BazTech - Yadda

1

An other proof of the Reich fixed point theorem

Miarka Marek

Fasciculi Mathematici

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2023

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nr 66

77--79

EN

We give a simple and nonconstructive proof of the Reich fixed point theorem which generalizes both Banach and Kannan fixed point theorems.

2

Ergodic properties of random infinite products of nonexpansive mappings

Reich S., Zaslavski A. J.

Journal of Mathematics and Applications

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2017

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Vol. 40

149--159

EN

In this paper we are concerned with the asymptotic behavior of random (unrestricted) infinite products of nonexpansive selfmappings of closed and convex subsets of a complete hyperbolic space. In contrast with our previous work in this direction, we no longer assume that these subsets are bounded. We first establish two theorems regarding the stability of the random weak ergodic property and then prove a related generic result. These results also extend our recent investigations regarding nonrandom infinite products.

3

De la Vallée Poussin Summability, the Combinatorial Sum [wzór] and the de la Vallée Poussin Means Expansion

Ali Z. S.

Journal of Mathematics and Applications

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2017

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Vol. 40

5--20

EN

In this paper we apply the de la Vallee Poussin sum to a combinatorial Chebyshev sum by Ziad S. Ali in [1]. One outcome of this consideration is the main lemma proving the following combinatorial identity: with Re(z) standing for the real part of z we have (wzór). Our main lemma will indicate in its proof that the hypergeometric factors 2F1(1, 1/2 + n; 1 + n; 4); and 2F1(1, 1/2 + 2n; 1 + 2n; 4) are complex, each having a real and imaginary part. As we apply the de la Vallee Poussin sum to the combinatorial Chebyshev sum generated in the Key lemma by Ziad S. Ali in [1], we see in the proof of the main lemma the extreme importance of the use of the main properties of the gamma function. This represents a second important consideration. A third new outcome are two interesting identities of the hypergeometric type with their new Meijer G function analogues. A fourth outcome is that by the use of the Cauchy integral formula for the derivatives we are able to give a dierent meaning to the sum: (wzór). A fifth outcome is that by the use of the Gauss-Kummer formula we are able to make better sense of the expressions (wzór) by making use of the series denition of the hypergeometric function. As we continue we notice a new close relation of the Key lemma, and the de la Vallee Poussin means. With this close relation we were able to talk about P the de la Vallee Poussin summability of the two innite series (wzór). Furthermore the application of the de la Vallee Poussin sum to the Key lemma has created two new expansions representing the following functions: (wzór).

4

Fixed points of generalized (α,ψ,φ)-rational contractive mappings in -complete metric spaces

Babu G. V. R., Tolera M. D.

Fasciculi Mathematici

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2017

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Nr 59

13--28

EN

In this paper, we introduce generalized (α, ψ, φ)-rational contractive mappings in α-complete metric spaces and prove some new fixed point results for this class of mappings. We provide examples in support of our results. Our results generalize the fixed point results of Singh, Kamal, Sen and Chugh [22] and Piri and Kumam [18].

5

Fixed points of F-weak contractions on complete metric spaces

Wardowski D., Dung N.V.

Demonstratio Mathematica

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2014

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Vol. 47, nr 1

147--155

EN

In this paper, we introduce the notion of an F-weak contraction and prove a fixed point theorem for F-weak contractions. Examples are given to show that our result is a proper extension of some results known in the literature.

6

Fixed points for k mappings on a complete metric spaces

Kikina L., Kikina K.

Demonstratio Mathematica

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2011

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Vol. 44, nr 2

349--357

EN

A fixed point theorem for three mappings on a metric space into itself is proved. This result extends the results obtained in [1] from two mappings to three map pings, and after that, a generalization for an arbitrary number of mappings is obtained. As corollaries of these results we obtain the extending of Theorems of Nesic, Rhoades, Chatterjea, Rus and Kannan for an arbitrary number of mappings.

7

A note on stability of the popoviciu functional equation on restricted domain

Brzdęk J.

Demonstratio Mathematica

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2010

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Vol. 43, nr 3

635-641

EN

We prove the Hyers-Ulam stability, on restricted domain, of a functional equation of Jensen type, introduced by T. Popoviciu (1965).

8

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

Zaslavski A. J.

Journal of Mathematics and Applications

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2008

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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.

9

Two results on Jachymski-Schörder-Stein contractions

Reich S., Zaslavski A. J.

Bulletin of the Polish Academy of Sciences. Mathematics

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2008

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Vol. 56, no 1

53-58

EN

We establish two fixed point theorems for certain mappings of contractive type.

10

Asymptotic behavior of inexact orbits for a class of operators in complete metric spaces

Butnariu D., Reich S., Zaslavski A. J.

Journal of Applied Analysis

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2007

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Vol. 13, nr 1

1-11

EN

We exhibit a class of nonlinear operators with the property that their iterates converge to their unique fixed points even when com- putational errors are present. We also showthat most (in the sense of the Baire category) elements in an appropriate complete metric space of operators do, in fact, possess this property.

11

Strong variational principles and generic well-posedness

Turinici M.

Demonstratio Mathematica

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2005

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Vol. 38, nr 4

935--941

EN

The strong version of Ekeland's variational principle [JMAA, 47(1974), 324-353] due to Georgiev [JMAA, 131(1988), 1-21] is deductible in a direct way from the standard one. In addition, a substitution between them is possible for many generic well-posed optimization problems.