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

100%

Olatinwo M. O.

Fasciculi Mathematici

2010

tom Nr 43

101-114

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].

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

75%

Park W.-G. , Bae J.-H.

Demonstratio Mathematica

2019

tom Vol. 52, nr 1

496--502

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.

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

75%

Liu Y. , Yang X. , Liu G.

Demonstratio Mathematica

2019

tom Vol. 52, nr 1

130--146

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.

On the Torricellian point in inner product spaces

75%

Dragomir S. , Comanescu D.

2008

tom Vol. 41, nr 3

639-650

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.

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

75%

Abbas M. , Rhoades B.

2008

tom Vol. 41, nr 1

137-144

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.

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

63%

Thanyacharoen A. , Sintunavarat W.

tom Vol. 54, nr 1

68--84

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.

A closedness theorem for normed spaces

63%

Poppe H.

2008

tom Vol. 41, nr 1

123-127

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.