偏序偏度量空间中有理分式型广义弱压缩的公共不动点结果

Abstract

Abstract: In this paper, some common fixed point results for four mappings satisfying generalized weakly contractive conditions with a rational type expression are obtained in partially ordered complete partial metric spaces. A sufficient condition for the uniqueness of common fixed point is proved, an examples are given to support our results, and also, a homotopy result, as an application, is discussed.

Key words: Partially ordered partial metric space, Common fixed point, Generalized weak contraction

CLC Number:

O177.91

Song Jiping, Wang Maofa. Common Fixed Point Results for Generalized Weak Contractions with a Rational Expression in Ordered Partial Metric Spaces[J].Acta mathematica scientia,Series A, 2017, 37(3): 401-415.

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References

[1] Alber Y, Guerre-Delabriere S. Principles of weakly contractive maps in Hilbert spaces. Oper Theory Adv Appl, 1997, 98:7-22
[2] Rhoades B E. Some theorems on weakly contractive maps. Nonlinear Anal, 2001, 47:2683-2693
[3] Khan M S, Swaleh M, Sessa S. Fixed point theorems by altering distances between the points. Bull Austral Math Soc, 1984, 30(1):1-9
[4] Nashine H K, Samet B, Kim J K. Fixed point results for contractions involving generalized altering distances in partially ordered metric spaces. Fixed Point Theory Appl, 2011, 2011:5
[5] Nashine H K, Samet B. Fixed point results for mppings satisfying (ψ, φ)-weakly contractive condition in partially ordered metric spaces. Nonlinear Anal, 2011, 74:2201-2209
[6] Pathak H K, Shahzad N. Fixed point results for set-valued contractions by altering distances in complete metric spaces. Nonlinear Anal, 2009, 70:2634-2641
[7] Naidu S V R. Some fixed point theorems in metric spaces by altering distances. Czechoslovak Math, 2003, 53:205-212
[8] Sastry K P R, Babu G V R. Some fixed point theorems by altering distances between the points. Indian J Pure Appl Math, 1999, 30:641-647
[9] Dhananjay G, Mujahid A, Deepesh Kumar P, Calvgero V. Fixed points of α-type F -contractive mappings with an application to nonlinear fractional differential equation. Acta Math Sci, 2016, 36B(3):957-970
[10] Zhang Q, Song Y. Fixed point theory for generalized φ-weak contractions. Appl Math Lett, 2009, 22:75-78
[11] Dorić D. Common fixed point theorem for generalized (ψ, φ)-weak contractions. Appl Math Lett, 2009, 22:1896-1900
[12] Mujahid A, Dorić D. Common fixed point theorem for four mappings satisfying generalized weak contractive condition. Filomat, 2010, 24(2):1-10
[13] Jungck G. Common fixed points for noncontinuous nonself maps on non-metric spaces. Far East J Math Sci, 1996, 4:199-215
[14] Esmaily J, Vaezpour S M, Rhoades B E. Coincidence and common fixed point theorems for a sequence of mappings in ordered metric spaces. Appl Math Comput, 2013, 219(10):5684-5692
[15] Mujahid A, Nazir T, Radenović S. Common fixed points of four maps in partially ordered metric spaces. Appl Math Lett, 2011, 24:1520-1526
[16] Esmaily J, Vaezpour S M, Rhoades B E. Coincidence point theorem for generalized weakly contractions in ordered metric spaces. Appl Math Comput, 2012, 219:1536-1548
[17] Shatanawi W, Samet B. On (ψ, φ)-weakly contractive condition in partially ordered metric spaces. Comput Math Appl, 2011, 62:3204-3214
[18] 罗婷, 朱传喜. 半序概率度量空间中压缩条件下相容映射的三元重合点与三元不动点定理. 数学物理学报, 2016, 36A(1):157-167 Luo T, Zhu C X. Tripled coincidence and tripled fixed point theorems for compatible mappings under contractive conditions in partially ordered probabilistic spaces. Acta Math Sci, 2016, 36A(1):157-167
[19] Jaggi D S. Some unique fixed point theorems. Indian J Pure Appl Math, 1977, 8(2):223-230
[20] Aydi H, Amor S H, karapinar E. Berinde-type generalized contractions on partial metric spaces. Abstr Appl Anal, 2013, Article ID:312479
[21] Turkoglu A D, Ozturk V. Common fixed point results for four mapping on partial metric spaces. Abstr Appl Anal, 2012, Article ID:190862
[22] Abdeljawad T. Fixed points for generalized weakly contractive mappings in partial metric spaces. Math Comput Model, 2011, 54:2923-2927
[23] Karapinar E, Marudai M, Pragadeeswarar V. Fixed point theorems for generalized weak contractions satisfying rational expression on a ordered partial metric space. Lobachevskii J Math, 2013, 34(1):116-123
[24] Matthews S G. Partial metric topology. Ann New York Acad Sci, 1994, 728:183-197

Common Fixed Point Results for Generalized Weak Contractions with a Rational Expression in Ordered Partial Metric Spaces

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