We prove some common fixed point theorems for two pairs of weakly compatible mappings in 2-metric spaces via an implicit relation. As an application to our main result, we derive Bryant's type generalized fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any finite number of mappings. Our results improve and extend a host of previously known results. Moreover, we study the existence of solutions of a nonlinear integral equation.
Chauhan, S., Imdad, M., Vetro, C. (2013). Unified metrical common fixed point theorems in 2-metric spaces via an implicit relation. JOURNAL OF OPERATORS, 2013, 1-11 [10.1155/2013/186910].
Unified metrical common fixed point theorems in 2-metric spaces via an implicit relation
VETRO, Calogero
2013-01-01
Abstract
We prove some common fixed point theorems for two pairs of weakly compatible mappings in 2-metric spaces via an implicit relation. As an application to our main result, we derive Bryant's type generalized fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any finite number of mappings. Our results improve and extend a host of previously known results. Moreover, we study the existence of solutions of a nonlinear integral equation.
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