α-ψ-contractive type mappings on quasi-metric spaces

Romaguera, Salvador; Tirado, Pedro

doi:10.2298/fil2105649r

Cited by 5 publications

(1 citation statement)

References 14 publications

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“…Partly stimulated by these developments, the research about the fixed point theory on quasi-metric spaces has received a powerful boost in the last 12 years, during which many papers have been published in this area, so we will limit ourselves here to citing some of the most recent ones [15][16][17][18][19][20][21][22] with the references therein.…”

Section: Introductionmentioning

confidence: 99%

Basic Contractions of Suzuki-Type on Quasi-Metric Spaces and Fixed Point Results

Romaguera

2022

Mathematics

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This paper deals with the question of achieving a suitable extension of the notion of Suzuki-type contraction to the framework of quasi-metric spaces, which allows us to obtain reasonable fixed point theorems in the quasi-metric context. This question has no an easy answer; in fact, we here present an example of a self map of Smyth complete quasi-metric space (a very strong kind of quasi-metric completeness) that fulfills a simple and natural contraction of Suzuki-type but does not have fixed points. Despite it, we implement an approach to obtain two fixed point results, whose validity is supported with several examples. Finally, we present a general method to construct non-T1 quasi-metric spaces in such a way that it is possible to systematically generate non-Banach contractions which are of Suzuki-type. Thus, we can apply our results to deduce the existence and uniqueness of solution for some kinds of functional equations which is exemplified with a distinguished case.

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Section: Introductionmentioning

confidence: 99%

Basic Contractions of Suzuki-Type on Quasi-Metric Spaces and Fixed Point Results

Romaguera

2022

Mathematics

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Rings of quotients of the ring consisting of ordered field valued continuous functions with countable range

Veisi

2022

Filomat

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For a zero-dimensional topological space X and a totally ordered field F with interval topology, Cc(X, F) denotes the ring consisting of ordered field-valued continuous functions with countable range on X. This article aims to study and investigate the rings of quotients of Cc(X,F). Qc(X,F) (resp. qc(X,F)), the maximal (resp. classical) ring of quotients of Cc(X,F) as a modified countable analogue of Q(X) (resp. q(X)), the maximal (resp. classical) ring of quotients of C(X) are characterized. It is proved that Qc(S), the maximal ring of quotients of the subring S of Cc(X,F), is a subring of Qc(X, F) if and only if every dense ideal in S has dense cozero-set in X. Also, the coincidence of rings of quotients of Cc(X, F) is investigated. We show that qc(X,F)=Cc(X, F) if and only if the set of non-units and zero-divisors in Cc(X,F) coincide if and only if X is almost CPF-space. Finally, it is shown that the fixed ring of quotients and the cofinite ring of quotients of Cc(X) coincide if and only if Hom(Mcp) = Cc(Xp) for every p ? X.

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The structure of F2 as an associative algebra via quadratic forms

Veisi,

Delbaznasab

2023

Filomat

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Let F be a totally ordered field and ? ? F (a field extension of F) be a solution to the equation x2 = ax + b ? F[x], where a and b are fixed with b ? 0. With the help of this idea, we convert the F-vector space F2 into an associative F-algebra. As far as F2 can even be converted into a field. In the next step, based on a quadratic form, we define an inner product on F2 with values in F and call it the F-inner product. The defined inner product is mostly studied for its various properties. In particular, when F = R, we show that R2 with the defined product satisfies well-known inequalities such as the Cauchy-Schwarz and the triangle inequality. Under certain conditions, the reverse of recent inequalities is established. Some interesting properties of quadratic forms on F2 such as the invariant property are presented. In the sequel, we let SL(2,R) denote the subgroup of M(2,R) that consists of matrices with determinant 1 and set G = SL(2,R) ?MR, where MR is the matrix representation of R2. We then verify the coset space SL(2,R)/G with the quotient topology is homeomorphic to H (the upper-half complex plane) with the usual topology. Finally, we determine some families of functions in C(H,C), the ring consisting of complex-valued continuous functions onH; related to elements of G for which the functional equation f ?1 = 1? f is satisfied.

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α-ψ-contractive type mappings on quasi-metric spaces

Cited by 5 publications

References 14 publications

Basic Contractions of Suzuki-Type on Quasi-Metric Spaces and Fixed Point Results

Basic Contractions of Suzuki-Type on Quasi-Metric Spaces and Fixed Point Results

Rings of quotients of the ring consisting of ordered field valued continuous functions with countable range

The structure of F2 as an associative algebra via quadratic forms

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