Fixed point theory for simulation functions in G-metric spaces: A novel approach

Narinder Kumar, Manoj Kumar, Ashish -

Abstract


In this paper, with the aid of simulation mapping 𝜂: [0,∞) × [0,∞)->ℝ, we prove some Lemmas and fixed point result for generalized 𝒵 − contraction of the mapping 𝑔: 𝑋->𝑋 satisfying the following conditions:
𝜂(𝒢(𝑔𝑥, 𝑔𝑦, 𝑔𝑧),ℳ(𝑥, 𝑦, 𝑧)) ≥ 0,
for all 𝑥, 𝑦, 𝑧 ∈ 𝑋, where
ℳ(𝑥, 𝑦, 𝑧) = max {𝒢(𝑥, 𝑔𝑦, 𝑔𝑦), 𝒢(𝑦, 𝑔𝑥, 𝑔𝑥), 𝒢(𝑦, 𝑔𝑧, 𝑔𝑧), 𝒢(𝑧, 𝑔𝑦, 𝑔𝑦), 𝒢(𝑧, 𝑔𝑥, 𝑔𝑥), 𝒢(𝑥, 𝑔𝑧, 𝑔𝑧)}. and (𝑋, 𝒢) is a 𝒢 − metric space. An example is also given to support our results.

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Published: 2022-03-30

How to Cite this Article:

Narinder Kumar, Manoj Kumar, Ashish -, Fixed point theory for simulation functions in G-metric spaces: A novel approach, Adv. Fixed Point Theory, 12 (2022), Article ID 5

Copyright © 2022 Narinder Kumar, Manoj Kumar, Ashish -. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Advances in Fixed Point Theory

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