Fixed Points of Generalized Contractive Multi-valued Mappings

Common coincidence points of R‐weakly commuting maps

“…Therefore, the sequence {d(y 2k+1 ,y 2k )} is monotone nonincreasing. Then, as in the proof of Theorem 2.1 in [2], {y n } is a Cauchy sequence in X. Further, equation (2.2) ensures that {A n } is a Cauchy sequence in CB(X).…”

“…Recently Daffer and Kaneko [2] reaffirmed the positive answer [5] to the conjecture of Reich [8] by giving an alternative proof to Theorem 5 of Mizoguchi and Takahashi [5]. We state Theorem 2.1 of Daffer and Kaneko [2] for convenience.…”

“…We follow the same technique used in [2]. The notion of R-weak commutativity for single-valued mappings was defined by Pant [7] to generalize the concept of commuting and weakly commuting mappings [9].…”

On a conjecture of S. Reich

“…Specifically the question is whether or not the range of T , K(X), can be replaced by CB(X). In response to Reich's conjecture, the following theorem was recently proved by Mizoguchi and Takahashi [4], and other proofs have been given by Daffer and Kaneko [3] and Tong-Huei Chang [2].…”

Fixed points of some set-valued F-contractions

“…In 1995, Daffer [5] provided an alternative and somewhat more straightforward proof of Theorem 1.2. In 2006, Feng and Liu [7] obtained an interesting generalization of Theorem 1.1.…”