In this paper we provide first existence results for solutions of the generalized equilibrium problem with composed functions (GEPC) under generalized convexity assumptions. Then we construct by employing some tools specific to the theory of conjugate duality two gap functions for (GEPC). The importance of these gap functions is to be seen in the fact that they equivalently characterize the sol...

We develop a renormalization-group formalism for non-renormalizable theories and apply it to Einstein gravity theory coupled to a scalar field with the Lagrangian L = √ g [RU(φ) − 1 2 G(φ) gμν ∂μφ∂νφ − V (φ)], where U(φ), G(φ) and V (φ) are arbitrary functions of the scalar field. We calculate the one-loop counterterms of this theory and obtain a system of renormalization-group equations in par...

In this paper, using Clarke’s generalized directional derivative and dI-invexity we introduce new concepts of nonsmooth K-α-dI-invex and generalized type I univex functions over cones for a nonsmooth vector optimization problem with cone constraints. We obtain some sufficient optimality conditions and Mond-Weir type duality results under the foresaid generalized invexity and type I cone-univexi...

a general notion of completely monotone functionals on an ordered banach algebra b into a proper h*-algebra a with an integral representation for such functionals is given. as an application of this result we have obtained a characterization for the generalized completely continuous monotone functions on weighted foundation semigroups. a generalized version of bochner’s theorem on foundation se...

In these lecture notes we present an introduction to non-standard analysis especially written for the community of mathematicians, physi­ cists and engineers who do research on J. F. Colombeau’ theory of new generalized functions and its applications. The main purpose of our non-standard approach to Colombeau’ theory is the improvement of the properties of the scalars of the varieties of spaces...

Using Serre’s adelic interpretation of the cohomology, we develop “differential and integral calculus” on an algebraic curve X over an algebraically closed constant field k of characteristic zero, define an algebraic analogs of additive and multiplicative multi-valued functions on X, and prove corresponding generalized residue theorem and A. Weil reciprocity law. Using the representation theory...

[E ]u ⊂ L2(E∗, μ) ⊂ [E ]u, and to characterize white noise test function space [E ]u and generalized function space [E ]u in the series of papers [1],[2],[3],[4],[5]. The notion of Legendre transformation plays important roles to examine relationships between the growth order of holomorphic functions (S-transform) and the CKS-space of white noise test and generalized functions. It is well-known...