Fixed Point Theorem in Fuzzy b-Metric Space Using Compatible Mapping of Type (A)

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One of the most active and developing fields in both pure and applied mathematics is the theory of fixed points. It is possible to formulate a large number of nonlinear issues that arise in many scientific domains as fixed point problems. Since Zadeh first introduced the concept of fuzzy mathematics in 1965, the interest in fuzzy metrics has grown to the point that several studies have concentrated on examining their topological characteristics and applying them to mathematical issues. This was primarily because, in certain situations, fuzziness rather than randomization was the cause of uncertainty in the distance between two spots. Many mathematicians have examined and developed the concept of distance in relation to fuzzy frameworks because it is a naturalist concept. Generally speaking, it is impossible to determine the precise distance between any two locations. Thus, we deduce that if we measure the same distance between two locations at different times, the results will differ. There are two approaches that can be used to manage this situation: statistical and probabilistic. But instead of employing non-negative real numbers, the probabilistic approach makes use of the concept of a distribution function. Since fuzziness, rather than randomness, is the cause of the uncertainty in the distance between two places. Because of the positive real number <i>b</i> ≥ 1, the area of fuzzy b-metric space is larger than fuzzy metric space. Thus, this field is the source of our concern. This study aims to use the notion of compatible mappings and semicompatible mappings of type (A) to develop some common fixed point theorems in fuzzy b- metric space. A few ramifications of our primary discovery are also provided. Included are pertinent examples to highlight the importance of these key findings. Our results add to a number of previously published findings in the literature.