On Existence of Common Fixed Points Under Lipschitz-Type Mapping Pairs with Applications. (2nd November 2017)

• Record Type: Journal Article
• Authors: Bisht, Ravindra K.
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 11(2017)
• Page Start: 1446
• Page End: 1457
• Publication Date: 2017-11-02
• Subjects: Eigenvalue -- eigenvector -- fixed point -- Lipschitz-type mapping; 47H10 -- 54H25; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1338297
• Languages: English
• ISSNs: 0163-0563

Abstract

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.