FIXED POINT THEOREMS FOR CYCLIC CONTRACTIONS WITH C-CLASS FUNCTIONS ON B-METRIC SPACES

Abstract

Let 𝐹 be a 𝐶−𝑐𝑙𝑎𝑠𝑠 function [A. H. Ansari, Note on 𝜑−𝜓−contractive type mappings and related fixed point, The 2nd Regional Conference on Mathematics and Applications, PNU, September 2014, pages 377-380] and let 𝜓 𝑎𝑛𝑑 𝜙 be altering distance functions [M.S. Khan, M. Swaleh, S. Sessa, Fixed point theorems by altering distances between the points, Bull. Aust. Math. Soc. 30 (1984), 12-18]. In this paper we introduce a concept of cyclic generalized 𝐹(𝜓,𝜙)-rational contraction and use it to prove the existence and uniqueness of fixed points of this type of contraction mapping in b-metric spaces. We apply our results to obtain fixed points of certain contractions of integral type.