Let K be a nonempty subset of a p-uniformly convex Banach space E, G a left reversible semitopological semigroup, and = {Tt : t ∈G} a generalized Lipschitzian semigroup of K into itself, that is, for s ∈ G, ‖Tsx−Tsy‖ ≤ as‖x−y‖+bs(‖x−Tsx‖+ ‖y−Tsy‖)+cs(‖x−Tsy‖+‖y−Tsx‖), for x,y ∈ K where as,bs ,cs > 0 such that there exists a t1 ∈ G such that bs +cs < 1 for all s t1. It is proved that if there ex...

This paper deals with Lipschitzian t-norms. A partial answer to an open problem of Alsina, Frank and Schweizer is given with regard to strict t-norms with smooth additive generators. A new notion of local Lipschitzianity for arbitrary tnorms is introduced. Some remarkable examples of non-Lipschitzian continuous triangular norms are provided.

This paper concerns applications of advanced techniques of variational analysis and generalized differentiation to parametric problems of semi-infinite and infinite programming, where decision variables run over finite-dimensional and infinite-dimensional spaces, respectively. Part I is primarily devoted to the study of robust Lipschitzian stability of feasible solutions maps for such problems ...

In the present paper, the concepts of module (uniform) approximate amenability and contractibility of Banach algebras that are modules over another Banach algebra, are introduced. The general theory is developed and some hereditary properties are given. In analogy with the Banach algebraic approximate amenability, it is shown that module approximate amenability and contractibility are the same ...

The authors have obtained the following results: 1 the definition of uniformly closed countable family of nonlinear mappings, 2 strong convergence theorem by the monotone hybrid algorithm for two countable families of hemirelatively nonexpansive mappings in a Banach space with new method of proof, 3 two examples of uniformly closed countable families of nonlinear mappings and applications, 4 an...

Let L be a second order elliptic operator on R with a constant diffusion matrix and a dissipative (in a weak sense) drift b ∈ L loc with some p > d. We assume that L possesses a Lyapunov function, but no local boundedness of b is assumed. It is known that then there exists a unique probability measure μ satisfying the equation Lμ = 0 and that the closure of L in L1(μ) generates a Markov semigro...

A convergence theorem of Rhoades [18] regarding the approximation of fixed points of some quasi contractive operators in uniformly convex Banach spaces using the Ishikawa iterative procedure, is extended to arbitrary Banach spaces. The conditions on the parameters {αn} that define the Ishikawa iteration are also weakened.