Existence of fixed point in c-contraction

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dc.authorid0000-0001-5091-8555en_US
dc.contributor.authorAzhdari, Parvin
dc.date.accessioned2024-07-12T20:49:47Z
dc.date.available2024-07-12T20:49:47Z
dc.date.issued2009en_US
dc.departmentFakülteler, İnsan ve Toplum Bilimleri Fakültesi, Matematik Bölümüen_US
dc.description.abstractKramosil and Michalek introduced the notion of fuzzy metric space which is similar to generalized Menger space. Then George and Veeramani imposed some stronger conditions on fuzzy metric space in order to obtain a Hausdorff topology. Many authors have extended fixed point theorem to different type of contraction in both probabilistic and fuzzy metric space. Mihet also showed fixed point theorem for fuzzy contractive mappings by using point convergence. In this paper we use the concept of point convergence for showing the existence of fixed point for B-contractions and C-contractions mapping. We notice that the condition of point convergency is weaker than convergency. Definition 1: A B-contraction on a probabilistic space (X, F) is a sel fmapping f of X for which Ff(p)f(q)(kt) Fpq(t) 8p, q 2 X, 8t ¿ 0, k 2 (0, 1). A mapping f : X ! X is called a C-contraction if there exists k 2 (0, 1) such that for all Fxy(t) ¿ 1 - t ) Ff(x)f(y)(kt) ¿ 1 - kt 8x, y 2 X , t ¿ 0. Definition 3: Let (X,M, T) be a fuzzy metric space. A sequence xn in X is said to be point convergent to x 2 X if there exists t ¿ 0 such that limn!1M(xn, x, t) = 1 Theorem 1: [1]: Let (X,M, T) be George and Veeramani fuzzy metric space and sup 0 a ¡1 T(a, a) = 1 and A : X ! X be a B-contraction. Suppose that for some x 2 X the sequence of An(x) has a p-convergent subsequence. Then A has a unique fixed point. Theorem 2 [1]: Let (X,M, T) be a George and Veermani fuzzy metric space and A : X ! X be a C-contraction and sup 0 a¡1T(a, a) = 1. Suppose that for some x 2 X the sequence of An(x) has a p-convergent subsequence. Then A has a unique fixed point. Existence of fixed point when the subsequence satisfied in p-convergency condition can extended to generalized C-contraction. Theorem [2]: Let (X,M, T) be a George and Veermani fuzzy metric space and A : X ! X be a generalized C-contraction and sup 0 a¡1T(a, a) = 1. Suppose that for some x 2 X the sequence An(x) has a p-convergent subsequence. Then, A has a fixed point.en_US
dc.identifier.citationAzhdari, P. (2009). Existence of fixed point in c-contraction. Maltepe Üniversitesi. s. 323.en_US
dc.identifier.endpage324en_US
dc.identifier.isbn9.78605E+12
dc.identifier.startpage323en_US
dc.identifier.urihttps://hdl.handle.net/20.500.12415/2234
dc.institutionauthorAzhdari, Parvin
dc.language.isoenen_US
dc.publisherMaltepe Üniversitesien_US
dc.relation.ispartofInternational Conference of Mathematical Sciencesen_US
dc.relation.publicationcategoryUluslararası Konferans Öğesi - Başka Kurum Yazarıen_US
dc.rightsCC0 1.0 Universal*
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.rights.urihttp://creativecommons.org/publicdomain/zero/1.0/*
dc.snmzKY07561
dc.titleExistence of fixed point in c-contractionen_US
dc.typeConference Object
dspace.entity.typePublication

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