USING IMPLICIT RELATION TO PROVE COMMON COUPLED FIXED POINT THEOREMS FOR TWO HYBRID PAIRS OF MAPPINGS

USING IMPLICIT RELATION TO PROVE COMMON COUPLED
FIXED POINT THEOREMS FOR TWO HYBRID PAIRS OF
MAPPINGS

BHAVANA DESHPANDE1, AMRISH HANDA, DEEPMALA

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Abstract

Using implicit relation we establish two common coupled xed point theo-
rems under the conditions of weakly commutativity and w-compatibility on a complete
metric space, which is not partially ordered. We do not use the condition of continuity
of any mapping for proving the existence of coupled coincidence and common coupled
xed point.

Keywords

Keywords:Coupled xed point, coupled coincidence point, implicit relation, w-compatibility,
weakly commuting mappings.