Relation-Theoretic Contraction Principle In Metric Spaces Using Multiplicative Contraction
DOI:
https://doi.org/10.23755/rm.v47i0.730Abstract
Alam and Imdad have presented a novel application of the Banach contraction principle on a complete metric spaces with a binary relation. We have extended the concept of binary relation with the multiplicative contraction in a complete metric spaces. We have also included corollary to demonstrate our results.
References
A.Alam and M.Imdad. Relation-theoretic contraction principle. J. Fixed Point Theory Appl., 17(4):693-702, 2015.
MD.Ahmadullah, M.Imdad and R.Gurban. Relation-Theoretic Metrical Fixed Point Theorems under Nonlinear Contractions. Fixed Point Theory, 20(1):3-18, 2019.
S.Banach. Sur les operations dans les ensembles abstraits et leur applications aux equations integrales. Fundamental Mathematicae, 3(7):133-181, 1922.
L. E. J.Brouwer. Uber abbildung von mannigfaltigkeiten. Math. Ann 71(1):97-115, 1911.
L.B.'Ciri'c. A new fixed point theorem for contractive mappings. Inst. Mathematique Publ., Nouvelle Serie., 30(44):25-27, 1981.
V.Flaska, J.Jezek, T.Kekpa and J.Kortelainen. Transitive closures of binary relations I. Acta Univ. Carolin. Math. Phys., 44:55-59, 2007.
M.M.Frechet. Sur quelques points du calcul functionnel. Rendiconti del Circolo Mathematico di Palermo, 22(1):1-72, 1906.
R.Kannan. Some results on fixed points. Bull. Cal. Math. Soc., 60:71-76, 1968.
R. Kannan. Some results on fixed points II. Am. Math. Mon., 76:405-408, 1969.
S.Lipschutz. Schaum's outlines of theory and problems of set theory and problems of set theory and related topics. McGraw-Hill, New York, 1964.
H.L.Skala. Trellis theory. Algebra universalis, 1:218-233, 1971.
R.D.Maddux and Rodrigue-Lopez. Relation Algebras. Stud. Logic Found. Math. 150, Elsevier B. V., Amesterdam, 2006.
M.Ozavsar and A.C.Cevikel. Fixed point of multiplicative contraction mappings on multiplicative metric space. arXiv:1205.5131v [math. GM], 2012.
J.Slapal. Relations and topologies. Czechoslovak Mathematical Journal, 43(1):141-150, 1993.
A.Stouti and A. Maaden. Fixed points and common fixed points theorems in pseudo-ordered sets. Proycecciones, 32:409-418, 2019.
M.Turinici. Product fixed point results in ordered metric spaces. arXiv:1110.3079v1, 2011.
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