On a general class of weakly Picard operators

Altun, İshak; Hançer, Hatice Aslan; Mınak, Gülhan

doi:10.18514/mmn.2015.1168

Cited by 10 publications

(6 citation statements)

References 1 publication

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“…It is well known that almost all contractive-type mappings are Picard operators on complete metric spaces. (See for more details [2][3][4][5][6]).…”

Section: Introductionmentioning

confidence: 99%

A new aspect to Picard operators with simulation functions

Olgun

Biçer²,

Alyıldız³

2016

Turk J Math

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“…It is well known that almost all contractive-type mappings are Picard operators on complete metric spaces. (See for more details [2][3][4][5][6]).…”

Section: Introductionmentioning

confidence: 99%

A new aspect to Picard operators with simulation functions

Olgun

Biçer²,

Alyıldız³

2016

Turk J Math

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“…In Theorem 4.1 (respectively in 4.3) (i). If we take α(x, y) = 1, we obtain the main results of Durmaz [16] and Altun [3].…”

Section: Fixed Point Results For Single and Multi-valued Mappingsmentioning

confidence: 59%

Best Proximity Point Results in b-Metric Space and Application to Nonlinear Fractional Differential Equation

et al. 2018

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Brinde [Approximating fixed points of weak contractions using the Picard itration, Nonlinear Anal. Forum 9 (2004), 43-53] introduced almost contraction mappings and proved Banach contraction principle for such mappings. The aim of this paper is to introduce the notion of multivalued almost Θcontraction mappings and present some best proximity point results for this new class of mappings. As applications, best proximity point and fixed point results for weak single valued Θ-contraction mappings are obtained. An example is presented to support the results presented herein. An application to a nonlinear differential equation is also provided.Mathematics Subject Classification 2010: 55M20, 47H10

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“…In the theory of fixed point literature, we can find more papers dealing with θ -contraction mappings (see [1,12]).…”

Section: Theorem 2 (Reichmentioning

confidence: 99%

Overall approach to Mizoguchi--Takahashi type fixed point results

Miknak¹,

Altun²

2016

Turk J Math

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In this work, inspired by the recent technique of Jleli and Samet, we give a new generalization of the wellknown Mizoguchi-Takahashi fixed point theorem, which is the closest answer to Reich's conjecture about the existence of fixed points of multivalued mappings on complete metric spaces. We also provide a nontrivial example showing that our result is a proper generalization of the Mizoguchi-Takahashi result.

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On a general class of weakly Picard operators

Abstract: In this paper we show that on complete metric spaces the class of weakly Picard operators contains some operators which are more general than the class of almost contractions.

Cited by 10 publications

References 1 publication

A new aspect to Picard operators with simulation functions

A new aspect to Picard operators with simulation functions

Best Proximity Point Results in b-Metric Space and Application to Nonlinear Fractional Differential Equation

Overall approach to Mizoguchi--Takahashi type fixed point results

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