Best proximity point theorem for integral-type cyclic contractions
Keywords:
Branciaris contraction, cyclic contraction, Integral-Type cyclic contraction, Best proximity pointAbstract
A. Branciaris (2002) introduced Banach contraction principle in the form of integraltype, where the contractive inequality is expressed as in terms of an integrable control function. This paper presents a generalized form of Branciaris’ integral-type contraction by incorporating a cyclic structure suitable for disjoint domains, and establishes the best proximity point theorem for integral-type cyclic contractions. We prove that such mappings guarantee the existence and convergence of best proximity points, ensuring stability in alternating processes where fixed points are absent. The theoretical framework is validated through illustrative numerical examples and a real-world logistics routing model between disjoint delivery and pickup zones. This generalization not only subsumes Branciaris’
integral-type contraction as a special case but also offers a more flexible analytical tool for proximity based problems in nonlinear analysis.
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