Afrika Matematika

, Volume 25, Issue 4, pp 1043–1051

Prešić type results in 2-Banach spaces

Article

DOI: 10.1007/s13370-013-0174-2

Cite this article as:
Shukla, S. Afr. Mat. (2014) 25: 1043. doi:10.1007/s13370-013-0174-2

Abstract

In this paper, we generalize the Banach contraction principle by proving common fixed point theorems for mappings satisfying Prešić type conditions in 2-Banach spaces. The common fixed point is approximated by the \(k\)-Picard type and \(k\)-Mann type iteration schemes in product spaces. The results in this paper extend the results of Prešić in the framework of a 2-Banach space. An example is provided which illustrate the results.

Keywords

2-Banach spacePrešić type mappingCommon fixed point\(k\)-Mann iteration

Mathematics Subject Classification (2000)

54H2547H10

Copyright information

© African Mathematical Union and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Applied MathematicsShri Vaishnav Institute of Technology and ScienceIndoreIndia