Certain dynamic iterative scheme families and multi-valued fixed point results-Reference-Cited by-同舟云学术

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

Published:2022 Issue:7 Volume:7 Page:12177-12202
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Ali Amjad¹,Arshad Muhammad¹,Emeer Eskandar²,Aydi Hassen³⁴⁵,Mukheimer Aiman⁶,Abodayeh Kamal⁶

Affiliation:

1. Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan

2. Department of Mathematics, Taiz University, Taiz, Yemen

3. Université de Sousse, Institut Supérieur d'Informatique et des Techniques de Communication, H. Sousse 4000, Tunisia

4. China Medical University Hospital, China Medical University, Taichung 40402, Taiwan

5. Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa

6. Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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