• Honam Mathematical Journal
• /
• v.39 no.2
• /
• pp.161-174
• /
• 2017

The objective of this manuscript is to continue the study of fixed point theory in dislocated metric spaces, introduced by Hitzler et al. [12]. Concretely, we apply the concept of dislocated metric spaces and obtain theorems asserting the existence of common fixed points for a pair of mappings satisfying new generalized rational contractions in such spaces.

• Korean Journal of Mathematics
• /
• v.26 no.4
• /
• pp.809-822
• /
• 2018

In this paper, we introduce complex valued dislocated metric spaces. We prove Banach contraction principle, Kannan and Chatterjea type fixed point theorems in this new space. Moreover, we give some applications of the results to differential equations and iterated functions.

• Korean Journal of Mathematics
• /
• v.32 no.2
• /
• pp.245-257
• /
• 2024

In this paper, we prove some new fixed point results for expansive type mappings in complete dislocated quasi-metric space. A common fixed point result is also established considering such mappings. Suitable examples are provided to demonstrate our results. The solution to a system of Fredholm integral equations is also established to show the applicability of our results.

• Kyungpook Mathematical Journal
• /
• v.60 no.4
• /
• pp.767-779
• /
• 2020

This paper primarily discusses and proves the Hyers-Ulam stability of three types of polynomial equations: xn+a1x+a0 = 0, anxn+⋯+a1x+a0 = 0, and the infinite series equation: ${\sum\limits_{i=0}^{\infty}}\;a_ix^i=0$, in dislocated quasi-metric spaces under certain conditions by constructing contraction mappings and using fixed-point methods. We present an example to illustrate that the Hyers-Ulam stability of polynomial equations in dislocated quasi-metric spaces do not work when the constant term is not equal to zero.

• Nonlinear Functional Analysis and Applications
• /
• v.27 no.2
• /
• pp.271-287
• /
• 2022

In this article, we shall prove a common fixed point theorem for two weakly compatible self-maps 𝒫 and 𝔔 on a dislocated metric space (M, d^*) satisfying the following ξ-weakly expansive condition: d^*(𝒫c, 𝒫d) ≥ d^* (𝔔c, 𝔔d) + ξ(∧(𝔔c, 𝔔d)), ∀ c, d ∈ M, where $${\wedge}(Qc,\;Qd)=max\{d^*(Qc,\;Qd),\;d^*(Qc,\;\mathcal{P}c),\;d^*(Qd,\;\mathcal{P}d),\;\frac{d^*(Qc,\;\mathcal{P}c){\cdot}d^*(Qd,\;\mathcal{P}d)}{1+d^*(Qc,\;Qd)},\;\frac{d^*(Qc,\;\mathcal{P}c){\cdot}d^*(Qd,\;\mathcal{P}d)}{1+d^*(\mathcal{P}c,\;\mathcal{P}d)}\}$$. Also, we have proved common fixed point theorems for the above mentioned weakly compatible self-maps along with E.A. property and (CLR) property. An illustrative example is also provided to support our results.