Wyniki wyszukiwania - BazTech

1

Introducing and solving the hesitant fuzzy system AX = B

Babakordi Fatemeh, Allahviranloo Tofigh

Control and Cybernetics

|

2021

|

Vol. 50, No. 4

553--574

EN

In this paper the solution for hesitant fuzzy system as AX = B is introduced where A is an n×n known hesitant fuzzy matrix, B is an n×1 known hesitant fuzzy vector and X is an n×1 unknown hesitant fuzzy vector. First, L∞-norm and L1-norm of a hesitant fuzzy vector are introduced. Then, the concepts of hesitant fuzzy zero, ’almost equal’ and ’less than’ and ’equal’ are defined for two hesitant fuzzy numbers. Finally, using a minimization problem; the hesitant fuzzy system is solved. At the end, some numerical examples are presented to show the effectiveness of the proposed method.

2

Strong convergence of an inertial extrapolation method for a split system of minimization problems

Gebrie Anteneh Getachew, Wangkeeree Rabian

Demonstratio Mathematica

|

2020

|

Vol. 53, nr 1

332--351

EN

In this article, we propose an inertial extrapolation-type algorithm for solving split system of minimization problems: finding a common minimizer point of a finite family of proper, lower semicontinuous convex functions and whose image under a linear transformation is also common minimizer point of another finite family of proper, lower semicontinuous convex functions. The strong convergence theorem is given in such a way that the step sizes of our algorithm are selected without the need for any prior information about the operator norm. The results obtained in this article improve and extend many recent ones in the literature. Finally, we give one numerical example to demonstrate the efficiency and implementation of our proposed algorithm.

3

On the proximal point algorithm and demimetric mappings in CAT(0) spaces

Aremu K. O., Izuchukwu C., Ugwunnadi G. C., Mewomo O. T.

Demonstratio Mathematica

|

2018

|

Vol. 51, nr 1

277--294

EN

In this paper, we introduce and study the class of demimetric mappings in CAT(0) spaces. We then propose a modified proximal point algorithm for approximating a common solution of a finite family of minimization problems and fixed point problems in CAT(0) spaces. Furthermore, we establish strong convergence of the proposed algorithm to a common solution of a finite family of minimization problems and fixed point problems for a finite family of demimetric mappings in complete CAT(0) spaces. A numerical example which illustrates the applicability of our proposed algorithm is also given. Our results improve and extend some recent results in the literature.

4

Porous sets for mutually nearest points in Banach spaces

Li C., Myjak J

Opuscula Mathematica

|

2008

|

Vol. 28, no. 1

73-82

EN

Let B(X) denote the family of all nonempty closed bounded subsets of a real Banach space X, endowed with the Hausdorff metric. For E, F ∈ B (X) we set [formula]. Let D denote the closure (under the maximum distance) of the set of all (E, F) ∈ B (X) x B (X) such that λE,F > 0. It is proved that the set of all (E, F) ∈ D for which the minimization problem [formula] fails to be well posed in a σ-porous subset of D.

5

Stability of solutions for a class of convex minimization problems on reflective Banach spaces

Zaslavski A. J.

Journal of Mathematics and Applications

|

2008

|

Vol. 30

151-160

EN

In this paper we study stability of solutions of minimization problems �(x) → min, x ∈ C, where � is a convex lower semicontinuous function and a set C is the countable intersection of a decreasing sequence of closed sets Ci in a reflexive Banach space X.