Integral Methods in Science and Engineering pp 437-450 | Cite as

# Existence of Nonlinear Problems: An Applicative and Computational Approach

## Abstract

In this paper, we initiate the variants of (*F*, *ψ*)-rational type contractions and prove some fixed point results for such mappings in a complete metric space endowed with partial order. Some examples are given to illustrate the usability of the established concept. Application to integral equation is given to highlight the usability of the obtained results. We explain an illustrative example with computer simulation to validate the application of our result to integral equation, which includes some surfaces demonstrating the justification of approximate solution of the integral equation along with error function. With this execution, we provide an access to the theory of fixed point with some relevant and innovative applications.

## References

- [Ag08]Agarwal, R.P., EI-Gebeily, M.A. and OŔegan, D. : Generalized contractions in partially ordered metric spaces.
*Appl. Anal.*,**87**, 1–8(2008).MathSciNetCrossRefGoogle Scholar - [Al10]Altun, I. and Simsek, H. : Some fixed point theorems on ordered metric spaces and application.
*Fixed Point Theory Appl.*,**2010**, Article ID 621492(2010).Google Scholar - [Jl16]Jleli, M. and Samet, B. : A fixed point problem under two constraint inequalities.
*Fixed Point Theory Appl.*,**2016**, 18(2016).Google Scholar - [La09]Lakshmikantham, V. and Ciric, L. : Coupled foxed point theorems for nonlinear contractions in partially ordered metric spaces.
*Nonlinear Anal.,***70**136, 4341–4349(2009).MathSciNetCrossRefGoogle Scholar - [Pi14]Piri, H. and Kumam, P. : Some fixed point theorems concerning
*F*-contraction in complete metric spaces.*Fixed Point Theory and Appl.*,**2014**, 210(2014).Google Scholar - [RaEtAl04]Ran, A.C.M. and Reurings, M.C.B. : A fixed point theorem in partially ordered sets and some applications to matrix equations.
*Proc. Am. Math. Soc.*,**132**, 1435–1443(2004).MathSciNetCrossRefGoogle Scholar - [Se13]Secelean, N.A. : Iterated function system consisting of
*F*-contractions.*Fixed Point Theory and Appl.,***2013**, https://doi.org/10.1166/1687-1812-2013-277, 277(2013). - [Wa12]Wardowski, D. : Fixed points of a new type of contractive mappings in complete metric spaces.
*Fixed Point Theory and Appl.*,**2012**, 94(2012).Google Scholar