Caristi-Browder Operator Theory in Distance Spaces

Berinde, Vasile; Rus, İoan A.

doi:10.1016/b978-0-12-804295-3.50001-2

Cited by 2 publications

(2 citation statements)

References 105 publications

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“…This implies that f : (X, d s p ) → (X, d s p ) is a ψ-Caristi-Browder operator, with ψ : X → R + , ψ(x) = 2ϕ(x) − p(x, x). From the Caristi-Browder theorem (see [6]) in (X, d s p ), we have that F f = ∅ and f is a weakly Picard operator with respect to d s p →.…”

Section: From a Partial Metric Space To A Metric Spacementioning

confidence: 99%

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Conversions between generalized metric spaces and standard metric spaces with applications in fixed point theory

Filip

2021

CJM

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In this paper we discuss similar problems posed by I. A. Rus in Fixed point theory in partial metric spaces (Analele Univ. de Vest Timişoara, Mat.-Inform., 46 (2008), 149–160) and in Kasahara spaces (Sci. Math. Jpn., 72 (2010), No. 1, 101–110). We start our considerations with an overview of generalized metric spaces with \mathbb{R}_+-valued distance and of generalized contractions on such spaces. After that we give some examples of conversions between generalized metric spaces and standard metric spaces with applications in fixed point theory. Some possible applications to theoretical informatics are also considered.

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Section: From a Partial Metric Space To A Metric Spacementioning

confidence: 99%

“…If ϕ is lower semi-continuous, then the ϕ-Caristi operator f is called a ϕ-Caristi-Kirk operator and if f is a ϕ-Caristi operator with f continuous with respect to the metric d s p , then f is called a ϕ-Caristi-Browder operator (see [6]).…”

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Conversions between generalized metric spaces and standard metric spaces with applications in fixed point theory

Filip

2021

CJM

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Saturated contraction principles for non self operators, generalizations and applications

Berinde

Maruster

Rus

2017

Filomat

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Let (X, d) be a metric space, Y ⊂ X a nonempty closed subset of X and let f : Y → X be a non self operator. In this paper we study the following problem: under which conditions on f we have all of the following assertions: 1. The operator f has a unique fixed point; 2. The operator f satisfies a retraction-displacement condition; 3. The fixed point problem for f is well posed; 4. The operator f has the Ostrowski property. Some applications and open problems related to these questions are also presented.

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Caristi-Browder Operator Theory in Distance Spaces

Cited by 2 publications

References 105 publications

Conversions between generalized metric spaces and standard metric spaces with applications in fixed point theory

Conversions between generalized metric spaces and standard metric spaces with applications in fixed point theory

Saturated contraction principles for non self operators, generalizations and applications

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