On Existence of Common Fixed Points Under Lipschitz-Type Mapping Pairs with Applications

ABSTRACT

In this paper, we propose some sufficient conditions to obtain the existence of common fixed points for a pair of self-mappings satisfying Lipschitz-type conditions in noncomplete metric space. Our results improve and extend the results of Pant [Common fixed points of Lipschitz-type mapping pairs, J. Math. Anal. Appl. 240, (1999), 280–283] and Khan et al. [Coincidences of Lipschitz-type hybrid maps and invariant approximation, Numer. Funct. Anal. Optim. 28(9–10), (2007), 1165–1177]. As an application of our results we solve an eigenvalue problem for operators defined on a normed space.

KEYWORDS:

• Eigenvalue
• eigenvector
• fixed point
• Lipschitz-type mapping

MATHEMATICS SUBJECT CLASSIFICATION:

• 47H10
• 54H25

Acknowledgement

Dedicated to professor R. P. Pant on the occasion of his 62th birthday.