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    An Existence Result for Second-Order Boundary-Value Problems via New Fixed-Point Theorems on Quasi-Metric Space
    (Mdpi, 2024) Gungor, Gonca Durmaz; Altun, Ishak
    We introduce the new idea of (alpha - theta(sigma))-contraction in quasi-metric spaces in this paper. For these kinds of mappings, we then prove new fixed-point theorems on left K, left M, and left Smyth-complete quasi-metric spaces. We also apply our results to infer the existence of a solution to a second-order boundary-value problem.
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    Fixed point results for almost (? - ?? )-contractions on quasi metric spaces and an application
    (Amer Inst Mathematical Sciences-Aims, 2024) Gungor, Gonca Durmaz; Altun, Ishak
    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 quasimetric 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.
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    On relaxing the constant of Chatterjea contraction
    (Springernature, 2023) Gungor, Gonca Durmaz; Altun, Ishak
    In this paper, we present some fixed point results for Chatterjea type mappings on metric space. Here, by considering some additional condition we relaxed the contractive constant up to 1.