In this paper, we introduce a new type of a projective algorithm for a pair of quasi-φ-nonexpansive mappings. We establish strong convergence theorems of common fixed points in uniformly smooth and strictly convex Banach spaces with the property(K). Our results improve and extend the corresponding results announced by many others. AMS subject classifications: 47H09, 47H10

In this paper, we study the behavior and sensitivity analysis of the solution set for a new system of parametric generalized nonlinear mixed quasi-variational inclusions with (A, η)-accretive mappings in quniformly smooth Banach spaces. The present results improve and extend many known results in the literature.

We study a new simple quadrature rule based on integrating a C1 quadratic spline quasi-interpolant on a bounded interval. We give nodes and weights for uniform and non-uniform partitions. We also give error estimates for smooth functions and we compare this formula with Simpson’s rule.

We prove the complete asymptotic expansion of the spectral function (the integral kernel of the spectral projection) of a Schrödinger operator H = −∆ + b acting in R when the potential b is real and either smooth periodic, or generic quasi-periodic (finite linear combination of exponentials), or belongs to a wide class of almost-periodic functions.

We analyze existing discontinuous Galerkin methods on quasi-uniform meshes for singularly perturbed problems. We prove weighted L2 error estimates. We use the weighted estimates to prove L2 error estimates in regions where the solution is smooth. We also prove pointwise estimates in these regions.

Rates of convergence of limit theorems are established for a class of random processes called here quasi-additive smooth Euclidean functionals. Examples include the objective functions of the traveling salesman problem, the Steiner tree problem, the minimumspanning tree problem, the minimumweight matching problem, and a variant of the minimum spanning tree problem with power weighted edges.

In this paper, we study the convergence of time-dependent Euler–Poisson equations to incompressible type Euler equations via the quasi-neutral limit. The local existence of smooth solutions to the limit equations is proved by an iterative scheme. The method of asymptotic expansion and the symmetric hyperbolic property of the systems are used to justify the convergence of the limit.

We give a completely algebraic proof of the Bogomolov-Tian-Todorov theorem. More precisely, we shall prove that if X is a smooth projective variety with trivial canonical bundle defined over an algebraically closed field of characteristic 0, then the L∞-algebra governing infinitesimal deformations of X is quasi-isomorphic to an abelian differential graded Lie algebra.

We prove strong convergence theorem for infinite family of uniformly L−Lipschitzian total quasi-φ-asymptotically nonexpansive multi-valued mappings using a generalized f−projection operator in a real uniformly convex and uniformly smooth Banach space. The result presented in this paper improve and unify important recent results announced by many authors.

We study numerically the “analyticity breakdown” transition in 1-dimensional quasi-periodic media. This transition corresponds physically to the transition between pinned down and sliding ground states. Mathematically, it corresponds to the solutions of a functional equation losing their analyticity properties. We implemented some recent numerical algorithms that are efficient and backed up by ...