Fixed Point Theorem in MR-metric Spaces VIA Integral Type Contraction

We present new fixed point theorems in M R-metric spaces using integral-type contractions.These results build upon and extend previous research.The concept of an M R-metric space was originally introduced by Malkawi, who also outlined the idea of sequence convergence in such spaces.Additionally, methods for constructing M R-metrics from certain real-valued partial functions in three-dimensional Euclidean space were proposed, along with a study of various convergence types in M R-metric spaces, analyzing the implications and non-implications among them.In 2002, Branciari introduced a new generalization of the contractive condition of the integral type.His work focused on the existence of fixed points for mappings defined over complete metric spaces (X, d), subject to a broad integral-type contractive inequality.This condition is reminiscent of the Banach-Caccioppoli criterion.Specifically, the study involves mappings f : X X for which there exists a constant c (0, 1) such that for any x, y X:Here, (t) : [0, +) [0, +] is a Lebesgue-integrable function.It is nonnegative, summable on every compact subset of [0, +), and satisfies 0 (t) dt > 0 for each > 0.