The International Journal of Applied Sciences

ABSTRACT
This paper establishes fundamental advances in fixed point theory within M∗-metric spaces, introducing a unified framework that extends and generalizes previous results in b-metric and MR-metric spaces. We present new fixed point theorems for various contraction types, including (ψ,L)-weak contractions and (H,Ωb)-interpolative contractions, while developing innovative connections between M∗-metrics and other generalized distance structures. Our work demonstrates significant applications to nonlinear analysis and fractional differential equations, particularly through the lens of the atomic solution method. The theoretical developments are complemented by concrete examples and computational applications, providing a comprehensive bridge between abstract fixed point theory and practical problem-solving in mathematical analysis.

References

REFERENCES
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Article history

Received : Apr 27, 2025

Revised : Apr 27, 2025

Accepted : Jun 11, 2025

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