一致空间中带推广q-距离的(φ,Ψ,p)-弱压缩映射的不动点定理
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摘要
在一致空间引入了推广的q-距离(特殊地,推广的P-距离)和关于推广q-距离序列完备的概念.通过运用推广的q-距离和新的完备性,在一致空间中建立了满足(φ,ψ,p)-弱压缩映射的不动点定理.
In the framework of uniform spaces, we introduce the concepts of generalized q-distances(particularly, generalized p-distances) and sequential completeness with respect to a generalized q-distance. By using generalized q-distances and the new type of completeness, we establish a fixed point theorem for mappings satisfying(φ,ψ,p)-weakly contractive conditions in uniform spaces.
In the framework of uniform spaces, we introduce the concepts of generalized q-distances(particularly, generalized p-distances) and sequential completeness with respect to a generalized q-distance. By using generalized q-distances and the new type of completeness, we establish a fixed point theorem for mappings satisfying(φ,ψ,p)-weakly contractive conditions in uniform spaces.
引文
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[13]Qiu J H,He F.P-distances,Q-distances and a generalized Ekeland's variational principle in Uniform spaces[J].Acta Math Sin Engl Ser,2012,28(2):235-254.
[14]Qiu J H,He F.A generalized vectorial Ekeland's variational principle with a P-distance[J].Acta Math Sin Engl Ser,2013,29(9):1655-1678.
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[18]Altun I,Imdad M.Some fixed point theoremson ordered uniform spaces[J].Filomat,2009,23(3):15-22.
[19]Hussain N,Karapinar E,Sedghi S,et al.Cyclic(φ)-contractions in uniform spaces and related fixed point results[J].Abstract and Applied Analysis,2014,Article ID 985080.
[2]Das P,Lahiri K B.Fixed point of contractive mappings in generalized metric spaces[J].Math Slovaca,2009,59(4):499-504.
[3]Fora A,Bellour A,Al-Bsoul A.Some results in fixed point theory concerning generalized metric spaces[J].Math Vesnik,2009,61(3):203-208.
[4]Samet B.A fixed point theorem in a generalized metric space for mappings satisfying a contractive condition of integral type[J].Int J Math Anal,2009,3(26):1265-1271.
[5]Sarma R I,Rao M J,Rao S S.Contractions over generalized metric spaces[J].J Nonlinear Sci Appl,2009,2(3):180-182.
[6]Lakzian H,Samet B.Fixed points for(ψ,φ)-weakly contractive mappings in generalized metric spaces[J].Appl Math Lett,2012,25:902-906.
[7]Aydi H,Karapinar E,Samet B.Fixed points for generalized(α,ψ)-contractions on generalized metric spaces[J].Journal of Inequalities and Applications,2014,Article 229.
[8]Alghamdi A M,Chen M C,Karapinar E.The Generalized weaker(α-φ-ψ)-contractive mappings and related fixed point results in complete generalized metric spaces[J].Abstract and Applied Analysis,2014,Article ID 985080.
[9]La Rosa V,Vetro P.Common fixed points forα-ψ-φ-contractions in generalized metric spaces[J].Nonlinear Analysis:Modelling and Control,2014,19(1):43-54.
[10]Lakzian H,Aydi H,Rhoades E B.Fixed points for(φ,ψ,p)-weakly contractive mappings in metric spaces withψ-distances[J].Appl Math Comput,2013,219:6777-6782.
[11]Dutta N P,Choudhury S B.A generalization of contraction principle in metric spaces[J].Fixed point Theory Appl,2008,Article ID 406368.
[12]Rhoades E B.Some theorems on weakly contractive maps[J].Nonlinear Anal,2001,47:2683-2693.
[13]Qiu J H,He F.P-distances,Q-distances and a generalized Ekeland's variational principle in Uniform spaces[J].Acta Math Sin Engl Ser,2012,28(2):235-254.
[14]Qiu J H,He F.A generalized vectorial Ekeland's variational principle with a P-distance[J].Acta Math Sin Engl Ser,2013,29(9):1655-1678.
[15]Kelly L J.General topology[M].New York:Springer-Verlag,1953.
[16]Kothe G.Topological vector spaces I[M].Berlin:Springer-Verlag,1969.
[17]Aamri M,Bennani S,El Moutawakil D.Fixed points and variational principle in uniform spaces[J].Siberian Electronic Mathematical Reports,2006,3:137-142.
[18]Altun I,Imdad M.Some fixed point theoremson ordered uniform spaces[J].Filomat,2009,23(3):15-22.
[19]Hussain N,Karapinar E,Sedghi S,et al.Cyclic(φ)-contractions in uniform spaces and related fixed point results[J].Abstract and Applied Analysis,2014,Article ID 985080.