New Types of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>F</mml:mi><mml:mo>-</mml:mo></mml:math>Contraction for Multivalued Mappings and Related Fixed Point Results in Abstract Spaces

Alshoraify, Shaif Saleh; Shoaib, Abdullah; Arshad, Muhammad

doi:10.1155/2019/1812461

Cited by 6 publications

(6 citation statements)

References 32 publications

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“…In this section, motivated by the applications given in [28][29][30] and [31], we establish the sufficient conditions for the existence of a common solution of a pair of nonlinear Volterra-type integral equations.…”

Section: Application To the Integral Equationmentioning

confidence: 99%

“…Remark 29. Taking Qðt, sÞ = 0, P ðt, sÞ = 1, qðtÞ = 0, μðtÞ = t and a = 0 in (64), we get the Volterra-type integral equations considered in Rasham et al [31] and Alshoraify et al [30].…”

Section: Conflicts Of Interestmentioning

confidence: 99%

“…Applications of fixed-point results in dealing with solutions of nonlinear problems arising in engineering and science are an important area in present-day research. Fruitful applications of fixed-point problems in solution of various types of integral equations, fractional differential equations, and optimization problems can be found in [28][29][30][31][32]. Barnsley [33] introduced the idea of data interpolation using the fractal methodology of iterated function systems.…”

Section: Introductionmentioning

confidence: 99%

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$H^{β}$ -Hausdorff Functions and Common Fixed Points of Multivalued Operators in a $b$

Alshammari

Alrashedi

George

2022

Journal of Function Spaces

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H β -Hausdorff functions for β ∈ 0 , 1 are introduced, and common fixed-point theorems for a pair of multivalued operators satisfying generalized contraction conditions are proven in a b -metric space. Our results are proper extensions and new variants of many contraction conditions existing in literature. In order to demonstrate applications of our result, we have proven an existence theorem for a unique common multivalued fractal of a pair of iterated multifunction systems and also an existence theorem for a common solution of a pair of Volterra-type integral equations.

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Section: Application To the Integral Equationmentioning

confidence: 99%

Section: Conflicts Of Interestmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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$H^{β}$ -Hausdorff Functions and Common Fixed Points of Multivalued Operators in a $b$

Alshammari

Alrashedi

George

2022

Journal of Function Spaces

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“…e commutativity condition does not hold in general in quasi-metric spaces. Several authors used this concept to prove some fixed point results, see [6][7][8][9][10][11][12][13][14][15][16][17][18]. On the other hand, Bakhtin [19] and Czerwik [20] established the idea of b-metric spaces.…”

Section: Introductionmentioning

confidence: 99%

Double Controlled Quasi-Metric Type Spaces and Some Results

et al. 2020

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Abdeljawad et al. (2018) introduced a new concept, named double controlled metric type spaces, as a generalization of the notion of extended b-metric spaces. In this paper, we extend their concept and introduce the concept of double controlled quasi-metric type spaces with two incomparable functions and prove some unique fixed point results involving new types of contraction conditions. Also, we introduce the concept of α−μ−k double controlled contraction and prove some related fixed point results. We give several examples to show that our results are the proper generalization of the existing works.

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“…Dislocated quasi-metric also generalizes dislocated metric, partial metric, and quasi-metric. Fixed point results in dislocated quasi-metric space can be seen in [18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Double Controlled Dislocated Quasi-Metric Type Spaces and Some Results

Shoaib

Alshoraify

Arshad

2020

Journal of Mathematics

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The aim of this work is to introduce double controlled dislocated quasi-metric type spaces and to obtain fixed point results for a pair of multivalued mappings satisfying Kannan-type double controlled contraction in such spaces. An example has been built and a remark has been given which shows that how our result can be used when a corresponding new result in dislocated quasi b-metric type spaces cannot be used. Our results generalize and extend many existing results in the literature.

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New Types of F-Contraction for Multivalued Mappings and Related Fixed Point Results in Abstract Spaces

Cited by 6 publications

References 32 publications

$H^{β}$ -Hausdorff Functions and Common Fixed Points of Multivalued Operators in a $b$

$H^{β}$ -Hausdorff Functions and Common Fixed Points of Multivalued Operators in a $b$

Double Controlled Quasi-Metric Type Spaces and Some Results

Double Controlled Dislocated Quasi-Metric Type Spaces and Some Results

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New Types of F-Contraction for Multivalued Mappings and Related Fixed Point Results in Abstract Spaces

Cited by 6 publications

References 32 publications

H β -Hausdorff Functions and Common Fixed Points of Multivalued Operators in a b

H β -Hausdorff Functions and Common Fixed Points of Multivalued Operators in a b

Double Controlled Quasi-Metric Type Spaces and Some Results

Double Controlled Dislocated Quasi-Metric Type Spaces and Some Results

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Product

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$H^{β}$ -Hausdorff Functions and Common Fixed Points of Multivalued Operators in a $b$

$H^{β}$ -Hausdorff Functions and Common Fixed Points of Multivalued Operators in a $b$