Yazar "Sahin, Hakan" seçeneğine göre listele

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    A new approach to fractals via best proximity point
    (Pergamon-Elsevier Science Ltd, 2021) Altun, Ishak; Sahin, Hakan; Aslantas, Mustafa
    In this paper, we present a new approach to fractals through best proximity points, inspired by the remarkable relationship between fixed point theory and fractal theory. In this way, we introduce the concept of proximal IFS generated by a finite set of proximal contractions to expand the concept of IFS, one of the most common methods of creating fractals. Thus, as a new method of obtaining fractal we present a result showing that the proximal IFS has a unique best attractor under the certain conditions on metric spaces. To support our new result an illustrative example is given. (c) 2021 Elsevier Ltd. All rights reserved.
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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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    Caristi-Type Fixed Point Theorems and Some Generalizations on M-Metric Space
    (MALAYSIAN MATHEMATICAL SCIENCES SOC, 2020) Altun, Ishak; Sahin, Hakan; Turkoglu, Duran
    In this paper, taking into account Caristi's fixed point results on both metric spaces and partial metric spaces, we present their some extensions and generalizations on M-metric spaces. First, by providing a counter example, we noticed that a recent result on Caristi-type fixed point theorem on M-metric space is not suitable. Then we propounded two versions of Caristi's inequality and proved some related fixed point results on M -metric space.
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    Ciric type cyclic contractions and their best cyclic periodic points
    (North Univ Baia Mare, 2022) Aslantas, Mustafa; Sahin, Hakan; Altun, Ishak
    In the present paper, by introducing a new notion named as nonunique cyclic contractions, we give some best proximity point results for such mappings. Then, we indicate the shortcoming of the concept of best periodic proximity point which is defined for cyclic mapping by giving a simple example. To overcome this deficiency, we give a more suitable definition named as best cyclic periodic point. Finally, we obtain some best cyclic periodic point theorems, including the famous periodic point result of Ciric [8], for nonunique cyclic contractions. We also provide some illustrative and comparative examples to support our results.
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    Feng-Liu type approach to best proximity point results for multivalued mappings
    (SPRINGER BASEL AG, 2020) Sahin, Hakan; Aslantas, Mustafa; Altun, Ishak
    Let (X, d) be a metric space, A and B be two nonempty subsets of X, and T : A. B be a mapping. In this case, since the equation x = Tx may not have an exact solution, it is meaningful to explore the approximate solution. The best approximation results in the literature are related to investigate such solutions. Further, best proximity point theorems not only investigate the approximate solution of the equation x = Tx, but also an optimal solution of the minimization problem min{d(x, Tx) : x is an element of A}. Such points are called the best proximity points of the mapping T. In this paper, considering the Feng and Liu's approach in fixed point theory, we present some new results for best proximity points of nonself multivalued mappings.
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    Fixed Point Results for Mixed Multivalued Mappings of Feng-Liu Type on Mb-Metric Spaces
    (Springer International Publishing Ag, 2019) Sahin, Hakan; Altun, Ishak; Turkoglu, Duran
    [Abstract No tAvailable]
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    Fixed Point Results For Multivalued Mappings Of Feng-Liu Type On M-Metric Spaces
    (Mathematical Research Press-Math Res, 2018) Altun, Ishak; Sahin, Hakan; Turkoglu, Duran
    In this paper, we present some fixed point theorems for multivalued mappings of Feng-Liu type on complete M-metric spaces. Some illustrative examples are also provided to support our main results.
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    ?iri? type cyclic contractions and their best cyclic periodic points
    (SINUS Association, 2022) Aslantas, Mustafa; Sahin, Hakan; Altun, Ishak
    In the present paper, by introducing a new notion named as nonunique cyclic contractions, we give some best proximity point results for such mappings. Then, we indicate the shortcoming of the concept of best periodic proximity point which is defined for cyclic mapping by giving a simple example. To overcome this deficiency, we give a more suitable definition named as best cyclic periodic point. Finally, we obtain some best cyclic periodic point theorems, including the famous periodic point result of ?iri? [8], for nonunique cyclic contractions. We also provide some illustrative and comparative examples to support our results. © 2022, SINUS Association. All rights reserved.
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    Some fixed point theorems for contractive mapping in ordered vector metric spaces
    (Int Scientific Research Publications, 2017) Cevik, Cuneyt; Altun, Ishak; Sahin, Hakan; Ozekena, Cetin Cemal
    In this paper, considering an order relation on a vector metric space which is introduced by Cevik and Altun in 2009, we present some fundamental fixed point results. Then, we provide some nontrivial examples show that the investigation of this work is significant. (C) 2017 All rights reserved.
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    Two fixed point results for multivalued F-contractions on M-metric spaces
    (Springer-Verlag Italia Srl, 2019) Sahin, Hakan; Altun, Ishak; Turkoglu, Duran
    In this article, by considering Feng-Liu's technique, we present new fixed point results for multivalued mappings which are regarding to F-contraction on M-complete M-metric space. Then, we provide some nontrivial examples showing that our main results proper extension of some earlier results in the literature.