Certain dynamic iterative scheme families and multi-valued fixed point results

Amjad Ali; Muhammad Arshad; Eskandar Emeer; Hassen Aydi; Aiman Mukheimer; Kamal Abodayeh

doi:10.3934/math.2022677

Certain dynamic iterative scheme families and multi-valued fixed point results

Amjad Ali
, Muhammad Arshad
, Eskandar Emeer
, Hassen Aydi^*
, Aiman Mukheimer
, Kamal Abodayeh

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

The article presents a systematic investigation of an extension of the developments concerning F-contraction mappings which were proposed in 2012 by Wardowski. We develop the notion of F-contractions to the case of non-linear (F, F_H )-dynamic-iterative scheme for Branciari Ćirić type-contractions and prove multi-valued fixed point results in controlled-metric spaces. An approximation of the dynamic-iterative scheme instead of the conventional Picard sequence is determined. The paper also includes a tangible example and a graphical interpretation that displays the motivation for such investigations. The work is illustrated by providing an application of the proposed non-linear (F, F_H )-dynamic-iterative scheme to the Liouville-Caputo fractional derivatives and fractional differential equations.

Original language	English
Pages (from-to)	12177-12202
Number of pages	26
Journal	AIMS Mathematics
Volume	7
Issue number	7
DOIs	https://doi.org/10.3934/math.2022677
Publication status	Published - 2022
Externally published	Yes

Keywords

(F, F )-dynamic-iterative scheme
Liouville-Caputo fractional differential equation
controlled-metric space
fixed points

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10.3934/math.2022677

Cite this

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title = "Certain dynamic iterative scheme families and multi-valued fixed point results",

abstract = "The article presents a systematic investigation of an extension of the developments concerning F-contraction mappings which were proposed in 2012 by Wardowski. We develop the notion of F-contractions to the case of non-linear (F, FH )-dynamic-iterative scheme for Branciari {\'C}iri{\'c} type-contractions and prove multi-valued fixed point results in controlled-metric spaces. An approximation of the dynamic-iterative scheme instead of the conventional Picard sequence is determined. The paper also includes a tangible example and a graphical interpretation that displays the motivation for such investigations. The work is illustrated by providing an application of the proposed non-linear (F, FH )-dynamic-iterative scheme to the Liouville-Caputo fractional derivatives and fractional differential equations.",

keywords = "(F, F )-dynamic-iterative scheme, Liouville-Caputo fractional differential equation, controlled-metric space, fixed points",

author = "Amjad Ali and Muhammad Arshad and Eskandar Emeer and Hassen Aydi and Aiman Mukheimer and Kamal Abodayeh",

note = "Publisher Copyright: {\textcopyright} 2022 Author(s), licensee AIMS Press.",

year = "2022",

doi = "10.3934/math.2022677",

language = "English",

volume = "7",

pages = "12177--12202",

journal = "AIMS Mathematics",

issn = "2473-6988",

publisher = "American Institute of Mathematical Sciences",

number = "7",

}

TY - JOUR

T1 - Certain dynamic iterative scheme families and multi-valued fixed point results

AU - Ali, Amjad

AU - Arshad, Muhammad

AU - Emeer, Eskandar

AU - Aydi, Hassen

AU - Mukheimer, Aiman

AU - Abodayeh, Kamal

PY - 2022

Y1 - 2022

N2 - The article presents a systematic investigation of an extension of the developments concerning F-contraction mappings which were proposed in 2012 by Wardowski. We develop the notion of F-contractions to the case of non-linear (F, FH )-dynamic-iterative scheme for Branciari Ćirić type-contractions and prove multi-valued fixed point results in controlled-metric spaces. An approximation of the dynamic-iterative scheme instead of the conventional Picard sequence is determined. The paper also includes a tangible example and a graphical interpretation that displays the motivation for such investigations. The work is illustrated by providing an application of the proposed non-linear (F, FH )-dynamic-iterative scheme to the Liouville-Caputo fractional derivatives and fractional differential equations.

AB - The article presents a systematic investigation of an extension of the developments concerning F-contraction mappings which were proposed in 2012 by Wardowski. We develop the notion of F-contractions to the case of non-linear (F, FH )-dynamic-iterative scheme for Branciari Ćirić type-contractions and prove multi-valued fixed point results in controlled-metric spaces. An approximation of the dynamic-iterative scheme instead of the conventional Picard sequence is determined. The paper also includes a tangible example and a graphical interpretation that displays the motivation for such investigations. The work is illustrated by providing an application of the proposed non-linear (F, FH )-dynamic-iterative scheme to the Liouville-Caputo fractional derivatives and fractional differential equations.

KW - (F, F )-dynamic-iterative scheme

KW - Liouville-Caputo fractional differential equation

KW - controlled-metric space

KW - fixed points

UR - https://www.scopus.com/pages/publications/85129426994

U2 - 10.3934/math.2022677

DO - 10.3934/math.2022677

M3 - Article

AN - SCOPUS:85129426994

SN - 2473-6988

VL - 7

SP - 12177

EP - 12202

JO - AIMS Mathematics

JF - AIMS Mathematics

IS - 7

ER -

Certain dynamic iterative scheme families and multi-valued fixed point results

Abstract

Keywords

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