Integral Type Generalizations of Ćirić Fixed Point Theorems in Metric Spaces with Binary Operation

This paper establishes and proves Ciric fixed point theorems of integral type generalizations in metric spaces equipped with a binary operation. The obtained results extend existing fixed point theory by incorporating the additional structure induced by the binary operation. The results generalize corresponding fixed point principles in classical and generalized metric spaces and demonstrate how the interaction between an integral contractive condition and an underlying binary operation can be used to guarantee the existence and uniqueness of fixed points. Consequently, the study contributes to the development of a broader framework for fixed point theory in operational metric structures and provides a foundation for further investigations involving different binary operations and generalized contractive conditions. To demonstrate the validity, novelty, and applicability of the proposed results, illustrative example is provided.