A.U Terrang, S.A. Akinwunmi, D.O. Oyewola, & M.M. Bitrus
Abstract
Let A and B be non-empty subset of a multiplicative metric space (π, π) and π: π΄ βͺ π΅ β π΄ βͺ π΅ be a multiplicative R-cyclic contraction with respect to πΉ. Then there exists a sequence {π₯π}πββ β π΄ βͺ π΅ such that limπββ π(π₯π, π₯π+1) = ππππββπ(π₯π, π₯π+1 ) = π(π΄, π΅), then limπββ π(π₯π, π₯π+1) = ππππββπ(π₯π, π₯π+1 ) = πππ π‘(π΄, π΅). The current article provides solutions to numerous problems in Physics, Optimization and Economics, which can be reduced to finding a common best proximity point of some non-linear operator. We considered the application of cyclic contraction mapping on the multiplicative metric space then we obtain limπββ π(π₯π, π₯π+1) = ππππββ π(π₯π, π₯π+1 ) = πππ π‘(π΄, π΅), π(π΄, π΅) β€ π(π£, ππ£) β€ π(π΄, π΅), π(π£, ππ£) = π(π΄, π΅), π(ππ₯, ππ¦) β€ (π(π₯, π¦)) πΉ(π(π₯,π¦)) β π(π΄, π΅) 1βπΉ(π(π₯,π¦)) β€ (max {π(π₯, π¦),[π(ππ₯, π₯) β π(ππ¦, π¦) β min {π(π₯, ππ¦), π(π¦, ππ₯)}] 1 2) π(π(π₯,π¦)) β π(π΄, π΅) 1βπ(π(π₯,π¦)) for all π₯ β π΄ and π¦ β π΅. Read full PDF
Keywords: Contraction mapping, Collapse, Height, Waist, 2010 Mathematics Subject Classification: 16W2, 10X2, 06F05 and 09F06
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