Abstract metric spaces and Hardy-Rogers-type theorems

作者：Radojevic Slobodan; Paunovic Ljiljana; Radenovic Stojan^*

来源：Applied Mathematics Letters, 2011, 24(4): 553-558.

DOI：10.1016/j.aml.2010.11.012

• Common fixed point
• Cone metric space
• Normal and nonnormal cone
• Coincidence point
• Symmetric space

The purpose of the present paper is to establish coincidence point theorem for two mappings and fixed point theorem for one mapping in abstract metric space which satisfy contractive conditions of Hardy-Rogers type. Our results generalize fixed point theorems of Nemytzki [V.V. Nemytzki, Fixed point method in analysis, Uspekhi Mat. Nauk 1 (1936) 141-174], Edelstein I M. Edelstein, On fixed and periodic point under contractive mappings, J. Lond. Math. Soc. 37 (1962) 74-79] and Huang, Zhang [LG. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2)(2007) 1468-1476] from abstract metric spaces to symmetric spaces (Theorem 2.1) and to metric spaces (Theorem 2.4, Corollaries 2.6-2.8). Two examples are given to illustrate the usability of our results.

• 出版日期2011-4