Coincidence Point Theorems on Odered 𝑏-Metric Spaces via 𝑤𝑡-Distance with Application to Matrix Equations and Numerical Experiments

Article Sidebar

PDF
Published: Dec 26, 2024
Keywords:
𝑏-metric spaces coincidence point Extended simulation function Matrix equations 𝑤𝑡-distance

Main Article Content

Tippawan Puttasontiphot
Department of Computational Science and Digital Technology, Faculty of Liberal Arts and Sciences, Kasetsart University, Nakhon Pathom 73140, Thailand
Sujitra Sanhan
Department of Computational Science and Digital Technology, Faculty of Liberal Arts and Sciences, Kasetsart University, Nakhon Pathom 73140, Thailand
Chirasak Mongkolkeha
Department of Computational Science and Digital Technology, Faculty of Liberal Arts and Sciences, Kasetsart University, Nakhon Pathom 73140, Thailand

Abstract

This article aims to create a new type of generalized contraction mapping to modify the concept of an 𝑒𝐾 -simulation function which is defined by Yamaod and Sintunavarat [2019, J. Nonlinear Convex Anal.], we investigate the existence and uniqueness of a point of coincidence in the mapping with respect to a 𝑤𝑡- distance in a partially ordered 𝑏-metric space which extends the results of Roldán López de Hierro et al. [2015, J. Comput. Appl. Math.]. Furthermore, we prove the existence of Hermitian positive definite solutions of nonlinear matrix equations with some examples and numerical experiments.

Article Details

How to Cite
Tippawan Puttasontiphot, Sujitra Sanhan, & Chirasak Mongkolkeha. (2024). Coincidence Point Theorems on Odered 𝑏-Metric Spaces via 𝑤𝑡-Distance with Application to Matrix Equations and Numerical Experiments. Science & Technology Asia, 29(4), 14–31. retrieved from https://ph02.tci-thaijo.org/index.php/SciTechAsia/article/view/250097
Issue
Vol.29 No.4 (October-December 2024)
Section
Physical sciences
Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

References

Berinde V. Generalized contractions in quasimetric spaces. Seminar on Fixed Point Theory. 1993;3-9.

Mongkolkeha C., Cho Y.J. Kumam P. Fixed point theorems for simulation functions in b-metric spaces via the wt-distance. Applied General Topology. 2017;18(1):91-105.

Mongkolkeha C. Gopal D. Some Common Fixed Point Theorems for Generalized F-Contraction Involving w-Distance with Some Applications to Differential Equations. Mathematics. 2019;7(1):32.

Czerwik S. Contraction mappings in 𝑏-metric space. Acta Math. Inform. Univ. Ostrav. 1993;1:5-11.

Czerwik S. Nonlinear set-valued contraction mappings in 𝑏-metric spaces. Atti Semin. Mat. Fis. Univ. Modena. 1998;46:263-76.

Darko K., Lakzian H., Rakocevic V. Ciric’s and Fisher’s quasi-contractions in the framework of wt-distance. Rendiconti del Circolo Matematico di Palermo Series 2. 2023;72:377-91.

Ghosh S.K., Nahak C. An extension of Lakzian-Rhoades results in the structure of ordered b-metric spaces via wt-distance with an application. Applied Mathematics and Computation. 2020;378:125197.

Hussain N., Saadati R., Agrawal R.P. On the topology and wt-distance onmetric type spaces. Fixed Point Theory and Applications. 2014;88.

Heinonen J. Lectures on Analysis on Metric Spaces. Springer Berlin. 2001.

Hossein L., Rhoades B.E. Some fixed point theorems using weaker MeirKeeler function in metric spaces with w-distance. Applied Mathematics and Computation. 2019;342:18-25.

Liu Z., Lu Y., Kang S.M. Fixed point theorems for multi-valued contractions with w-distance. Applied Mathematics and Computation. 2013;224:535-52.

Kada O., Suzuki T., Takahashi W. Nonconvex minimization theorems and fixed point theorems in complete metric spaces. Math. Japonica. 1996;44:381-91.

Khojasteh F., Shukla S., Radenovic S. A New Approach to the Study of Fixed Point Theory for Simulation Functions. Filomat. 2015;29:6:1189-94.

Ran A.C.M., Reurings M.C.B. A fixed point theorem in partially ordered sets and some applications to matrix equations. Proc. Amer. Math. Soc. 2003;132:1435-43.

Roldán-López-de-Hierro A., Karapinar E., Roldán-López-de-Hierro d C., Martínez-Moreno J. Coincidence point theorems on metric spaces via simulation functions. J. Comput. Appl.Math. 2015;275:345-55.

Roldán López de Hierro A. F., Samet B. 𝜑-admissibility results via extended simulation functions. J. Fixed Point Theory Appl. 2017;19:1997-2015.

Demma M., Saadati R., Vetro P. Multivalued operators with respect wt-distance on metric type spaces. Bull Iranian Math Soc. 2016;42(6):1571-82.

Suzuki T. Generalized Distance and Existence Theorems in Complete Metric Spaces. 2001;253(2):440-58.

Takahashi W. Nonlinear Functional Analysis ”Fixed Point Theory and its Applications”. Yoka-hama Publishers, Yokahama, Japan. 2000.

Yamaod O., Sintunavarat W. An approach to the existence and uniqueness of fixed point results in 𝑏-metric spaces via 𝑠- simulation functions.J. Fixed Point Theory Appl. 2017;19:2819-30.

Yamaod O., Sintunavarat W. On new homotopy results via a generalized extended simulation function in b-metric spaces. J. Nonlinear Convex Anal. 2019;20(10):2225-38.