Wyniki wyszukiwania - BazTech

1

On new stability results for composite functional equations in quasi-β-normed spaces

Thanyacharoen Anurak, Sintunavarat Wutiphol

Demonstratio Mathematica

|

2021

|

Vol. 54, nr 1

68--84

EN

In this article, we prove the generalized Hyers-Ulam-Rassias stability for the following composite functional equation: f(f(x) – f(y)) = f(x + y) + f(x – y) – f(x) – f(y), where f maps from a(β, p)-Banach space into itself, by using the fixed point method and the direct method. Also, the generalized Hyers-Ulam-Rassias stability for the composite s-functional inequality is discussed via our results.

2

Stability of an AQCQ functional equation in non-Archimedean (n, β)-normed spaces

Liu Yachai, Yang Xiuzhong, Liu Guofen

Demonstratio Mathematica

|

2019

|

Vol. 52, nr 1

130--146

EN

In this paper, we adopt direct method to prove the Hyers-Ulam-Rassias stability of an additive-quadratic-cubic-quartic functional equation f(x+2y)+f(x-2y) = 4f(x+y)+4f(x-y)-6f(x)+f(2y)+f(-2y)-4f(y)-4f(-y) in non-Archimedean (n,β)-normed spaces.

3

Hyers-Ulam stability of quadratic forms in 2-normed spaces

Park Won-Gil, Bae Jae-Hyeong

Demonstratio Mathematica

|

2019

|

Vol. 52, nr 1

496--502

EN

In this paper, we obtain Hyers-Ulam stability of the functional equations f(x+y, z+w) + f(x-y, z-w) = 2f(x, z) + 2f(y, w), f(x+y, z-w) + f(x-y, z+w) = 2f(x, z) + 2f(y, w) and f(x+y, z-w) + f(x-y, z+w) = 2f(x, z) - 2f(y, w) in 2-Banach spaces. The quadratic forms ax2+bxy+cy2, ax2+by2 and axy are solutions of the above functional equations, respectively.

4

Porosity and the bounded linear regularity property

Reich S., Zaslavski A. J.

Journal of Applied Analysis

|

2014

|

Vol. 20, nr 1

1--6

EN

H. H. Bauschke and J. M. Borwein showed that in the space of all tuples of bounded, closed, and convex subsets of a Hilbert space with a nonempty intersection, a typical tuple has the bounded linear regularity property. This property is important because it leads to the convergence of infinite products of the corresponding nearest point projections to a point in the intersection. In the present paper we show that the subset of all tuples possessing the bounded linear regularity property has a porous complement. Moreover, our result is established in all normed spaces and for tuples of closed and convex sets, which are not necessarily bounded.

5

Some stability results for nonexpansive and quasi-nonexpansive operators in uniformly convex Banach space using two new iterative processes of Kirk-type

Olatinwo M. O.

Fasciculi Mathematici

|

2010

|

Nr 43

101-114

EN

In this paper, we examine the stability of Kirk-Ishikawa and Kirk-Mann iteration processes for nonexpansive and quasi-nonexpansive operators in uniformly convex Banach space. To the best of our knowledge, apart from the results of Olatinwo [19], stability of fixed point iteration processes has not been investigated in uniformly convex Banach space. Our results generalize, extend and improve some of the results of Harder and Hicks [11], Rhoades [26, 27], Osilike [23], Berinde [2, 3] as well as Imoru and Olatinwo [12].

6

On the Torricellian point in inner product spaces

Dragomir S., Comanescu D.

Demonstratio Mathematica

|

2008

|

Vol. 41, nr 3

639-650

EN

The concept of Torricellian point related to a set of n vectors in normed linear spaces is introduced and the general properties obtained. The existence and uniqueness of the Torricellian point in inner product spaces are established.

7

Common fixed point, best approximation and generalized f-weak contraction multivalued mapping in p-normed spaces

Abbas M., Rhoades B.

Demonstratio Mathematica

|

2008

|

Vol. 41, nr 1

137-144

EN

We establish coincidence point and common fixed point results for multivalued f-weak contraction mappings which assume closed values only. As an application, related common fixed point and invariant approximation are obtained in the setup of certain metrizable topological vector spaces. Our results provide extensions as well as substantial improvements of several well known results in the literature.

8

A closedness theorem for normed spaces

Poppe H.

Demonstratio Mathematica

|

2008

|

Vol. 41, nr 1

123-127

EN

For spaces X, Y, for which some algebraic operations are defined and in some cases topologies for X, Y are defined too, we define for the space X a dual space Xd with respect to the space Y. If [..] is a topology for Y (compatible with the algebraic operations of Y), then the pointwise topology rp for Yx is defined. We show that Xd is (algebraically)rp-closed in Yx. For normed spaces is shown that suitable subspaces of Xd are rp-closed in a product space K C Yx. As a corollary we obtain a generalization of Alaoglu's theorem.

9

Asymptotic correctness of the evolutionary algorithm in Banach space

Arabas J.

Prace Naukowe Politechniki Warszawskiej. Elektronika

|

2006

|

z. 156

21-30

EN

The paper gives two theorems for the asymptotic correctness of an evolutionary algorithm (EA) that processes chromosomes from an arbitrary Banach space. It is argued that even if the mutation cannot yield an arbitrarily far offspring, the EA may be asymptotically correct provided that the selection is nonelitist and each feasible individual may reproduce with nonzero probability. An illustrative example accompanies the paper.

10

Stability of the Euler-Lagrange-Rassias functional equation

Pietrzyk A.

Demonstratio Mathematica

|

2006

|

Vol. 39, nr 3

523-530

EN

Let F be a field, a1, a2 is an element of F, K is an element of {R, C}, s an element of K\{0,1}, X be a linear space over F, S C is contained in X be nonempty, and Y be a Banach space over K. Under some additional assumptions on S we show some stability results for the functional equation Q (a1x + a2y) + Q (a2X - a1y) = s[Q{x) + Q{y)} in the class of function Q : S -> Y.