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Zbl 1226.47061
Pathak, Hemant Kumar; Tiwari, Rakesh
A Gregus type common fixed point theorem in normed spaces with applications.
(English)
[J] Banach J. Math. Anal. 5, No. 1, 136-147, electronic only (2011). ISSN 1735-8787/e

Summary: We introduce the notion of $\varphi$-weakly compatible mapping for a pair of mappings. A fixed point theorem for two pairs of $\varphi$-weakly compatible mappings satisfying a rational type contraction in a normed space is also established. Subsequently, we use our result to find the existence of solutions of variational inequalities.
MSC 2000:
*47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
54H25 Fixed-point theorems in topological spaces
47J20 Inequalities involving nonlinear operators

Keywords: $\varphi$-weakly compatible mappings; variational inequality

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