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In this paper, we prove a fixed point theorem for a system of maps on the finite product of metric spaces. Our result generalizes the result of Matkowski (Bull Acad Pol Sci Sér Sci Math Astron Phys 21:323-324, 1973), Cosentino and Vetro (Filomat 28(4):715-722, 2014) and Hardy and Rogers (Can Math Bull 16(2):201-206, 1973) and other results in the literature. Moreover, we have an application for a system of functional equations and an example to illustrate our result. [ABSTRACT FROM AUTHOR]

In this paper, we employ the well-known Krasnoselskii fixed point theorem to study the existence and n-multiplicity of positive periodic solutions for the periodic impulsive functional differential equations with two parameters. The form including an impulsive term of the equations in this paper is rather general and incorporates as special cases various problems which have been studied extensively in the literature. Easily verifiable sufficient criteria are obtained for the existence and n-multiplicity of positive periodic solutions of the impulsive functional differential equations. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the strong convergence of an implicit iteration process with errors to a common fixed point for a finite family of asymptotically pseudocontractive mappings and nonexpansive mappings in normed linear spaces. The results in this paper improve and extend the corresponding results of Xu and Ori, Zhou and Chang, Sun, Yang and Yu in some aspects. [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 the recent paper [1] the claim is made that a probabilistic version of a common fixed point theorem of Pant holds. We provide some examples to demonstrate that this claim is false unless some additional conditions are imposed. Our note is desired to complete the interesting results in the quoted paper. [ABSTRACT FROM AUTHOR]

In this paper, we study the symmetric solutions of second-order BVP with integral boundary conditions. By using a generalized Leggett-Williams fixed point theorem and some other techniques, we obtain sufficient conditions for the existence of symmetric positive solutions for the system. Meanwhile, an example is devoted to demonstrate our results in the end. [ABSTRACT FROM AUTHOR]

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]

Take three integers $$m\ge 0,\,k\ge 1$$ , and $$n\ge 2$$ . Let $$a\ (\not \equiv 0)$$ be a holomorphic function in a domain $$D$$ of $$\mathbb {C}$$ such that multiplicities of zeros of $$a$$ are at most $$m$$ and divisible by $$n+1$$ . In this paper, we mainly obtain the following normality criterion: Let $${{{\fancyscript{F}}}}$$ be the family of meromorphic functions on $$D$$ such that multiplicities of zeros of each $$f\in {{\fancyscript{F}}}$$ are at least $$k+m$$ and such that multiplicities of poles of $$f$$ are at least $$m+1$$ . If each pair $$(f,g)$$ of $${{\fancyscript{F}}}$$ satisfies that $$f^{n}f^{(k)}$$ and $$g^{n}g^{(k)}$$ share $$a$$ (ignoring multiplicity), then $${{\fancyscript{F}}}$$ is normal. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the Morgenstern type bivariate-generalized exponential distribution. This distribution is an extension of Morgenstern type bivariate exponential distribution (MTBED), and the marginal distributions are generalized exponential distribution. We study some properties of this bivariate distribution. Also, some distributional properties of concomitants of order statistics as well as record values for the MTBED are studied. Recurrence relations between moments of concomitants are also obtained. [ABSTRACT FROM AUTHOR]

The b-chromatic index $$\varphi '(G)$$ of a graph $$G$$ is the largest integer $$k$$ such that $$G$$ admits a proper $$k$$ -edge coloring in which every color class contains at least one edge incident to some edge in all the other color classes. The b-chromatic index of trees is determined and equals either to a natural upper bound $$m'(T)$$ or one less, where $$m'(T)$$ is connected with the number of edges of high degree. Some conditions are given for which graphs have the b-chromatic index strictly less than $$m'(G)$$ , and for which conditions it is exactly $$m'(G)$$ . In the last part of the paper, regular graphs are considered. It is proved that with four exceptions, the b-chromatic index of cubic graphs is $$5$$ . The exceptions are $$K_4$$ , $$K_{3,3}$$ , the prism over $$K_3$$ , and the cube $$Q_3$$ . [ABSTRACT FROM AUTHOR]

A connected graph $$G$$ is said to be factor-critical if $$G-v$$ has a perfect matching for every vertex $$v$$ of $$G$$ . Lovász proved that every factor-critical graph has an ear decomposition. In this paper, the ear decomposition of the factor-critical graphs $$G$$ satisfying that $$G-v$$ has a unique perfect matching for any vertex $$v$$ of $$G$$ with degree at least 3 is characterized. From this, the number of maximum matchings of factor-critical graphs with the special ear decomposition is obtained. [ABSTRACT FROM AUTHOR]

An $$m\times n\,\{0,1\}$$ -matrix $$A$$ is said to be totally convertible if there exists a matrix $$B$$ obtained from $$A$$ by changing some 1's in $$A$$ to $$-1$$ 's such that for any submatrix $$A^{\prime }$$ of $$A$$ of order $$m$$ , the corresponding submatrix $$B^{\prime }$$ of $$B$$ satisfies $$\mathrm{per}(xI-A^{\prime })=\det (xI-B^{\prime })$$ . In this paper, motivated by the well-known Pólya's problem, our object is to characterize those totally convertible matrices. Associate a matrix $$A$$ with a bipartite graph $$G^{*}_A$$ . We first prove that a square matrix $$A$$ is totally convertible if and only if $$G^{*}_A$$ is Pfaffian, and then we generalize this result to an $$m\times n$$ $$\{0,1\}$$ -matrix. Moreover, the characterization of a totally convertible matrix provides an equivalent condition to compute the permanental polynomial of a bipartite graph by the characteristic polynomial of the skew adjacency matrix of its orientation graph. As applications, we give some explicit expressions of the permanental polynomials of two totally convertible matrices by the technique of Pfaffian orientation. [ABSTRACT FROM AUTHOR]

In this paper, we present some results on the existence of random coincidence points of expansive type completely random operators. Some applications to random fixed point theorems and random equations are given. [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 paper direct proofs of some common fixed point results for two and three mappings under weak contractive conditions are given. Some of these results are improved by using different arguments of control functions. Examples are presented showing that some generalizations can not be obtained and also that our results are distinct from the existing ones. [ABSTRACT FROM AUTHOR]

The matrix rank minimization problem has applications in many fields, such as system identification, optimal control, low-dimensional embedding, etc. As this problem is NP-hard in general, its convex relaxation, the nuclear norm minimization problem, is often solved instead. Recently, Ma, Goldfarb and Chen proposed a fixed-point continuation algorithm for solving the nuclear norm minimization problem ( Math. Program., doi:, ). By incorporating an approximate singular value decomposition technique in this algorithm, the solution to the matrix rank minimization problem is usually obtained. In this paper, we study the convergence/recoverability properties of the fixed-point continuation algorithm and its variants for matrix rank minimization. Heuristics for determining the rank of the matrix when its true rank is not known are also proposed. Some of these algorithms are closely related to greedy algorithms in compressed sensing. Numerical results for these algorithms for solving affinely constrained matrix rank minimization problems are reported. [ABSTRACT FROM AUTHOR]

This paper deals with the existence of triple positive solutions for a type of second-order singular boundary problems with general differential operators. By using the Leggett-Williams fixed point theorem, we establish an existence criterion for at least three positive solutions with suitable growth conditions imposed on the nonlinear term. [ABSTRACT FROM AUTHOR]

The aim of this paper is to review some classical results and present new theorems of existence and extend- ability of solutions to the following second-order nonlinear Cauchy problem: This equation cannot be represented in ASCII code value. where f : [0, T ] · R → R is continuous, derivative independent and T > 0, u0 , u1 are real numbers. We ?rst consider the model case of autonomous equations and some classical results are surveyed. Particular attention is then paid to the cases where f has either the form f (x, u) = q(x)ψ(u) or f (x, u) = h(x, u) + g(x, u) where ? is nondecreasing, h is dominated by nondecreasing functions in u while g looks like a contraction in the second argument. Methods based on the Leray-Schauder nonlinear alternative and the Krasnosel'skii ?xed point theorem are used to prove new existence theorems. Several examples and counterexamples illustrate the obtained results. [ABSTRACT FROM AUTHOR]

In this paper we prove, among other results, that near the equilibirum position, any periodic FPU chain with an odd number N of particles admits a Birkhoff normal form up to order 4, whereas any periodic FPU chain with N even admits a resonant normal form up to order 4. This resonant normal form of order 4 turns out to be completely integrable. Further, for N odd, we obtain an explicit formula of the Hessian of its Hamiltonian at the fixed point. [ABSTRACT FROM AUTHOR]

The article provides an overview of the study which examines the locally uniform nonsquare in generalized Cesàro sequence spaces. It found that the generalized Cesàro sequence spaces possessed the locally uniform nonsquare and have the fixed point property, but they are not uniformly nonsquare. It specified that the result is related to the result of the paper J. False and colleagues in 2006. It was done through giving examples and the motivation to find the geometric properties that are weaker than uniformly nonsquare, but still possessed the fixed point property in any Banach spaces .

In this paper, by means of Sadovskii fixed point theorem, the authors establish a result concerning the controllability for a class of abstract neutral functional differential systems where the linear part is non-densely defined and satisfies the Hille-Yosida condition. As an application, an example is provided to illustrate the obtained result. [ABSTRACT FROM AUTHOR]

We extend the notion of R-weak commutativity and its variants to probabilistic metric spaces and prove common fixed point theorems concerning them. Examples are included to reflect upon the distinctiveness of the types of mappings defined in the paper. [ABSTRACT FROM AUTHOR]

Recently, Pathak [13] has made an extension of the notion of compatibility to weak compatibility, and extended the coincidence theorem for compatible mappings in Kaneko and Sessa [11] to weakly compatible mappings [13]. In the present paper, we define a new class of weakly compatible mappings (Definition 4) and prove some common fixed point theorems for these mappings, which satisfy Condition (2) below. Although our main theorem is formulated for weakly compatible mappings, its corresponding formulation for commutative mappings is also a new result, thus presenting a generalization of some theorems of Fisher, Das and Naik, Khan and Kubiaczyk, Reich, Ćirić and Rhoades and Watson. [ABSTRACT FROM AUTHOR]

In this paper, two concepts of well-posedness for quasivariational inequalities having a unique solution are introduced. Some equivalent characterizations of these concepts and classes of well-posed quasivariational inequalities are presented. The corresponding concepts of well-posedness in the generalized sense are also investigated for quasivariational inequalities having more than one solution. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an iterative process for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping. The iterative process is based on the so-called extragradient method. We obtain a weak convergence theorem for two sequences generated by this process. [ABSTRACT FROM AUTHOR]

In the present paper, some new almost fixed point theorems and fixed point theorems for lower semicontinuous type multivalued mappings are obtained in metrizable H–spaces. [ABSTRACT FROM AUTHOR]

Letdenote the ideal in MO* of cobordism classes containing a representative that admits (Z2)k-actions with a fixed point set of constant codimensionr. In this paper we determineand. [ABSTRACT FROM AUTHOR]

A few weak and strong convergence theorems of the modified three-step iterative sequence with errors and the modified Ishikawa iterative sequence with errors for asymptotically non-expansive mappings in any non-empty closed convex subsets of uniformly convex Banach spaces are established. The results presented in this paper substantially extend the results due to Chang (2001), Osilike and Aniagbosor (2000), Rhoades (1994) and Schu (1991). [ABSTRACT FROM AUTHOR]

This paper deals with the first-order delayed differential systems {u′+a(t)u=h(t)v+f(t,u(t−τ(t))),v′+b(t)v=g(t,u(t−τ(t))), where a, b, τ, h are continuous ω-periodic functions with ∫0ωa(t)dt=0 and ∫0ωb(t)dt>0; f∈C(R×[0,∞),R) and g∈C(R×[0,∞),[0,∞)) are ω-periodic with respect to t. By means of the fixed point theorem in cones, several new existence theorems on positive periodic solutions are established. Our main results enrich and complement those available in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the nonlinear boundary problem for first-order impulsive semilinear differential inclusions. We establish existence results by using Martelli’s fixed point theorem with upper and lower solutions method. We find that by giving different definitions of lower and upper solutions we can get all existence results. We also present an example. [ABSTRACT FROM AUTHOR]