Unique Common Fixed Point for Occasionally Weakly Biased Mappings of Type (A) In Ultrametric Space

Abstract

In this paper, we have established the existence and uniqueness of a common fixed point for occasionally weakly biased mappings of type (A) in an ultrametric space employing an implicit function. Our result accredits us to ameliorate some fixed point theorems specifically Alinejad and Mirmostafaee [2]. In the sequel, we have provided a novel explanation to a problem of Rhoades [B. E. Rhoades, Contractive definitions and continuity, Fixed Point Theory and its Applications (Berkeley 1986), Contemp. Math. (Amer. Math. Soc.), 72 (1988), 233-245.] on the question of the existence of contractive mapping having a fixed point at the point of discontinuity in a non-complete ultrametric space via implicit relations. Our theorems and corollaries are improved and enhanced versions of renowned conclusions wherein completeness and continuity have not been utilized.