Abstract
Abstract In this paper, we first introduce the concepts of generalized ( ψ , f ) λ -expansive mappings and generalized ( ϕ , g , h ) λ -weakly expansive mappings designed for three mappings. Then we establish some common fixed point results for such two new types of mappings in partial b-metric spaces. These results generalize and extend the main results of Karapınar et al. (J. Inequal. Appl. 2014:22, 2014), Nashine et al. (Fixed Point Theory Appl. 2013:203, 2013) and many comparable results from the current literature. Moreover, some examples and an application to a system of integral equations are given here to illustrate the usability of the obtained results. MSC:47H10, 54H25.
Highlights
1 Introduction and preliminaries Fixed point theory in metric spaces is an important branch of nonlinear analysis, which is closely related to the existence and uniqueness of solutions of differential equations and integral equations
Matthews [ ] introduced the concept of a partial metric space as a part of the study of denotational data for networks and proved that the Banach contraction mapping theorem can be generalized to the partial metric context for applications in program verification
After that, fixed point results in partial metric spaces have been studied by many authors
Summary
Introduction and preliminariesFixed point theory in metric spaces is an important branch of nonlinear analysis, which is closely related to the existence and uniqueness of solutions of differential equations and integral equations.There are many generalizations of the concept of metric spaces in the literature. After that, fixed point results in partial metric spaces have been studied by many authors (see [ – ]). A mapping pb : X × X → R+ is said to be a partial b-metric on X if for all x, y, z ∈ X, the following conditions are satisfied: (pb ) pb(x, x) = pb(y, y) = pb(x, y) if and only if x = y, (pb ) pb(x, x) ≤ pb(x, y), (pb ) pb(x, y) = pb(y, x), (pb )
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