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Some common fixed point theorems for selfmappings satisfying two contractive conditions of integral type in a uniform space

100%

Olatinwo M.

Open Mathematics

2008

tom 6

nr 2

335-341

In this paper, we establish some common fixed point theorems for selfmappings of a uniform space by employing both the concepts of an A-distance and an E-distance introduced by Aamri and El Moutawakil [1] and two contractive conditions of integral type. Our results are generalizations and extensions of the classical Banach’s fixed point theorem of [2, 3, 19], some results of Aamri and El Moutawakil [1], Theorem 2.1 of Branciari [5] as well as a result of Jungck [7].

Uniform Space

75%

Coghetto R.

Formalized Mathematics

2016

tom 24

nr 3

215-226

In this article, we formalize in Mizar [1] the notion of uniform space introduced by André Weil using the concepts of entourages [2]. We present some results between uniform space and pseudo metric space. We introduce the concepts of left-uniformity and right-uniformity of a topological group. Next, we define the concept of the partition topology. Following the Vlach’s works [11, 10], we define the semi-uniform space induced by a tolerance and the uniform space induced by an equivalence relation. Finally, using mostly Gehrke, Grigorieff and Pin [4] works, a Pervin uniform space defined from the sets of the form ((X\A) × (X\A)) ∪ (A×A) is presented.

Ograniczanie wyników

1 Formalized Mathematics

1 Open Mathematics

1 Coghetto R.

1 Olatinwo M.

1 2016

1 2008

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Some common fixed point theorems for selfmappings satisfying two contractive conditions of integral type in a uniform space

Uniform Space