Some Fixed Point Theory Results for the Interpolative Berinde Weak Operator

Abstract

Partially inspired by [Erdal Karapinar, Ravi Agarwal and Hassen Aydi, Interpolative Reich-Rus-Ćirić type contractions on partial metric spaces, Mathematics 6 (2018), 256] and [V. Berinde, Approximating fixed points of weak contractions using the Picard iteration, Nonlinear Anal. Forum 9(1) (2004), 43-53], we introduce a concept of interpolative Berinde weak contraction, and obtain some existence theorems for mappings satisfying such a contractive definition, and some of its extensions.

From interpolative contractive mappings to generalized Ciric-quasi contraction mappings

“…Recently C. B. Ampadu [1] has defined interpolative Berinde weak operator in his paper. The definition is given as follows:…”

The Fuzzy Interpolative Berinde Weak Mapping Theorem in Metric Space

“…Lemma 1.11. [4] Let A and B be nonempty closed and bounded subsets of a metric space (X, d). If a ∈ A, then d(a, B) ≤ H(A, B).…”

“…Lemma 1.12. [4] Let A and B be nonempty closed and bounded subsets of a metric sapce (X, d), and 0 < α ∈ R. Then for any a ∈ A, there exists b ∈ B such that d(a, b) ≤ H(A, B) + α.…”

The Interpolative Berinde Weak Mapping Theorem in η-Cone Pentagonal Metric Space

“…1 Introduction and Premilinaries Definition 1.1. [4] Let E be a real Banach space with norm • and P be a subset of E. Then P is called a cone if and only if (a) P is closed, nonempty, and P = {θ}, where θ is the zero vector in E;…”

“…Definition 1.2. [4] Given a cone P in a Banach space E, we define on E a partial order with respect to P by x y ⇐⇒ y − x ∈ int(P ).…”