Yazar "Altun, Ishak" seçeneğine göre listele

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    A NEW METHOD FOR THE CONSTRUCTION OF FRACTALS VIA BEST PROXIMITY POINT THEORY
    (House Book Science-Casa Cartii Stiinta, 2024) Aslantas, Mustafa; Sahin, Hakan; Altun, Ishak
    In this paper, taking into account the P-property in the best proximity point theory, we present a new and interesting construction method that is different from the method given in [3] for fractals. First, we introduce the concept of a generalized iterated function system (in short GIFS) constructed by a finite family of lambda-contractions. Then, we present our main theorem in which sufficient conditions are determined to obtain a fractal which is also an attractor of the mentioned system. Finally, we support our results with some illustrative and attractive examples.
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    A new type of R-contraction and its best proximity points
    (Amer Inst Mathematical Sciences-Aims, 2024) Aslantas, Mustafa; Sahin, Hakan; Altun, Ishak; Saadoon, Taif Hameed Saadoon
    In this paper, we aim to overcome the problem given by Abkar et al. [Abstr. Appl. Anal., 2013 (2013), 189567], and so to obtain real generalizations of fixed point results in the literature. In this direction, we introduce a new class of functions, which include R-functions. Thus, we present a new type of R-contraction and weaken R-contractions that have often been studied recently. We also give a new definition of the P-property. Hence, we obtain some best proximity point results, including fixed point results for the new kind of R-contractions. Then, we provide an example to show the effectiveness of our results. Finally, inspired by a nice and interesting technique, we investigate the existence of a best proximity point of the homotopic mappings with the help of our main result.
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    Optimal solutions of minimization problems via new best proximity point results on quasi metric spaces
    (North Univ Baia Mare, 2025) Alabdullah, Raid Abdulhadi Abdulqader; Sahin, Hakan; Aslantas, Mustafa; Altun, Ishak
    In this paper, we prove some Boyd-Wong type best proximity point results in the setting of quasi metric spaces via Q-functions. First, we modify the fundamental concepts and notations in the best proximity point theory by taking into account unsymmetrical condition of quasi metric spaces. We provide some illustrative examples to examine our notations. Then, we introduce new concepts so called proximal BW-contraction and best BW-contraction mappings. Hence, we obtain best proximity point results for such mappings. Also, we give some nontrivial and comparative examples to show the effectiveness of our results. Next, we provide some corollaries and consequences to partial metric spaces of our main results. Finally, we present an existence and uniqueness result for nonlinear Volterra integral equations.