Yazar "Aslantas, Mustafa" 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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    Best proximity point results of iterated function systems for ?-?-contractions
    (Amer Inst Mathematical Sciences-Aims, 2025) Aslantas, Mustafa; Bachay, Ali Hussein; Sahin, Hakan; Turkoglu, A. Duran
    In this paper, we present two new concepts, called alpha-psi-iterated function system and alpha-psi proximal iterated function system, by using alpha-psi-contractions and alpha-psi-proximal contractions. Hence, we extended and generalized some definitions existing in the literature. We present some results that determine the necessary conditions to obtain a fractal with an attractor in the mentioned systems. Finally, some interesting examples are presented to apply our results.
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    Finding a solution to an optimization problem for the homotopic mappings via some best proximity point results
    (Springernature, 2024) Sahin, Hakan; Aslantas, Mustafa; Simo, Layla Khudhur Saeed
    In this paper, we introduce the concepts of the modified weak P-rho-property and Suzuki type F-alpha,F-rho-contraction mapping on quasi metric spaces. Then, we prove some left and right best proximity point results for such mappings on quasi metric spaces. Hence, we give an affirmative answer to the question in Altun (Journal of Nonlinear and Convex Analysis 16(4):659-666, 2015) for closed and bounded valued mappings. Also, we provide some comparative examples to show the effectiveness of the results in the current paper. Finally, we obtain a best proximity point result for the homotopic mappings by using our results.
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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.
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    Some best proximity point results on best orbitally complete quasi metric spaces
    (Amer Inst Mathematical Sciences-Aims, 2023) Aslantas, Mustafa; Sahin, Hakan; Al-Okbi, Raghad Jabbar Sabir
    In this paper, we first introduce the concepts of d- and d(-1)-proximal Ciric contraction mappings. Also, we present new definitions and notations by taking into account the lack of symmetry property of quasi-metric spaces. Moreover, we give some examples to support our definitions and notations. Then, we prove some right and left best proximity point results for these mappings on best orbitally complete quasi-metric spaces. Hence, we obtain some generalizations of famous results in the literature.
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    Some Extended Results for Multivalued F-Contraction Mappings
    (Mdpi, 2023) Sahin, Hakan; Aslantas, Mustafa; Nasir, Ali Abdulkareem Nasir
    In this study, we introduce a new notion, so-called KW-type F-contraction mapping, inspired by the ideas of Wardowski and Klim-Wardowski. Then, we investigate the existence of a best proximity point for such mappings by considering a new family, which is larger than the family of functions that is often used in fixed-point results for multivalued mappings. To demonstrate the effectiveness of our result, we also give a comparative example to which similar results in the literature cannot be applied. Moreover, we present an application of our main result to homotopic mappings.