10.57647/cna.2025.sxwx-8yah.7

Common Fixed Point Theorem of Brancieri’s IntegralType in Quasi b-Metric Space

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  • Mujeeb Ur Rahman1,
  • Abid Ullah Khan2,
  • Asif Khan*2,
  1. Department of Mathematics, Government PG Jahanzeb College, Saidu Sharief Swat, Khyber Pakhtunkhwa, Pakistan
  2. Department of Mathematics, University of Malakand, Chakdara, Dir Lower, Khyber Pakhtunkhwa, Pakistan

Received: 2025-02-12

Revised: 2025-03-25

Accepted: 2025-04-15

Published in Issue 2025-06-30

Copyright (c) 2025 Mujeeb Ur Rahman, Abid Ullah Khan, Asif Khan (Author)

Creative Commons License

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

How to Cite

Common Fixed Point Theorem of Brancieri’s IntegralType in Quasi b-Metric Space. (2025). Communications in Nonlinear Analysis, 13(1). https://doi.org/10.57647/cna.2025.sxwx-8yah.7

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Abstract

Let $P(z)= \sum_{j=0}^{n}a_{j}{z}^{j}\in \mathcal{P}_{n}$, with $P(z)$ not vanishing in $|z|<1$. In this paper, we investigate a common fixed point theorem for a pair of continuous self-mappings satisfying integral-type contractions in the setting of a \dqbm\ space. The established theorem extends and generalizes several well-known results in the literature. Moreover, the constructed result can be extensively applied in the fields of integral equations and ordinary differential equations. An example is provided to support the established result.

Keywords

  • Complete dislocated quasi b-metric space,
  • Cauchy sequence,
  • Self-mapping,
  • Contraction,
  • Common fixed point
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