Fixed point theory for cyclic (ϕ - ψ)-contractions

Abstract

In this article, the concept of cyclic (j -ψ)-contraction and a fixed point theorem for this type of mappings in the context of complete metric spaces have been presented. The results of this study extend some fixed point theorems in literature. 2000 Mathematics Subject Classification: 47H10;46T99 54H25.

Fixed point theory for cyclic generalized contractions in partial metric spaces

“…In [13], Păcurar and Rus discussed fixed point theorey for cyclic -contractions in metric spaces and in [14], Karapinar obtained a fixed point theorem for cyclic weak -contraction mappings still in metric spaces.…”

Fixed point theory for the cyclic weaker Meir-Keeler function in complete metric spaces

“…Recently, the fixed theorems for an operator f: X X that defined on a metric space X with a cyclic representation of X with respect to f had appeared in the literature. (see, e.g., [6][7][8][9][10]). In 2010, Pǎcurar and Rus [7] introduced the following notion of cyclic weaker -contraction.…”

Best proximity points of Kannan type cyclic weak ϕ-contractions in ordered metric spaces

“…Notice that if ϕ is a lower semi-continuous mapping, then Φ(u) = u − ϕ(u) becomes Φ-contraction [5]. The notions Φ-contraction and weak ϕ-contraction have been studied by many authors, (e.g., [11,25,26,27,13,14,15]. )…”