one of which is isotone and the other one is orderly covering.

Applications of the KKM Property to Coincidence Theorems, Equilibrium Problems, Minimax Inequalities and Variational Relation Problems

ABSTRACTIn this paper, we establish coincidence-like results in the case when the values of the correspondences are not convex. To do this, we define new type of correspondences, namely, properly quasi-convex-like correspondences. Further, we apply the obtained theorems to solve equilibrium problems and to establish a minimax inequality. In the last part of the paper, we study the existence of solutions for generalized vector variational relation problems. Our analysis is based on the applications of the KKM principle. We establish existence theorems involving new hypothesis and we improve the results of some recent papers.

Relation-theoretic metrical coincidence theorems

In this article, we generalize some frequently used metrical notions such as: completeness, closedness, continuity, 1-continuity and compatibility to relation-theoretic setting and utilize these relatively weaker notions to prove our results on the existence and uniqueness of coincidence points involving a pair of mappings defined on a metric space endowed with an arbitrary binary relation. Particularly, under universal relation our results deduce the classical coincidence point theorems of Goebel, Jungck and others. Furthermore, our results generalize, modify, unify and extend several well-known results of the existing literature.

On coincidence point results of a pair of rational type contractions in quasi-symmetric spaces

In Almeida, Roldan-Lopez-de-Hierro and Sadarangani (2015) proved that whenever T is a rational type contraction mapping from a complete metric space into itself, then T has a unique fixed point. In this work, we establish some coincidence and common point theorems for a pair of rational type contractions in quasi-symmetric spaces.

On the existence of positive solutions for fractional differential inclusions at resonance.

In this paper, we discuss the existence of positive solutions for a boundary value problem of fractional differential inclusions with resonant boundary conditions. By using the Leggett–Williams theorem for coincidences of multi-valued operators due to O’Regan and Zima, results on the existence of positive solutions are established. An example is given to illustrate the efficiency of the main theorems.

(H,G)-coincidence theorems for free G-spaces

Let us consider G a group acting freely on a Hausdorff paracompact topological space X and let Y be a k-dimensional metrizable space (or k-dimensional CW-complex). In this paper, by using the genus of X, gen(X,G), we prove (H,G)-coincidence theorems for maps f:X→Y. Such theorems generalize the main theorem proved by Aarts, Fokkink and Vermeer in [1] and the main result proved by dos Santos and Coelho in [11].

Positive Solutions to Periodic Boundary Value Problems of Nonlinear Fractional Differential Equations at Resonance

By Leggett-Williams norm-type theorem for coincidences due to O’Regan and Zima, we discuss the existence of positive solutions to fractional order with periodic boundary conditions at resonance. At last, an example is presented to demonstrate the main results.

On the Composition Ideals of Schatten Class Type Mappings

We study the composition ideals of multilinear and polynomial mappings generated by Schatten classes. We give some coincidence theorems for Cohen strongly 2-summing multilinear operators and factorization results like that given by Lindenstrauss-Pełczński for Hilbert Schmidt linear operators.

Discussion on Some Recent Order-Theoretic Metrical Coincidence Theorems Involving Nonlinear Contractions

We prove some coincidence theorems involving a pair of self-mappingsfandgdefined on an ordered metric spaceXwhereinfisg-increasingφ-contractive mapping. In our results, neither the whole spaceXnor the range subspaces (f(X)org(X)) are required to be complete. Instead, we use the completeness of a subspace ofXsatisfying suitable conditions.

Coincidence of the Mas-Colell bargaining set and the set of competitive equilibria in a continuum coalition production economy

Mas-Colell (J Math Econ 18:129–139, 1989) proved that the bargaining set and the set of competitive allocations coincide in an exchange economy with a continuum of traders under some standard assumptions. We extend this result to continuum coalition production economies and prove that the bargaining set and the set of competitive allocations coincide in a coalition production economy with a continuum of traders under some standard assumptions. As a consequence, we obtain a coincidence theorem for the core and the set of competitive allocations in a coalition production economy which extends the well-known coincidence theorem by Aumann (Econometrica 32:39–50, 1964).

Enriching some recent coincidence theorems for nonlinear contractions in ordered metric spaces

AbstractIn this article, we generalize some frequently used metrical notions such as: completeness, continuity, g-continuity, and compatibility to order-theoretic setting especially in ordered metric spaces besides introducing some new notions such as: the ICC property, DCC property, MCC property etc. and utilize these relatively weaker notions to prove some coincidence theorems for g-increasing Boyd-Wong type contractions which enrich some recent results due to Alam et al. (Fixed Point Theory Appl. 2014:216, 2014).

EVEN-TUPLED COINCIDENCE THEOREMS IN GENERALIZED COMPLETE METRIC SPACES Vol. 3(2) July 2015, No. 20, pp. 257-271 AHMED H. SOLIMAN, MOHAMMAD IMDAD, AFTAB ALAM

EVEN-TUPLED COINCIDENCE THEOREMS IN GENERALIZED COMPLETE METRIC SPACES Vol. 3(2) July 2015, No. 20, pp. 257-271 AHMED H. SOLIMAN, MOHAMMAD IMDAD, AFTAB ALAM

English

English

Remarks on some recent M. Borcut's results in partially ordered metric spaces

In this paper, some recent results established by Marin Borcut [M. Borcut, Tripled xed point theorems for monotone mappings in partially ordered metric spaces, Carpathian J. Math. 28, 2 (2012), 207{214] and [M. Borcut, Tripled coincidence theorems for monotone mappings in partially ordered metric spaces, Creat. Math. Inform. 21, 2 (2012), 135{142] are generalized and improved, with much shorter proofs. Also, examples are given to support these improvements.

Shorter proofs of some recent even-tupled coincidence theorems for weak contractions in ordered metric spaces

In this paper, we prove some recent even coincidence theorems due to Imdad et al. (Bull Math Anal Appl 5(4): 19-39, 2013) using a method of reduction from the respective coincidence theorems for mappings with one variable in ordered complete metric spaces. Our technique of proof is different, slightly simpler, shorter and more effective than the ones used in Imdad et al.

A note on ‘ ( G , F ) -Closed set and tripled point of coincidence theorems for generalized compatibility in partially metric spaces’

Recently, some (common) multidimensional fixed theorems in partially ordered complete metric spaces have appeared as a generalization of existing (usual) fixed point results. Unexpectedly, we realized that most of such (common) coupled fixed theorems are either weaker or equivalent to existing fixed point results in the literature. In particular, we prove that the results included in the very recent paper (Charoensawan and Thangthong in Fixed Point Theory Appl. 2014:245, 2014) can be considered as a consequence of existing fixed point theorems on the topic in the literature.

Complete periodic adaptive antisynchronization of memristor-based neural networks with mixed time-varying delays

This paper is concerned with the complete periodic antisynchronization issue of memristor-based neural networks with mixed time-varying delays. Under the framework of Filippov solutions of the differential equations with discontinuous right-hand side, based on Mawhin-like coincidence theorem in set-valued analysis theory, the proof of the existence of periodic solution is presented. By applying the Lyapunov–Krasovskii functional approach, adaptive controller is designed and unknown control parameters of the slave system are determined by adaptive laws, and the complete periodic adaptive antisynchronization condition is addressed to ensure the slave system global antisynchronization with the master system. An illustrative example is given to demonstrate the effectiveness of the obtained results.

Some coincidence theorems for generalized nonlinear contractions in ordered metric spaces with applications

Abstract In this article, we prove some existence and uniqueness results on coincidence points for g-increasing mappings satisfying generalized φ-contractivity conditions in ordered metric spaces. As an application of one of our newly proved results, we indicate the formulation of a coupled coincidence theorem. Our results generalize, extend, modify, improve, sharpen, enrich, and complement several well-known results of the existing literature. Also, we point out that a recent coincidence point result proved in Dalal et al. (J. Adv. Math. 7(1):1084-1094, 2014) contains errors and omissions. MSC:47H10, 54H25.

Coincidence theorems via alpha cuts of L-fuzzy sets with applications

Abstract In the present paper, existence theorems of coincidence points of a crisp mapping and a sequence of L-fuzzy mappings have been established in a complete metric space under contractive type conditions in connection with newly defined notions of D α L and d L ∞ distances on the class of L-fuzzy sets. Furthermore, we obtain some fixed point theorems for L-fuzzy set-valued mappings to extend a variety of recent results on fixed points for fuzzy mappings and multivalued mappings in the literature. As applications, first we obtain coincidence points of a sequence of multivalued mappings with a self mapping and next established an existence and uniqueness theorem of the solution for a generalized class of nonlinear integral equations. MSC:46S40, 47H10, 54H25.