Suzuki type fixed point theorems for generalized multi-valued mappings on a set endowed with two b-metrics

Ćirić, Łjubomir; Abbas, Mujahid; Rajović, Miloje; Ali, Basit

doi:10.1016/j.amc.2012.08.011

Cited by 15 publications

(8 citation statements)

References 14 publications

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“…The concept of a b-metric space was introduced by Czerwik in [11]. Since then, several papers have been published on the fixed point theory of various classes of single-valued and multi-valued operators in b-metric space [3,6,7,8,9,10,11,12,13,24,29].…”

Section: Introductionmentioning

confidence: 99%

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Fractals of GeneralizedF-Hutchinson Operator inb-Metric Spaces

Nazır

Silvestrov

2016

Journal of Operators

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The aim of this paper is to construct a fractal with the help of a finite family of generalized F -contraction mappings, a class of mappings more general than contraction mappings, defined in the setup of b-metric space. Consequently, we obtain a variety of results for iterated function system satisfying a different set of contractive conditions. Our results unify, generalize and extend various results in the existing literature.---------------

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Section: Introductionmentioning

confidence: 99%

“…If b = 1, then b-metric space is a metric spaces. But the converse does not hold in general [3,9,11].…”

Section: Introductionmentioning

confidence: 99%

Fractals of GeneralizedF-Hutchinson Operator inb-Metric Spaces

Nazır

Silvestrov

2016

Journal of Operators

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“…Note that there are fixed point theorems (see [7]) that cannot be transported from metric to b∽MSs as in the case of BCP.…”

Section: Lemma 3 (Seementioning

confidence: 99%

“…A bifunction ρ: Z × Z ⟶ R + is a b ∼ metric on Z if there exists a κ ∈ R with κ ≥ 1 such that for u, y, z in Z, ρ satisfies (i) a 1 − ρ(u, y) � 0 if u � y (ii) a 2 − ρ(u, y) � ρ(y, u) (iii) a 3 − ρ(u, y) ≤ κρ(u, z) + κρ(z, y) e pair (Z, ρ) is known as b ∼ metric space (s) (shortly as b ∼ MS (s)) with b-metric constant κ. Clearly, for κ � 1, (Z, ρ) is a metric space, but there are b ∼ metrics that are not metrics (see [4,7,8]).…”

Section: Introductionmentioning

confidence: 99%

Completeness of b∼Metric Spaces and the Fixed Points of Generalized Multivalued Quasicontractions

Ali

Abbas

Sen

2020

Discrete Dynamics in Nature and Society

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In this article, we present a completeness characterization of b∼metric space via existence of fixed points of generalized multivalued quasicontractions. The purpose of this paper is twofold: (a) to establish the existence of fixed points of multivalued quasicontractions in the setup of b∼ metric spaces and (b) to establish completeness of a b∼ metric space which is a topological property in nature with existence of fixed points of generalized multivalued quasicontractions. Further, a comparison of our results with comparable results shows that the results obtained herein improve and unify the existing results in the literature applicable to the case where existing results fail.

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“…R + is said to be a b-metric if for any x; y; z 2 X; the following conditions hold: If b = 1; then b-metric space is a metric space. However, the converse does not hold in general ( compare [2,Example 3.9] and [8,9,20] ).…”

Section: Introductionmentioning

confidence: 99%

Existence and Ulam–Hyers stability of fixed point problem of generalized Suzuki type $$( \alpha _{*}{,\psi }_{\varphi })$$ ( α ∗ , ψ φ ) -contractive multivalued operators

Ali

Abbas

2016

RACSAM

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The aim of this paper is to introduce a class of generalized Suzuki type (; ') contractive multivalued operators and to prove the existence of …xed point and common …xed point of such operators in the setup of b-metric spaces. Some examples are presented to support the results proved herein. Our results generalize and extend various results in the existing literature. An estimate of Hausdor¤ distance between the …xed point sets of two generalized Suzuki type (; ') contractive multivalued operators is obtained. We further investigate the Ulam-Hyers stability of …xed point problem of operators considered herein in the framework of b-metric spaces.

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Suzuki type fixed point theorems for generalized multi-valued mappings on a set endowed with two b-metrics

Cited by 15 publications

References 14 publications

Fractals of GeneralizedF-Hutchinson Operator inb-Metric Spaces

Fractals of GeneralizedF-Hutchinson Operator inb-Metric Spaces

Completeness of b∼Metric Spaces and the Fixed Points of Generalized Multivalued Quasicontractions

Existence and Ulam–Hyers stability of fixed point problem of generalized Suzuki type $$( \alpha _{*}{,\psi }_{\varphi })$$ ( α ∗ , ψ φ ) -contractive multivalued operators

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