In this article, first we introduce new notions of a contractive mapping and establish some fixed point theorems for the contractive mapping in the setting of LG-complete LG-metric spaces. Further, we establish a new criterion between weakly regular cone and normal cone, and we also obtain a fixed point result in the same LG-complete LG-metric spaces by making use of analysis technique. Later, we give some examples to illustrate the valid of our main results.

weakly regular cone, fixed point, contractive mappings, existence.

Received: September 29, 2022; Revised: October 19, 2022; Accepted: November 21, 2022; Published: April 14, 2023

How to cite this article: Yan Sun and Ravi P. Agarwal, Existence of fixed point for nonlinear operator in partially ordered metric spaces, Advances in Differential Equations and Control Processes 30(2) (2023), 97-116. http://dx.doi.org/10.17654/0974324323007

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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