A hybrid fixed point result based on w-distances along with stability and well-posedness properties and an application

In this paper, we introduce two hybrid contraction mappings by combining the ideas of two types of existing contractions namely Kannan-type and Pata-type contractions with respect to [Formula: see text]-distances. We investigate the fixed point problem pertaining to the two contractions mentioned above. All our results are obtained by using [Formula: see text]-distance which is a distance-like function defined on a metric space in addition to the metric function and has been used by many researchers to produce new results in fixed point theory. We prove the existence and uniqueness of fixed points for these mappings. With the help of an illustrative example we show that the result obtained herein is an actual generalization of the corresponding result which follows by using the metric function. We also show that the fixed point problems discussed here possess Hyers–Ulam–Rassias stability property and also that the problems are well-posed. The above two concepts are formulated here in terms of [Formula: see text]-distances. Further, the two problems merge into a single problem of metric fixed point theory when the [Formula: see text]-distance is the same as the metric distance. This feature is central to our work which arises only due to the use of [Formula: see text]-distance. We also include an application of our result to a problem of integral equation.