Abstract
Based on a recent paper of Beg and Pathak (Vietnam J. Math. 46(3):693–706, 2018), we introduce the concept of mathcal{H}_{q}^{+}-type Suzuki multivalued contraction mappings. We establish a fixed point theorem for this type of mappings in the setting of complete weak partial metric spaces. We also present an illustrated example. Moreover, we provide applications to a homotopy result and to an integral inclusion of Fredholm type. Finally, we suggest open problems for the class of 0-complete weak partial metric spaces, which is more general than complete weak partial metric spaces.
Highlights
Throughout this paper, we use following notation: N is the set of all natural numbers, R is the set of all real numbers, and R+ is the set of all nonnegative real numbers.Definition 1.1 ([2]) A partial metric on a nonempty set X is a function p : X × X → R+ such that, for all x, y, z ∈ X:(P1) x = y if and only if p(x, x) = p(x, y) = p(y, y); (P2) p(x, x) ≤ p(x, y); (P3) p(x, y) = p(y, x); (P4) p(x, y) ≤ p(x, z) + p(z, y) – p(z, z).The pair (X, p) is called a partial metric space
Beg and Pathak [1] introduced a weaker form of partial metrics called a weak partial metric
Examples of weak partial metric spaces [1] are: (1) (R+, q), where q : R+ × R+ → R+ is defined as q(x, y) = |x – y| + 1 for x, y ∈ R+
Summary
Throughout this paper, we use following notation: N is the set of all natural numbers, R is the set of all real numbers, and R+ is the set of all nonnegative real numbers. Definition 1.1 ([2]) A partial metric on a nonempty set X is a function p : X × X → R+ such that, for all x, y, z ∈ X:. The pair (X, p) is called a partial metric space. A function q : X × X → R+ is called a weak partial metric on X if for all x, y, z ∈ X, the following conditions hold:. The pair (X, q) is called a weak partial metric space. Examples of weak partial metric spaces [1] are:. (3) (R+, q), where q : R+ × R+ → R+ is defined as q(x, y) = max{x, y} + e|x–y| + 1 for x, y ∈ R+
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