Some fixed point theorems for nonself generalized contraction

Rus, İoan A.; Şerban, Marcel-Adrian

doi:10.18514/mmn.2017.1186

Cited by 11 publications

(17 citation statements)

References 9 publications

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“…Rus and M.-A. Şerban [22], M.-A. Şerban [23], we shall analyze the results of this type in connection with Conti's remark and we shall present new fixed point results for non-self mappings.…”

Section: Adrian Petruşel Radu Precup and Marcel-adrian şErbanmentioning

confidence: 99%

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On the approximation of fixed points for non-self mappings on metric spaces

Petruşel¹,

Precup²,

Şerban³

2020

Discrete &Amp; Continuous Dynamical Systems - B

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Starting from some classical results of R. Conti, A. Haimovici and K. Iseki, and from a more recent result of S. Reich and A.J. Zaslavski, we present several theorems of approximation of the fixed points for non-self mappings on metric spaces. Both metric and topological conditions are involved. Some of the results are generalized to the multi-valued case. An application is given to a class of implicit first-order differential systems leading to a fixed point problem for the sum of a completely continuous operator and a nonexpansive mapping.

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Section: Adrian Petruşel Radu Precup and Marcel-adrian şErbanmentioning

confidence: 99%

“…for any countable bounded set M ⊂ Y, where ϕ is a comparison function (see [22]). Indeed, since ϕ n (t) → 0 as n → ∞, for all t > 0, one has that ϕ (t) < t for all t > 0.…”

Section: Adrian Petruşel Radu Precup and Marcel-adrian şErbanmentioning

confidence: 99%

On the approximation of fixed points for non-self mappings on metric spaces

Petruşel¹,

Precup²,

Şerban³

2020

Discrete &Amp; Continuous Dynamical Systems - B

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“…For more considerations on data dependence problem, see also [5], [14], [21], [24], [53], [60], [62], [70],...…”

Section: Data Dependencementioning

confidence: 99%

“…• Problem 1.1: [11], [52], [25], [5], [23], [29], [42], [47], [58], [70], [71], [16], [17], [21], [26], [31], [37], [40], [49], [60], [4], [6], [7], [8], [9], . .…”

Section: Introductionmentioning

confidence: 99%

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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“…There are several techniques in the fixed point theory for nonself operators on a complete metric space ( [7], [19], [13], [16], [15], [3], [9], [20], . .…”

Section: Introductionmentioning

confidence: 99%

2022/07/26 "Fixed point theorems for nonself generalized contractions on a large Kasahara space"

Filip¹

2022

CJM

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In this paper we give some fixed point theorems for nonself generalized contractions on a large Kasahara space, which generalize some results given by I.A. Rus and M.-A. \c Serban (I. A. Rus, M.-A. \c Serban, {\it Some fixed point theorems for nonself generalized contractions}, Miskolc Math. Notes, {\bf 17}(2016), no.2, 1021-1031) and by S. Reich and A.J. Zaslavski (S. Reich, A. J. Zaslavski, {\it A note on Rakotch contractions}, Fixed Point Theory, {\bf 9} (2008), no. 1, 267-273) in complete metric spaces. We prove our results without using the completeness of the metric structure.

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Some fixed point theorems for nonself generalized contraction

Abstract: In this paper we give a new proof of a result by S. Reich and A.J. Zaslavski (S. Reich and A.J. Zaslavski, A fixed point theorem for Matkowski contractions, Fixed Point Theory, 8(2007), No. 2, 303-307). Some new fixed point theorems for nonself generalized contractions are also given.

Cited by 11 publications

References 9 publications

On the approximation of fixed points for non-self mappings on metric spaces

On the approximation of fixed points for non-self mappings on metric spaces

Saturated contraction principles for non self operators, generalizations and applications

2022/07/26 "Fixed point theorems for nonself generalized contractions on a large Kasahara space"

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