Some recent research trends in fixed point theory with applications

Authors

Hasanen A. Hammad, Department of Mathematics, Unaizah College of Sciences and Arts, Qassim University, Buraydah 52571, Saudi Arabia\\ Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, EgyptFollow

Author Country (or Countries)

Egypt

Abstract

Inthisstudy,somefixed-point,coupled,tripled,andquadruplefixed-pointresultsforgeneralizedcontractivetypemappings under mild conditions in the setting of abstract spaces are obtained. Also, we established some solutions to integral equations, functional equations, functional Volterra-Fredholm integral equations, 2D Volterra integral equations, Riemann-Liouville integrals, Atangana- Baleanu integral operators, and the boundary value problem for singular coupled fractional differential equations are established. Moreover, a unique stationary distribution for the Markov process is discussed. Furthermore, a new faster iterative algorithm is created than the previous sober algorithms. The proposed algorithm is used to analyze convergence, stability, and data-dependence results. Finally, two numerical examples are also provided to highlight the behavior and effectiveness of our approach.

Digital Object Identifier (DOI)

https://dx.doi.org/10.18576/amis/180109

Recommended Citation

A. Hammad, Hasanen (2024) "Some recent research trends in fixed point theory with applications," Applied Mathematics & Information Sciences: Vol. 18: Iss. 1, Article 8.
DOI: https://dx.doi.org/10.18576/amis/180109
Available at: https://digitalcommons.aaru.edu.jo/amis/vol18/iss1/8