Some Generalizations of Weak Contractions

  • Clement Boateng Ampadu Independent Researcher, USA
  • Mohd Junaid Aligarh Muslim University, India
Keywords: (δ, L)-weak contraction, (δ, 1 – δ) weak contraction, Reich contraction, Kannan contraction, Hardy-Rogers contraction, Chatterjea contraction

Abstract

The concept of weak contraction appeared in [6], and its extension appeared in [7]. In this paper we introduce weak contractions in the sense of [7] that advances the Kannan, Reich, Chatterjea and Hardy-Rogers contractions. Some results related to the fixed point of these new contractions are proved with illustrative examples.

Downloads

Download data is not yet available.

References

Kannan, R. (1968). Some results on fixed points. Bulletin of the Calcutta Mathematical Society, 60, 71-76. https://doi.org/10.2307/2316437

Kannan, R. (1969). Some results on fixed points II. The American Mathematical Monthly, 76(4), 405-408. https://doi.org/10.1080/00029890.1969.12000228

Reich, S. (1971). Some results concerning contraction mappings. Canadian Mathematical Bulletin, 14(1), 121-124. https://doi.org/10.4153/CMB-1971-024-9

Chatterjea, S. K. (1972). Fixed point theorems. Comptes Rendus de l'Academie Bulgare des Sciences, 25, 727-730.

Hardy, G. E., & Rogers, T. D. (1973). A generalization of a fixed point theorem of Reich. Canadian Mathematical Bulletin, 16(2), 201-206. https://doi.org/10.4153/CMB-1973-036-0

Berinde, V. (2004). Approximating fixed points of weak contractions using the Picard iteration. Nonlinear Analysis Forum, 9(1), 43-53.

Ampadu, C. B. (2019). An almost contraction mapping theorem in metric spaces with unique fixed point. Fundamental Journal of Mathematics and Mathematical Sciences, 11(2), 47-50.

Published
2026-05-29
How to Cite
Ampadu, C. B., & Junaid, M. (2026). Some Generalizations of Weak Contractions. Earthline Journal of Mathematical Sciences, 16(4), 707-715. https://doi.org/10.34198/ejms.16426.42.707715