Smooth convex optimization problems are solved over fixed point sets of quasi-nonexpansive mappings by using a distributed optimization technique. This is done for a networked system with an operator, who manages the system, and a finite number of users, by solving the problem of minimizing the sum of the operator’s and users’ differentiable, convex objective functions over the intersection of ...

K?nzi and Yilzid introduced the concept of convexity structures in sense Takahashi quasi-pseudometric spaces [7]. In this article, we continue study theory, introducing W-convexity for real-valued pair functions defined on an asymmetrically normed real vector space. Moreover, show that all minimal pairs space equipped with a convex structure which is W-convex whenever W translation-invariant.

‎Let $X$ be a real normed  space, then  $C(subseteq X)$  is  functionally  convex  (briefly, $F$-convex), if  $T(C)subseteq Bbb R $ is  convex for all bounded linear transformations $Tin B(X,R)$; and $K(subseteq X)$  is  functionally   closed (briefly, $F$-closed), if  $T(K)subseteq Bbb R $ is  closed  for all bounded linear transformations $Tin B(X,R)$. We improve the    Krein-Milman theorem  ...

Recently, a general class of the Hermit--Hadamard-Fejer inequality on convex functions is studied in [H. Budak, March 2019, 74:29, textit{Results in Mathematics}]. In this paper, we establish a generalization of Hermit--Hadamard--Fejer inequality for fractional integral based on co-ordinated convex functions.Our results generalize and improve several inequalities obtained in earlier studies.

Two properties concerning the space of differences of sublinear functions D(X) for a real Banach space X are proved. First, we show that for a real separable Banach space (X, ‖ · ‖) there exists a countable family of seminorms such that D(X) becomes a Fréchet space. For X = R this construction yields a norm such that D(R) becomes a Banach space. Furthermore, we show that for a real Banach space...

A bstract . Graph transformations tha.t ma.y be reduced to the form x(l +l) = x(I)+vu(Ax(I)), with x(I),x(I+1 ) E R , u convex function and A symmet ric mat rix, are studied. In par t icular , a reduction to t he class is exhibited for some graph t ransformations recentl y introduced by Odlyzko and Randall. Fur ther result s on periods, quasi-periods, and pre-periods are presented. A class of m...

Necessary and sufficient conditions are given so that the space C(X, E) of all continuous functions from a zero-dimensional topological space X to a nonArchimedean locally convex space E, equipped with the topology of uniform convergence on the compact subsets of X, to be polarly absolutely quasi-barrelled, polarly אo-barrelled, polarly `∞-barrelled or polarly co-barrelled. Also, tensor product...

In this paper, we are concerned with a nondifferentiable multiobjective programming problem with inequality constraints. We introduce four new classes of generalized convex functions by combining the concepts of weak strictly pseudoinvex, strong pseudoinvex, weak quasi invex, weak pseudoinvex and strong quasi invex functions in Aghezzaf and Hachimi [Numer. Funct. Anal. Optim. 22 (2001) 775], d-...