Common solutions to some extended system of fuzzy ordered variational inclusions and fixed point problems

Iqbal Ahmad; Mohd Sarfaraz; Syed Shakaib Irfan; Iqbal Ahmad; Mohd Sarfaraz; Syed Shakaib Irfan

doi:10.3934/math.2023919

AIMS Mathematics

2023, Volume 8, Issue 8: 18088-18110. doi: 10.3934/math.2023919

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Research article

Common solutions to some extended system of fuzzy ordered variational inclusions and fixed point problems

1.
Department of Mechanical Engineering, College of Engineering, Qassim University, P.O. Box 6677, Buraidah 51452, Al-Qassim, Saudi Arabia
2.
Department of Mathematics, Jaypee Institue of Information Technology, Noida, India
3.
Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India

Received: 22 November 2022 Revised: 08 April 2023 Accepted: 27 April 2023 Published: 25 May 2023
MSC : 47H09, 49J40

The main aim of this work is to use the XOR-operation technique to find the common solutions for a new class of extended system of fuzzy ordered variational inclusions with its corresponding system of fuzzy ordered resolvent equations involving the $ \oplus $ operation and fixed point problems, which are slightly different from corresponding problems considered in several recent papers in the literature and are more advantageous. We establish that the system of fuzzy ordered variational inclusions is equivalent to a fixed point problem and a relationship between a system of fuzzy ordered variational inclusions and a system of fuzzy ordered resolvent equations is shown. We prove the existence of a common solution and discuss the convergence of the sequence of iterates generated by the algorithm for a considered problem. The iterative algorithm and results demonstrated in this article have witnessed, a significant improvement for many previously known results of this domain. Some examples are constructed in support of the main results.
- algorithm,
- fuzzy inference,
- iterative methods,
- nonlinear system,
- resolvent operator,
- sequence analysis
Citation: Iqbal Ahmad, Mohd Sarfaraz, Syed Shakaib Irfan. Common solutions to some extended system of fuzzy ordered variational inclusions and fixed point problems[J]. AIMS Mathematics, 2023, 8(8): 18088-18110. doi: 10.3934/math.2023919

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Abstract

The main aim of this work is to use the XOR-operation technique to find the common solutions for a new class of extended system of fuzzy ordered variational inclusions with its corresponding system of fuzzy ordered resolvent equations involving the $ \oplus $ operation and fixed point problems, which are slightly different from corresponding problems considered in several recent papers in the literature and are more advantageous. We establish that the system of fuzzy ordered variational inclusions is equivalent to a fixed point problem and a relationship between a system of fuzzy ordered variational inclusions and a system of fuzzy ordered resolvent equations is shown. We prove the existence of a common solution and discuss the convergence of the sequence of iterates generated by the algorithm for a considered problem. The iterative algorithm and results demonstrated in this article have witnessed, a significant improvement for many previously known results of this domain. Some examples are constructed in support of the main results.

References

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