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Öğe A Fixed Point Result for ??contraction on M?metric Spaces(American Institute of Physics Inc., 2022) Taş, Maide Gökşin; Türkoğlu, Duran; Altun, IshakThe purpose of this note is to prove an existence theorem of fixed point for ?-type contraction in the setting of Mcomplete M-metric spaces. The results presented in the paper improve and extend the corresponding results in Banach [6], Asadi at. al. [5], Jleli and Samet [12]. We give an example to illustrate this fact. © 2022 American Institute of Physics Inc.. All rights reserved.Öğe A new approach to fractals via best proximity point(Pergamon-Elsevier Science Ltd, 2021) Altun, Ishak; Sahin, Hakan; Aslantas, MustafaIn 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.Öğe 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, IshakIn 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.Öğe A new result of preši? type theorems with applications to second order boundary value problems(University of Nis, 2021) Altun, Ishak; Qasim, Muhammad; Olgun, MuratIn this paper, taking into account the recent contractive technique we present a new result of Preši? type fixed point theorems. Then, we provide a comparative example to put forth the validity of our theoretical result. Finally, considering a special case of the main theorem, we give some existence results for the second order two point boundary value problems. © 2021, University of Nis. All rights reserved.Öğe A New Result of Presic Type Theorems with Applications to Second Order Boundary Value Problems(Univ Nis, Fac Sci Math, 2021) Altun, Ishak; Qasim, Muhammad; Olgun, MuratIn this paper, taking into account the recent contractive technique we present a new result of Presic type fixed point theorems. Then, we provide a comparative example to put forth the validity of our theoretical result. Finally, considering a special case of the main theorem, we give some existence results for the second order two point boundary value problems.Öğe 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 SaadoonIn 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.Öğe Almost Picard Operators(Amer Inst Physics, 2019) Altun, Ishak; Hancer, Hatice AslanThe concept of Picard operator is one of the most important concept of fixed point theory. As known, a self mapping T of a metric space X is called Picard operator (PO) if it has unique fixed point and every Picard iteration sequence converges to this fixed point. There are some weaker forms of PO in the literature as weakly Picard operator (WPO) and pseudo Picard operator (PPO). In this study, we present a new kind of PO as almost Picard operator (APO) and we show the differences from the others. Then we show that every continuous P-contractive self mapping of a compact metric space is APO. Also we present some open problems.Öğe An Existence Result for Second-Order Boundary-Value Problems via New Fixed-Point Theorems on Quasi-Metric Space(Mdpi, 2024) Gungor, Gonca Durmaz; Altun, IshakWe 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.Öğe Caristi's Type Mappings On Complete Partial Metric Spaces(House Book Science-Casa Cartii Stiinta, 2013) Acar, Ozlem; Altun, Ishak; Romaguera, SalvadorWe introduce a new type of Caristi's mapping on partial metric spaces and show that a partial metric space is complete if and only if every Caristi mapping has a fixed point. From this result we deduce a characterization of bicomplete weightable quasi-metric spaces. Several illustrative examples are given.Öğe Caristi-Type Fixed Point Theorems and Some Generalizations on M-Metric Space(MALAYSIAN MATHEMATICAL SCIENCES SOC, 2020) Altun, Ishak; Sahin, Hakan; Turkoglu, DuranIn 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.Öğe Characterizations of partial metric completeness in terms of weakly contractive mappings having fixed point(Univ Belgrade, Fac Electrical Engineering, 2012) Altun, Ishak; Romaguera, SalvadorWe characterize both complete and 0-complete partial metric spaces in terms of weakly contractive mappings having a fixed point. Our results extend a well-known characterization of metric completeness due to SUZUKI and TAKAHASHI to the partial metric framework.Öğe Ciric type cyclic contractions and their best cyclic periodic points(North Univ Baia Mare, 2022) Aslantas, Mustafa; Sahin, Hakan; Altun, IshakIn 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.Öğe Ciric Type Generalized F-contractions on Complete Metric Spaces and Fixed Point Results(Univ Nis, Fac Sci Math, 2014) Minak, Gulhan; Helvaci, Asuman; Altun, IshakRecently, Wardowski [15] introduced the concept of F-contraction on complete metric space. This type contraction is proper generalization of ordinary contraction. In the present paper, we give some fixed point results for generalized F-contractions including Ciric type generalized F-contraction and almost F-contraction on complete metric space. Also, we give some illustrative examples.Öğe Common fixed point of a power graphic (F, psi)-contraction pair on partial b-metric spaces with application(Inst Mathematics & Informatics, 2017) Singh, Deepak; Chauhan, Varsha; Altun, IshakThe aim of this paper is to inaugurate power graphic (F, psi)-contraction pair and to establish fixed point results for such mappings defined on partial b-metric spaces endowed with a graph. It is mentioning that, first time, we launch a class of fixed point results in the frame of partial b-metric spaces involving a graph. Results of this paper extend and generalize known results from metric, partial metric, and partial b-metric spaces in partial b-metric spaces with a graph. Further, appropriate examples are presented to emphasize the utility of the obtained results. At the end, an attempt to correlate the given work with application is turned out as solution for an integral equation.Öğe Common Fixed Point Result In Ordered Cone Metric Spaces(Hacettepe Univ, Fac Sci, 2013) Abbas, Mujahid; Altun, IshakFixed point and common fixed point results for generlized contractive mappings are obtianed in ordered cone metric spaces.Öğe Common Fixed Point Results for Generalized Wardowski Type Contractive Multi-Valued Mappings(Mdpi, 2019) Isik, Huseyin; Parvaneh, Vahid; Mohammadi, Babak; Altun, IshakIn this paper, we introduce generalized Wardowski type quasi-contractions called alpha-(phi,Omega)-contractions for a pair of multi-valued mappings and prove the existence of the common fixed point for such mappings. An illustrative example and an application are given to show the usability of our results.Öğe A Common Fixed Point Theorem For New Type Compatible Maps On Partial Metric Spaces(Math Soc Serbia-Drustvo Matematicara Srbije, 2015) Acar, Ozlem; Altun, IshakIn this paper, we introduce the concept of compatible maps of type (I) and of type (II) in partial metric space and prove a common fixed point theorem for four such maps on complete partial metric space.Öğe A common fixed point theorem on ordered metric spaces(Springer Singapore Pte Ltd, 2012) Nashine, Hemant Kumar; Altun, IshakA common fixed point result for weakly increasing mappings satisfying generalized contractive type of Zhang in ordered metric spaces are derived.Öğe A Common Fixed Point Theorem On Ordered Partial S-Metric Spaces And Applications(KANGWON-KYUNGKI MATHEMATICAL SOC, 2020) Soursouri, Sima; Shobkolaei, Nabi; Sedghi, Sahaban; Altun, IshakA common fixed point result for weakly increasing mappings satisfying generalized contractive type in ordered partial S-metric spaces are derived. Also as an application of our results we consider a couple integral equations.to guarantee the existence of a common solution.Öğe Common fixed point theorems for non compatible mappings in fuzzy metric spaces(Int Center Scientific Research & Studies, 2009) Abbas, Mujahid; Altun, Ishak; Gopal, DhananjayCommon fixed point theorems for the class of four non compatible mappings in fuzzy metric spaces are proved. These results are proved without exploiting the notion of continuity and without imposing any condition on t-norm.
