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In this paper, we study the tangential touch and C¹ regularity of the free boundary near the fixed boundary of the double obstacle problem for Laplacian and fully nonlinear operator. The main idea to have the properties is regarding the upper obstacle as a solution of the single obstacle problem. Then, in the classification of global solutions of the double problem, it is enough to consider only two cases for the upper obstacle, a/2 xn² or a/2 xn² + bxnx1 for some b ∈ ℝ, b ≠ 0. The second one is a new type of upper obstacle, which does not exist in the study of local regularity of the free boundary of the double problem. Thus, in this paper, a new type of difficulties that come from the second type upper obstacle is mainly studied. [ABSTRACT FROM AUTHOR]

In this paper, we prove a new coincidence and common fixed point theorem of hybrid mappings using the C-class function and T-weak commutativity. Finally, we give 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]

In this paper using new fixed point results of the author, we establish a variety of existence results for equilibria for abstract economies. [ABSTRACT FROM AUTHOR]

This paper is devoted to the qualitative properties of discretized parabolic operators, such as nonnegativity and nonpositivity preservation, maximum/minimum principles and maximum norm contractivity. In the linear case, earlier papers of the authors (Faragó and Horváth in SIAM Sci Comput 28:2313–2336, 2006, IMA J Numer Anal 29:606–631, 2009) have established the connections between the above qualitative properties and have given sufficient conditions for their validity. The present paper extends the above results to nonlinear discretized parabolic operators, also motivated by the authors' recent paper (Faragó and Horváth in J Math Anal Appl 448:473–497, 2017), which has given related results on the continuous PDE level. A systematic study is presented, ranging from general discrete mesh operators to proper finite element applications. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the existence of the best proximity points in binormed linear spaces. As a consequence, we obtain some fixed point results. We also provide some illustrations to support our claims. As applications, we obtain the existence of a solution to split feasible and variational inequality problems. [ABSTRACT FROM AUTHOR]

In the present paper, we characterize Lie (Jordan) σ-centralizers of generalized matrix algebras. More precisely, we obtain some conditions under which every Lie σ-centralizer of a generalized matrix algebra can be expressed as the sum of a σ-centralizer and a center- valued mapping. Further, it is shown that under certain appropriate assumptions every Jordan σ-centralizer of a generalized matrix algebra is a σ-centralizer. Finally, the main results are applied to triangular algebras. [ABSTRACT FROM AUTHOR]

The exponential space, which is a Banach function space, can be defined with two very differently looking, but equivalent norms. In this paper, we give estimates for the best constants of the ratio of these two norms. Our result answers a question of C. Bennett, and R. Sharpley. [ABSTRACT FROM AUTHOR]

The concept of a tolerance relation, shortly called tolerance, was studied on various algebras since the seventies of the twentieth century by B. Zelinka and the first author (see e.g. [6] and the monograph [1] and the references therein). Since tolerances need not be transitive, their blocks may overlap and hence in general the set of all blocks of a tolerance cannot be converted into a quotient algebra in the same way as in the case of congruences. However, G. Czédli ([7]) showed that lattices can be factorized by means of tolerances in a natural way, and J. Grygiel and S. Radeleczki ([8]) proved some variant of an Isomorphism Theorem for tolerances on lattices. The aim of the present paper is to extend the concept of a tolerance on a lattice to posets in such a way that results similar to those obtained for tolerances on lattices can be derived. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence and stability of solutions for impulsive pantograph fractional integro-differential equation via ψ-Hilfer fractional derivative in a appropriate Banach space. Our approach is based on fixed point theorems of Darbo’s and Mönch via Kuratowski measure of non-compactness. An example is given to illustrate our approach. [ABSTRACT FROM AUTHOR]

In this paper we design a family of cell-average nonlinear prediction operators that make use of the generalized harmonic means and we apply the resulting schemes to image processing. The new family of nonlinear schemes conserve the numerical properties of the linear schemes, such as the L 1 -stability, the order of accuracy or compression rate but avoiding Gibbs phenomenon close to the discontinuities. The generalized harmonic mean was introduced in the framework of point-values in [A. Guessab, M. Moncayo, and G. Schmeisser, A class of nonlinear four-point subdivision schemes. Properties in terms of conditions, Adv. Comput. Math. 37 (2012), pp. 151–190] in order to improve the results of the harmonic mean. However, in the cell-average setting our conclusion is that, from a numerical point of view, the advantage of using the new mean is not clear. [ABSTRACT FROM AUTHOR]

In this paper we first introduce N̅qΔ − summable difference sequence spaces and prove some properties of these spaces. We then obtain the necessary and sufficient conditions for infinite matrix A to map these sequence spaces on the spaces c, c0 and l∞. Finally, the Hausdorff measure of noncompactness is then used to obtain the necessary and sufficient conditions for the compactness of the linear operators defined on these spaces. [ABSTRACT FROM AUTHOR]

Let U be a Hilbert A-module and L(U) the set of all adjointable A-linear maps on U. Let K = {Λx ∈ L(U, Vx) : x ∈ X } and L = {Γx ∈ L(U, Vx) : x ∈ X } be two continuous g-frames for U, K is said to be similar with L if there exists an invertible operator J ∈ L(U) such that Γx = ΛxJ, for all x ∈ X . In this paper, we define the concepts of closeness and nearness between two continuous g-frames. In particular, we show that K and L are near, if and only if they are similar. [ABSTRACT FROM AUTHOR]

In this paper, we establish the generalized viscosity implicit rules of asymptotically nonexpansive mappings in CAT(0) spaces. The strong convergence theorems of the implicit rules proposed are proved under certain assumptions imposed on the control parameters. The results presented in this paper improve and extend some recent corresponding results announced. [ABSTRACT FROM AUTHOR]

In this paper, by using the dynamic system method and the known conservation laws of the gCH equation, and underlying features of the peakons, we study the peakon solutions and the orbital stability of the peakons for a nonlinear generalization of the Camassa-Holm equation (gCH). The gCH equation is first transformed into a planar system. Then, by the first integral and algebraic curves of this system, we obtain one heteroclinic cycle, which corresponds to a peakon solution. Moreover, we give a proof of the orbital stability of the peakons for the gCH equation. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new system of generalized mixed quasi-variational-like inclusions with ( A, η, m)-accretive operators and relaxed cocoercive mappings. By using the fixed point theorem of Nadler, we prove the existence of solutions for this general system of generalized mixed quasi-variational-like inclusions and its special cases. The results in this paper unify, extend and improve some known results in the literature. The novel proof method is simpler than those iterative algorithm approach for proving the existence of solutions of all classes of system of set-valued variational inclusions in the literature. [ABSTRACT FROM AUTHOR]

In this paper we derive explicit formulas for the normal form coefficients to verify the nondegeneracy of eight codimension two bifurcations of fixed points with one or two critical eigenvalues. These include all strong resonances, as well as the degenerate flip and Neimark--Sacker bifurcations. Applying our results to n-dimensional maps, one avoids the computation of the center manifold, but one can directly evaluate the critical normal form coefficients in the original basis. The formulas remain valid also for n=2 and allow one to avoid the transformation of the linear part of the map into Jordan form. The developed techniques are tested on two examples: (1) a three-dimensional map appearing in adaptive control; (2) a periodically forced epidemic model. We compute numerically the critical normal form coefficients for several codim 2 bifurcations occurring in these models. To compute the required derivatives of the Poincaré map for the epidemic model, the automatic differentiation package ADOL-C is used. [ABSTRACT FROM AUTHOR]

Motion-compensated temporal filtering (MCTF) is an essential ingredient of the recently developed wavelet-based scalable video coding schemes. Lifting implementation of these decompositions represents a versatile tool for spatiotemporal optimizations, and several improvements have already been proposed in this framework. In this paper, we propose new spatiotemporal update operators based either on weighted averages of multiple connected pixels or on nonlinear filtering of these pixels. We demonstrate the improved performance of the proposed operators, both theoretically and experimentally. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of weak Weak θ-φ-contraction ensuring a convergence of successive approximations but does not force the mapping to be continuous at the fixed point. Thus, we answer one more solution to the open question raised by Rhoades in [B. E. Rhoades, Fixed point theory Appl, Berkeley, CA, (1986), Contemp. Math., Amer. Math. Soc., Providence, RI, 72 (1988), 233-245]. [ABSTRACT FROM AUTHOR]

The problem of computing spectra of operators is arguably one of the most investigated areas of computational mathematics. However, the problem of computing spectra of general bounded infinite matrices has only recently been solved. We establish some of the foundations of computational spectral theory through the Solvability Complexity Index (SCI) hierarchy, an approach closely related to Smale’s program on the foundations of computational mathematics and McMullen’s results on polynomial root finding with rational maps. Infinite-dimensional problems yield an intricate infinite classification theory, determining which spectral problems can be solved and with what types of algorithms. We provide answers to many longstanding open questions on the existence of algorithms. For example, we show that spectra can be computed, with error control, from point sampling operator coefficients for large classes of partial differential operators on unbounded domains. Further results include: computing spectra of (possibly unbounded) operators on graphs and separable Hilbert spaces with error control; determining if the spectrum intersects a compact set; the computational spectral gap problem and computing spectral classifications at the bottom of the spectrum; and computing discrete spectra, multiplicities, eigenspaces and determining if the discrete spectrum is non-empty. Moreover, the positive results with error control can be used in computer-assisted proofs. In contrast, the negative results preclude computer-assisted proofs for classes of operators as a whole. Our proofs are constructive, yielding a library of new algorithms and techniques that handle problems that before were out of reach. We demonstrate these algorithms on challenging problems, giving concrete examples of the failure of traditional approaches (e.g., “spectral pollution”) compared to the introduced techniques. [ABSTRACT FROM AUTHOR]

In this paper, we establish and prove some common fixed points for self-maps in a complete cone metric space that generalize and improve earlier results in the literature. [ABSTRACT FROM AUTHOR]

In this paper we investigate the stability and asymptotic stability of the zero solution for the first order delay differential equation þ(t)=-ΣNj=1(t)y(t-τj(t))+f(t,y(t-964;(t)) where the delay is variable and by using Banach fixed point theorem. We give new conditions to ensure the stability and asymptotic stability of the zero solution of this equation. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to study the existence of a fixed point in locally convex topology generated by fuzzy n-normed spaces. We prove our main results, a fixed point theorem for a self mapping and a common fixed point theorem for a pair of weakly compatible mappings in locally convex topology generated by fuzzy n-normed spaces. Also we give some remarks in locally convex topology generated by fuzzy ra-normed spaces. [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]

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]

In this paper, we propose a new extragradient method with regularization for finding a common element of the solution set Γ of the split feasibility problem and the set Fix(S) of fixed points of a nonexpansive mapping S in infinitedimensional Hilbert spaces, combining the regularization method and the technique of averaged operator, we prove the sequences generated by the proposed algorithm converge weakly to an element of Fix(S)∩Γ under mild conditions. [ABSTRACT FROM AUTHOR]

In this paper, we prove several fixed point results for mappings of Caristi type in the setting of G-metric spaces. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to study the existence of solution of a system of differential equations using fixed point technique. In this regard, in the first part of this article, along with some properties of partial b-metric topology, we prove a common fixed point theorem for generalized Geraghty type contraction mappings in a complete partial b-metric spaces. Then in second part we apply this result to show the existence of the solution of a system of ordinary differential equations. [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 .

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 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]

This paper compares two scheme-based models of computation on abstract many-sorted algebras A: Feferman's system ACP(A) of "abstract computational procedures" based on a least fixed point operator, and Tucker and Zucker's system μPR(A) based on primitive recursion on the naturals together with a least number operator. We prove a conjecture of Feferman that (assuming contains sorts for natural numbers and arrays of data) the two systems are equivalent. The main step in the proof is showing the equivalence of both systems to a system Rec(A) of computation by an imperative programming language with recursive calls. The result provides a confirmation for a Generalized Church-Turing Thesis for computation on abstract data types. [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]

We consider the evolution problem associated to the infinity fractional Laplacian introduced by Bjorland et al. (Adv Math 230(4–6):1859–1894, 2012) as the infinitesimal generator of a non-Brownian tug-of-war game. We first construct a class of viscosity solutions of the initial-value problem for bounded and uniformly continuous data. An important result is the equivalence of the nonlinear operator in higher dimensions with the one-dimensional fractional Laplacian when it is applied to radially symmetric and monotone functions. Thanks to this and a comparison theorem between classical and viscosity solutions, we are able to establish a global Harnack inequality that, in particular, explains the long-time behavior of the solutions. [ABSTRACT FROM AUTHOR]

This paper is concerned with the following fourth-order three-point boundary value problem ... where n ∊ [1/3, 1). In spite of sign-changing Green's function, for arbitrary positive integer n (≥ 2), we still obtain the existence of at least n - 1 decreasing positive solutions to the above problem by imposing some suitable conditions on f . The main tool used is the fixed point index theory. [ABSTRACT FROM AUTHOR]

In this paper, we prove some common fixed point theorems for a pair of weakly compatible mappings satisfying (Ψ, α, β)-weak contractions in fuzzy metric spaces employing a control function. Our results improve and generalize several previously known relevant results of the existing literature. Some illustrative examples are alsofurnished to substantiate our main results. [ABSTRACT FROM AUTHOR]

In this article, two unique common fixed point theorems for four self-maps on a metric-like space by using the concept of occasionally weakly biased maps of type (A) are proved. Our results represent an improvement and extension of some fixed point findings. We justify our results by giving two appropriate examples. [ABSTRACT FROM AUTHOR]

This article has presented several generalized fixed point theorems with variations in S-metric space domains. In addition, several more fixed point results are obtained for different forms of contraction mappings that have closed graphs in S-metric spaces. [ABSTRACT FROM AUTHOR]

In this paper we will present an abstract point of view on iterative approximation schemes of fixed points for multivalued operators. More precisely, we suppose that the algorithms are convergent and we will study the impact of this hypothesis in the theory of operatorial inclusiosns: data dependence, stability and Gronwall type lemmas. Some open problems are also presented. [ABSTRACT FROM AUTHOR]

In this paper, we present existence, uniqueness and Ulam-Hyers stability results for the coupled fiixed points of a pair of contractive type singlevalued and respectively multivalued operators on complete metric spaces. The approach is based on Perov type fixed point theorem for contractions in spaces endowed with vector- valued metrics. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present a fixed point theory for S-contractions in generalized Kasahara spaces (X, →, d), where d : X ⨰ X → s(R+) is not necessarily an s(R+)-metric. [ABSTRACT FROM AUTHOR]

New fixed-point theorems on metric spaces are established, and analogous results on partial metric spaces are deduced. This work can be considered as a continuation of the paper Samet et al. (2013). [ABSTRACT FROM AUTHOR]

Abstract: Different from involutive negations on [0, 1], the fixed points of an involutive interval-valued negation are uncountable. In this paper, all the fixed points of an involutive interval-valued negation are characterized. Also, it is proved that an involutive interval-valued negation is uniquely determined by its fixed points. Moreover, a constructive representation of involutive interval-valued negations is obtained. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to prove the existence of common fixed points for two pairs of occasionally weakly compatible selfmaps satisfying property (E. A)/common property (E. A) using an inequality involving quadratic terms. [Copyright &y& Elsevier]