Abstract
The investigation of symmetric/asymmetric structures and their applications in mathematics (in particular in operator theory and functional analysis) is useful and fruitful. A metric space has the property of symmetry. By looking in the same direction and using the alpha-admissibility with regard to eta and theta-functions, we demonstrate some existence and uniqueness fixed point theorems. The obtained results extend and generalize the main result of Isik et al. (2019). At the end, some illustrated applications are presented.