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An iterative approximation of common solutions of split generalized vector mixed equilibrium problem and some certain optimization problems

Mewomo Oluwatosin T., Oyewole Olawale K.

Demonstratio Mathematica

2021

Vol. 54, nr 1

335--358

In this paper, we study the problem of finding a common solution of split generalized vector mixed equlibrium problem (SGVMEP), fixed point problem (FPP) and variational inequality problem (VIP). We propose an inertial-type iterative algorithm, which uses a projection onto a feasible set and a linesearch, which can be easily calculated. We prove a strong convergence of the sequence generated by the proposed algorithm to a common solution of SGVMEP, fixed point of a quasi- ϕ -nonexpansive mapping and VIP for a general class of monotone mapping in 2-uniformly convex and uniformly smooth Banach space E1 and a smooth, strictly convex and reflexive Banach space E2 . Some numerical examples are presented to illustrate the performance of our method. Our result improves some existing results in the literature.

Inverse limit representations of hereditarily indecomposable compacta

Krasinkiewicz J.

Bulletin of the Polish Academy of Sciences. Mathematics

2003

Vol. 51, no 1

31-41

We prove that any infinite-dimensional hereditarily indecomposable compactum can be represented as the limit of an inverse sequence of compacta X0 <-- X1 <-- X2 <--..., where each Xk, k > O, is hereditarily indecomposable, dim Xk = k, and the bonding maps pk k+1 : X k+1 --> Xk are 1-dimensional monotone and surjective. Moreover, each bonding map pk k+l : Xk,l > 1, is l-dimensional. For finite dimensional hereditarily indecomposable compacta there exist analogous finite inverse sequences. Much the same results hold also for hereditarily unicoherent compacta.