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1

On statistical convergence in quasi-metric spaces

İlkhan Merve, Kara Emrah Evren

Demonstratio Mathematica

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2019

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Vol. 52, nr 1

225--236

EN

A quasi-metric is a distance function which satisfies the triangle inequality but is not symmetric in general. Quasi-metrics are a subject of comprehensive investigation both in pure and applied mathematics in areas such as in functional analysis, topology and computer science. The main purpose of this paper is to extend the convergence and Cauchy conditions in a quasi-metric space by using the notion of asymptotic density. Furthermore, some results obtained are related to completeness, compactness and precompactness in this setting using statistically Cauchy sequences.

2

P-cyclic c-contraction result in Menger spaces using a control function

Choudhury B. S., Bhandari S. K.

Demonstratio Mathematica

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2016

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Vol. 49, nr 2

213--223

EN

The intrinsic flexibility of probabilistic metric spaces makes it possible to extend the idea of contraction mapping in several inequivalent ways, one of which being the C-contraction. Cyclic contractions are another type of contractions used extensively in global optimization problems. We introduced here p-cyclic contractions which are probabilistic C-contraction types. It involves p numbers of subsets of the spaces and involves two control functions for its definitions. We show that such contractions have fixed points in a complete probabilistic metric space. The main result is supported with an example and extends several existing results.

3

Fixed point theorems on generalized metric spaces for mappings in a class of almost φ-contractions

Kikina L., Kikina K.

Demonstratio Mathematica

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2015

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Vol. 48, nr 3

440--451

EN

In this paper, we obtain some new fixed point theorems in generalized metric spaces for maps satisfying an implicit relation. The obtained results unify, generalize, enrich, complement and extend a multitude of related fixed point theorems from metric spaces to generalized metric spaces.

4

Some fixed point results for mappings in G-metric spaces

Mohanta S. K., Mohanta S.

Demonstratio Mathematica

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2014

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Vol. 47, nr 1

179--191

EN

We prove a common fixed point theorem for a pair of self mappings satisfying a generalized contractive type condition in a complete G-metric space. We also deal with other fixed point results for a self mapping in the setting of generalized metric space. Our results generalize some recent results in the literature.

5

A fixed point theorem in generalized metric spaces

Kikina L., Kikina K.

Demonstratio Mathematica

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2013

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Vol. 46, nr 1

181--190

EN

A generalized metric space has been defined by Branciari as a metric space in which the triangle inequality is replaced by a more general inequality. Subsequently, some classical metric fixed point theorems have been transferred to such a space. In this paper, we continue in this direction and prove a version of Fisher’s fixed point theorem in generalized metric spaces.

6

Representations of reals in reverse mathematics

Hirst J. L.

Bulletin of the Polish Academy of Sciences. Mathematics

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2007

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Vol. 55, no 4

303-316

EN

Working in the framework of reverse mathematics, we consider representations of reals as rapidly converging Cauchy sequences, decimal expansions, and two sorts of Dedekind cuts. Converting single reals from one representation to another can always be carried out in RCA[sub]0. However, the conversion process is not always uniform. Converting infinite sequences of reals in some representations to other representations requires the use of WKU[sub]0 or ACA[sub]0.