we study the notion of bounded approximate connes-amenability for‎ ‎dual banach algebras and characterize this type of algebras in terms‎ ‎of approximate diagonals‎. ‎we show that bounded approximate‎ ‎connes-amenability of dual banach algebras forces them to be unital‎. ‎for a separable dual banach algebra‎, ‎we prove that bounded‎ ‎approximate connes-amenability implies sequential approximate...

 We study the notion of bounded approximate Connes-amenability for‎ ‎dual Banach algebras and characterize this type of algebras in terms‎ ‎of approximate diagonals‎. ‎We show that bounded approximate‎ ‎Connes-amenability of dual Banach algebras forces them to be unital‎. ‎For a separable dual Banach algebra‎, ‎we prove that bounded‎ ‎approximate Connes-amenability implies sequential approximat...

We survey the recent investigations on (bounded, sequential) approximate Connes amenability and pseudo-Connes amenability for dual Banach algebras. We will discuss the core problems concerning these notions and address the signicance of any solutions to them to the development of the eld.

we survey the recent investigations on (bounded, sequential) approximate connesamenability and pseudo-connes amenability for dual banach algebras. we will discuss thecore problems concerning these notions and address the signi cance of any solutions to themto the development of the eld.

Sequential optimality conditions provide adequate theoretical tools to justify stopping criteria for nonlinear programming solvers. Here, nonsmooth approximate gradient projection and complementary approximate Karush-Kuhn-Tucker conditions are presented. These sequential optimality conditions are satisfied by local minimizers of optimization problems independently of the fulfillment of constrai...

We introduce the notion of Johnson pseudo-Connes amenability for dual Banach algebras. study relation between this new with various notions Connes like amenability, approximate and pseudo amenability. also investigate some hereditary properties notion. prove that a locally compact group G,M(G) is amenable if only G amenable. Also we show every non-empty set I,MI(C) under forced to have finite i...

In recent years, sequential optimality conditions are frequently used for convergence of iterative methods to solve nonlinear constrained optimization problems. The sequential optimality conditions do not require any of the constraint qualications. In this paper, We present the necessary sequential complementary approximate Karush Kuhn Tucker (CAKKT) condition for a point to be a solution of a ...