ω-Interpolative Ćirić-Reich-Rus-Type Contractions

Abstract

In this paper, using the concept of ω -admissibility, we prove some fixed point results for interpolate Ćirić-Reich-Rus-type contraction mappings. We also present some consequences and a useful example.

Fixed-Points of Interpolative Ćirić-Reich–Rus-Type Contractions in b-Metric Spaces

“…Next, we prove an existence theorem for the aforementioned contraction where continuity of the self-map is assumed. It is to mention that the following theorem generalizes Theorem 1 due to Aydi et al [16], which may be obtained by taking s = 1 in the definition of the concerned bMS. The first half of the proof adopts similar techniques as that of [16].…”

“…It is to mention that the following theorem generalizes Theorem 1 due to Aydi et al [16], which may be obtained by taking s = 1 in the definition of the concerned bMS. The first half of the proof adopts similar techniques as that of [16]. The similar portion of the proof is retained here verbatim due to clarity of presentation.…”

“…In our next result, we drop the continuity of the self-map I, but we assume that ω is satisfying the Condition (A). The following result may be considered as a variant of Theorem 2 due to Aydi et al [16]. Proof.…”

“…Proof. Invoking a similar procedure as in the proof of Theorem 3, we can assert that the condition (16) is true, that is, that the sequence {µ n } constructed in such a way is convergent. Because of Condition (A), there exists a subsequence {µ n k } of µ n such that ω(µ n k , µ) ≥ 1 for each k.…”

“…The following condition is used (see [16]) when the continuity assumption of the underlying contractive map is to be avoided. Definition 4.…”