Fixed point results for almost ($ \zeta -\theta _{\rho } $)-contractions on quasi metric spaces and an application

Abstract

<abstract><p>This research paper investigated fixed point results for almost ($ \zeta-\theta _{\rho } $)-contractions in the context of quasi-metric spaces. The study focused on a specific class of ($ \zeta -\theta _{\rho } $)-contractions, which exhibit a more relaxed form of contractive property than classical contractions. The research not only established the existence of fixed points under the almost ($ \zeta -\theta _{\rho } $)-contraction framework but also provided sufficient conditions for the convergence of fixed point sequences. The proposed theorems and proofs contributed to the advancement of the theory of fixed points in quasi-metric spaces, shedding light on the intricate interplay between contraction-type mappings and the underlying space's quasi-metric structure. Furthermore, an application of these results was presented, highlighting the practical significance of the established theory. The application demonstrated how the theory of almost ($ \zeta -\theta _{\rho } $)-contractions in quasi-metric spaces can be utilized to solve real-world problems.</p></abstract>

An Existence Result for Second-Order Boundary-Value Problems via New Fixed-Point Theorems on Quasi-Metric Space

“…In our previous paper [22], by combining the concept of ζ-contraction, which was created with the simulation function used by Khojasteh et al [23] for the first time in fixedpoint theory, and Berinde's almostness idea [24], the concept of almost-ζ-contraction in quasi-metric space was defined, and then the related fixed-point theorem was established. Then, an application was made to a fractional order boundary-value problem.…”