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. Various common fixed point theorems have been proved for one or two pair of mappings using either (CLR) property ([24]), or by taking one of the range-subspace closed. In this paper, we introduce the notion of (CLCS)-property i.e., “common limit converging in the range sub-space”. Using this property, we prove common fixed point theorems for two pairs of weakly compatible mappings in complex valued b-metric spaces satisfying a collection of contractive conditions. Our notion is meaningful and valid because the required common fixed point will always lie on the range-subspace of the mapping-pair. We give some examples to show that if a mapping pair (f, g) of a closed complex valued b-metric space X satisfy the (CLRf ) property, then it is also (CLRg), and vice-versa.

FIXED POINT THEOREMS USING (CLCS) PROPERTY IN COMPLEX VALUED $b$-METRIC SPACES