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Advances in Fixed Point Theory ISSN 1927-6303 (Print)

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Adv. Fixed Point Theory 12 (2022), Article ID 5

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

Narinder Kumar, Manoj Kumar, Ashish -

PDF (225.5 KB) https://doi.org/10.28919/afpt/7256

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.

Published
30 March 2022
Volume
12 (2022)
License
CC BY 3.0

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.

Cite this article

N. Kumar, M. Kumar, A. -, Fixed point theory for simulation functions in G-metric spaces: A novel approach, Adv. Fixed Point Theory 12 (2022), 5. https://doi.org/10.28919/afpt/7256

BibTeX
@article{Kumar2022,
  author  = {Kumar, Narinder and Kumar, Manoj and -, Ashish},
  title   = {Fixed point theory for simulation functions in G-metric spaces: A novel approach},
  journal = {Adv. Fixed Point Theory},
  volume  = {12},
  year    = {2022},
  pages   = {5},
  doi     = {10.28919/afpt/7256}
}