Abstract

Two distinct theorems are presented in this manuscript. The first one establishes the existence of coincidence points and the $g$-weakness of $M_v^b$ metric space. The Reich contraction principle produces a unique common fixed point for two maps, as illustrated in various examples. Second, same concept is used to identify common fixed point for four self maps. The Kannan and Banach contraction principles were applied in conjunction with extra requirements to get the fixed points as corollaries. This theorem's approach was used to solve several examples.

Keywords and Phrases

Fixed point, self maps, Complete $M_v^b$ metric space, $m_v^b$- convergent, coincidence point.

A.M.S. subject classification

47H10, 54H25.

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