Fixed points of some set-valued F-contractions

Liu, Zeqing; Xue, Na; Kwun, Young Chel; Kang, Shin Min

doi:10.22436/jnsa.009.11.08

Cited by 3 publications

(3 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Klim and Wardowski [99] extend the concept of F-contractive mappings to the case of nonlinear F-contractions and prove a fixed point theorem via dynamic processes. Fixed point results for multivalued maps on complete metric spaces without using the Hausdorff metric are presented in [100,101]. Some Wardowski-Feng-Liu type fixed point theorems for multivalued mappings in complete (ordered) metric spaces are presented in [102].…”

Section: Multivalued Mappingsmentioning

confidence: 99%

On F-Contractions: A Survey

Fabiano

Kadelburg

Mirkov

et al. 2022

Contemporary Mathematics

View full text Add to dashboard Cite

D. Wardowski proved in 2012 a generalization of Banach Contraction Principle by introducing F-contractions in metric spaces. In the next ten years, a great number of researchers used Wardowski's approach, or some of its modifications, to obtain new fixed point results for single- and multivalued mappings in various kinds of spaces. In this review article, we present a survey of these investigations, including some improvements, in particular concerning conditions imposed on function F entering the contractive condition.

show abstract

Section: Multivalued Mappingsmentioning

confidence: 99%

On F-Contractions: A Survey

Fabiano

Kadelburg

Mirkov

et al. 2022

Contemporary Mathematics

View full text Add to dashboard Cite

show abstract

“…Such a metric function is referred to as the Hausdorff-Pompeiu metric. Banach's contraction principle was extended to a multivalued function in a metric space by Nadler [10] and in a b-metric space by Czerwik [2] using the Hausdorff-Pompeiu metric H. Further generalized results of multivalued contractions can be found in ( [11][12][13][14]). Czerwik's contraction was also generalized in many directions to name a few: q-quasi-contraction [15], Hardy-Rogers contraction [16], weak quasi-contraction [17], Ciric contraction [18], etc.…”

Section: Introductionmentioning

confidence: 99%

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

Alshammari

Alrashedi

George

2022

Journal of Function Spaces

View full text Add to dashboard Cite

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.

show abstract

“…Nadler [3] extending the Banach contraction principle introduced multi-valued contraction principle in a metric space using the Hausdorff-Pompieu metric H. Thereafter many extensions and generalizations of multi-valued contraction appeared (see [4][5][6][7]). In 1998, Czerwik [8] introduced the Hausdorff-Pompeiu b-metric H b as a generalization of Hausdorff-Pompeiu metric H and proved the b-metric space version of Nadler contraction principle.…”

Section: Introductionmentioning

confidence: 99%

Some New Extensions of Multivalued Contractions in a b-metric Space and Its Applications

George

Pathak

2020

Mathematics

View full text Add to dashboard Cite

The Hβ-Hausdorff–Pompeiu b-metric for β∈[0,1] is introduced as a new variant of the Hausdorff–Pompeiu b-metric H. Various types of multi-valued Hβ-contractions are introduced and fixed point theorems are proved for such contractions in a b-metric space. The multi-valued Nadler contraction, Czervik contraction, q-quasi contraction, Hardy Rogers contraction, weak quasi contraction and Ciric contraction existing in literature are all one or the other type of multi-valued Hβ-contraction but the converse is not necessarily true. Proper examples are given in support of our claim. As applications of our results, we have proved the existence of a unique multi-valued fractal of an iterated multifunction system defined on a b-metric space and an existence theorem of Filippov type for an integral inclusion problem by introducing a generalized norm on the space of selections of the multifunction.

show abstract

Fixed points of some set-valued F-contractions

Abstract: Fixed point theorems of several set-valued F -contractions without using the Hausdorff metric are provided. Our results extend substantially the results due

Cited by 3 publications

References 8 publications

On F-Contractions: A Survey

On F-Contractions: A Survey

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

Some New Extensions of Multivalued Contractions in a b-metric Space and Its Applications

Contact Info

Product

Resources

About

Fixed points of some set-valued F-contractions

Abstract: Fixed point theorems of several set-valued F -contractions without using the Hausdorff metric are provided. Our results extend substantially the results due

Cited by 3 publications

References 8 publications

On F-Contractions: A Survey

On F-Contractions: A Survey

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

Some New Extensions of Multivalued Contractions in a b-metric Space and Its Applications

Contact Info

Product

Resources

About

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