葉洪清,谷峰

(杭州師范大學(xué)應(yīng)用數(shù)學(xué)研究所/杭州師范大學(xué)數(shù)學(xué)系,杭州 浙江 310036)

G-度量空間中Altman積分型映象的幾個新的公共不動點定理

葉洪清,谷峰

(杭州師范大學(xué)應(yīng)用數(shù)學(xué)研究所/杭州師范大學(xué)數(shù)學(xué)系,杭州 浙江 310036)

在完備G-度量空間的框架下,利用R-弱交換映象的概念,證明了兩對R-弱交換A ltman積分型自映象的一個新的公共不動點定理,并給出了結(jié)論的有效性實例.所得的結(jié)果不同于已有文獻中的已知結(jié)果.

A ltman積分型映象;對稱G-度量空間;R-弱交換自映象;公共不動點

1 引言和預(yù)備知識

2 主要結(jié)果

[1]A ltm an M.A fixed point theorem in com pact m etric spaces[J].Am er.M ath.M onthly,1975,82(2):827-829.

[2]谷峰,鄧波.關(guān)于A ltm an型映象的公共不動點定理[J].哈爾濱師范大學(xué):自然科學(xué)學(xué)報,2001,17(5):44-46.

[3]劉慶澤.關(guān)于A ltm an型映射的公共不動點定理[J].遼寧師范大學(xué)學(xué)報,1993,16(1):1-4.

[4]張樹義.A ltman型映射的公共不動點定理[J].煙臺師范學(xué)院學(xué)報,2000,16(2):95-97.

[5]谷峰.關(guān)于?擴張相容映象的公共不動點定理[J].寶雞文理學(xué)院學(xué)報,2001,21(3):176-179.

[6]雷煊,嚴廣樂,楊漢生,等.p-距離空間中的一類壓縮映象的不動點定理[J].純粹數(shù)學(xué)與應(yīng)用數(shù)學(xué),2011,27(1):86-94.

[7]史紅波,朱江.局部凸空間中的不動點定理及其應(yīng)用[J].純粹數(shù)學(xué)與應(yīng)用數(shù)學(xué),2010,26(3):467-472.

[8]M ustafa Z,Sim sB.A new app roach to a generalizedm etric space[J].J.Nonlinear Convex Anal.,2006,7(2):289-297.

[9]M ustafa Z,Obiedat H.Som e fixed point theorem s form appings on com p lete G-m etric spaces[J].Fixed Point Theory and App lication,2008,25:11-12.

[10]M anro S,Bhatia SS,Kum ar S.Expansionm apping theorem s in G-m etric spaces[J].Int.J.Contem p.M ath. Sciences,2010,51(5):2529-2535.

[11]Mustafa Z,Awawdeh F,Shatanaw iW.Fixed point theorem s for expansivemappings in G-metric spaces[J]. Int.J.Contem p.M ath.Science,2010,50(5):2463-2472.

Several new comm on fi xed poin t theorem s for A ltm an in tegral type m app ings in G-m etric space

Ye Hongqing,Gu Feng
(Institute of App lied M athem atics and Departm ent of M athem atics, Hangzhou Norm al University,Hangzhou 310036,China)

The concept of R-weakly commuting mappings was used for proving a new common fixed point theorem for two pairs of R-weakly commuting A ltm an integral type self-m appings in com p lete G-m etric space. An exam p le is p rovided to support our result.The results obtained in this paper diff er from the recent relative resu lts in literature.

A ltm an integral typem appings,symm etric G-m etric space,R-weakly commuting self-m appings, comm on fixed point

O177.91

A

1008-5513(2012)06-0845-08

2011-12-05.

國家自然科學(xué)基金(10671155);浙江省自然科學(xué)基金(Y 6110287,Y 12A 010095).

葉洪清(1987-),碩士研究生,研究方向：非線性泛函分析.

谷峰(1960-),教授,研究方向：非線性泛函分析及應(yīng)用研究.

2010 M SC:47H10,54H25