In a previous paper, the authors introduced the monoidal category of left–left Yetter–Drinfeld modules over a weak braided Hopf algebra in a strict monoidal category. The main goal of this work is to define the categories of right–right, left–right and right–left Yetter–Drinfeld modules over a weak braided Hopf algebra and prove that there exists a categorical equivalence between...

In this paper, we introduce and study Kaplansky classes of complexes. We give some results by which one can construct many Kaplansky classes of complexes. We also give some relations between Kaplansky classes of complexes and cotorsion pairs.

This paper studies the D(m,n) equation, which is the generalized version of the Drinfeld–Sokolov equation. The traveling wave hypothesis and exp-function method are applied to integrate this equation. The mapping method and the Weierstrass elliptic function method also display an additional set of solutions. The kink, soliton, shock waves, singular soliton solution, cnoidal and...

This paper is concerned with stabilization for a class of Takagi-Sugeno fuzzy neural networks (TSFNNs) with time-varying delays. An impulsive control scheme is employed to stabilize a TSFNN. We firstly establish the model of TSFNNs by using fuzzy sets and fuzzy reasoning and propose the problem of impulsive stabilization for this model. Then, we present several stabilization...

Reversible difference sets have been studied extensively by many people. Dillon showed that reversible difference sets existed in groups \({(C_{2^{r}})^{2}}\) and C4. Davis and Polhill showed the existence of DRAD difference sets in the groups \({(C_{2^{r}})^{2}}\) for \({r\geq 2}\) and also for the group C4. This paper gives a construction technique utilizing character values...

In this paper, we first show the strong convergence of the modified Moudafi iteration process when E is a real uniformly convex Banach space, S is AQT self-mapping and T is ANI self-mapping satisfying Condition (B). Next, we show the strong convergence of the modified Mann iteration process when T is ANI self-mapping satisfying Condition (A), which generalizes the result due to...

We review some recent results in the theory of affine manifolds and bundles on them. Donaldson–Uhlenbeck–Yau type correspondences for flat vector bundles and principal bundles are shown. We also consider flat Higgs bundles and flat pairs on affine manifolds. A bijective correspondence between polystable flat Higgs bundles and solutions of the Yang–Mills–Higgs equation in the...

In this paper, we prove that the sequence {x n } generated by modified Krasnoselskii–Mann iterative algorithm introduced by Yao et al. [J Appl Math Comput 29:383–389, 2009] converges strongly to a fixed point of a nonexpansive mapping T in a real uniformly convex Banach space with uniformly Gâteaux differentiable norm. Furthermore, we present an example that illustrates our...

In this survey we present an exposition of the development during the last decade of metric fixed point theory on hyperconvex metric spaces. Therefore we mainly cover results where the conditions on the mappings are metric. We will recall results about proximinal nonexpansive retractions and their impact into the theory of best approximation and best proximity pairs. A central...

The purpose of this paper is to give an outline of the recent results in fixed point theory for asymptotic pointwise contractive and nonexpansive mappings, and semigroups of such mappings, defined on some subsets of modular function spaces. Modular function spaces are natural generalizations of both function and sequence variants of many important, from applications perspective...

A famous open question in metric Fixed Point Theory is whether every Banach space which is isomorphic to the Hilbert space ℓ2 has the fixed point property for nonexpansive mappings. We give an overview about the state of the advances towards their solution.

This paper reviews the old and new landmark extensions of the famous intermediate value theorem (IVT) of Bolzano and Poincaré to a set-valued operator \({\Phi : E \supset X \rightrightarrows E}\) defined on a possibly non- convex, non-smooth, or even non-Lipschitzian domain X in a normed space E. Such theorems are most general solvability results for nonlinear inclusions...

Recall that a Banach space X has the weak fixed point property if for any nonempty weakly compact subset C of X and any nonexpansive mapping T : C→ C, T has at least one fixed point. In this article, we present three recent results using the ultraproduct technique. We also provide some open problems in this area.

A new iterative scheme is introduced to approximate a common element of the solution set of a generalized mixed equilibrium problem, the solution set of a variational inequality problem, the set of common fixed points of two countable families of weak relatively nonexpansive mappings and the set of zeros of a maximal monotone operator in Banach spaces. The results obtained in...

It is shown that in many instances the fixed point property for nonexpansive mappings actually implies the fixed point property for a strictly larger family of mappings. This paper is largely expository, but some of the observations are not readily available, and some appear here for the first time. Several related open questions in are discussed. The emphasis is on accessible...

We prove that a nonlinear evolution equation which gives a novel approach to the X-ray tomography problem (see Kolehmainen et al., SIAM J. Sci. Comput. 30(3):1413–1429, 2008) has a solution. To this end, we list some of our results on theory of accretive operators and then we apply them to this concrete context.

An ordered set P has the fixed point property iff every order-preserving self-map of P has a fixed point. This paper traces the chronological development of research on this property, including most recent developments and open questions.

In this survey, we comment on the current status of several questions in Metric Fixed Point Theory which were raised by W. A. Kirk in 1995.

In this paper we apply the Du Fort–Frankel finite difference scheme on Burgers equation and solve three test problems. We calculate the numerical solutions using Mathematica 7.0 for different values of viscosity. We have considered smallest value of viscosity as 10−4 and observe that the numerical solutions are in good agreement with the exact solution. Open image in new window

In this paper, we consider the compound Poisson risk model involving two types of dependent claims, namely main claims and by-claims. The by-claim is induced by the main claim with a certain probability and the occurrence of a by-claim may be delayed depending on associated main claim amount. Using Rouché’s theorem, both of the survival probability with zero initial surplus and...

A dynamical system model is presented in this paper for genetic regulatory networks with hybrid regulatory mechanism. The sufficient conditions for the stability of the proposed model are established based on the Lyapunov functional method and linear matrix inequality techniques. To test the effectiveness and correctness of our theoretical results, illustrative examples regarding...

In this paper, two pivotal statistics are introduced to construct prediction intervals for future lifetime of three parameters Weibull observations based on generalized order statistics, which can be widely applied in reliability theory and lifetime problems. The probability density functions as well as the explicit form of the distribution functions of our pivotal statistics are...

We present a note on the paper by Brown and Wu (J Math Anal Appl 337:1326–1336, 2008). Indeed, we extend the multiplicity results for a class of semilinear elliptic system to the quasilinear elliptic system of the form: $$\left\{\begin{array}{ll}-\Delta_p u + m(x)\,|u|^{p-2}u = \frac{\alpha}{\alpha + \beta} \, |u|^{\alpha -2} \,u\,|v|^{\beta}, \quad\quad\quad\quad\quad\quad\quad...

In this paper we study the warped product submanifolds of a Lorentzian paracosymplectic manifold and obtain some nonexistence results. We show that a warped product semi-invariant submanifold in the form \({M=M_{\top}\times _{f}M_{\bot}}\) of a Lorentzian paracosymplectic manifold such that the characteristic vector field is normal to M is a usual Riemannian product manifold...

In this paper, we investigate separability of CP-graded ring extensions. With restrictions neither to graded fields nor to grading by torsion–free groups, we show that some results on graded field extensions given in Hwang and Wadsworth [Commun Algebra 27(2):821–840, 1999] hold.