Browsing by Author "Ege O."
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Item Cohomology theory for digital images(2013) Ege O.; Karaca I.In this paper we propose a mathematical framework that can be used for dening cohomology of digital images. We state the Eilenberg-Steenrod axioms and the Universal Coefficient Theorem for this cohomology theory. We show that the Künneth formula doesn't hold. A cup product is dened and its main properties are proved.Item Lefschetz fixed point theorem for digital images(Hindawi Publishing Corporation, 2013) Ege O.; Karaca I.In this article we study the fixed point properties of digital images. Moreover, we prove the Lefschetz fixed point theorem for a digital image. We then give some examples about the fixed point property. We conclude that sphere-like digital images have the fixed point property. ©2013 Ege and Karaca; licensee Springer.Item Relative homology groups of digital images(2014) Ege O.; Karaca I.; Ege M.E.In this paper we are interested in relative homology groups of digital images. Some properties of the Euler characteristics for digital images are given. We also present reduced homology groups for digital images. The main purpose is to obtain some differences between notions in digital topology and algebraic topology. © 2014 NSP Natural Sciences Publishing Cor.Item Some results of the nilpotence in the mod P steenrod algebra(Academic Publishing House, 2014) Ege O.; Karaca I.In this paper, we deal with a collection of left and right ideals of Ap which is the mod p Steenrod algebra. We also prove that for all odd prime numbers p, the nilpotence heights of P2p and P2p+1 are p and p — 1, respectively. © 2014 Academic Publishing House. All rights reserved.Item Applications of the lefschetz number to digital images(Belgian Mathematical Society, 2014) Ege O.; Karaca I.The goal of this paper is to develop some applications of the Lefschetz fixed point theoremto digital images. We also dealwith relative and reduced Lefschetz fixed point theoremfor digital complexes. We give some examples related to the topic. We calculate the degree of the antipodal map for spherelike digital images using fixed point properties. © 2014 Belgian Mathematical Society. All rights reserved.Item Digital homotopy fixed point theory(Elsevier Masson s.r.l., 2015) Ege O.; Karaca I.In this paper, we construct a framework which is called the digital homotopy fixed point theory. We get new results associating digital homotopy and fixed point theory. We also give an application on this theory. © 2015 Académie des sciences.Item Complex valued rectangular b-metric spaces and an application to linear equations(International Scientific Research Publications, 2015) Ege O.In this paper, we introduce complex valued rectangular b-metric spaces. We prove an analogue of Banach contraction principle. We also prove a different contraction principle with a new condition and a fixed point theorem in this space. Finally, we give an application of Banach contraction principle to linear equations. © 2015 All rights reserved.Item Banach fixed point theorem for digital imagesa(International Scientific Research Publications, 2015) Ege O.; Karaca I.In this paper, we prove Banach fixed point theorem for digital images. We also give the proof of a theorem which is a generalization of the Banach contraction principle. Finally, we deal with an application of Banach fixed point theorem to image processing. © 2015 All rights reserved.Item Digital fixed points, approximate fixed points, and universal functions(Universidad Politecnica de Valencia., 2016) Boxer L.; Ege O.; Karaca I.; Lopez J.; Louwsma J.A. Rosenfeld [23] introduced the notion of a digitally continuous function between digital images, and showed that although digital images need not have fixed point properties analogous to those of the Euclidean spaces modeled by the images, there often are approximate fixed point properties of such images. In the current paper, we obtain additional results concerning fixed points and approximate fixed points of digitally continuous functions. Among these are several results concerning the relationship between universal functions and the approximate fixed point property (AFPP). © AGT, UPV, 2016.Item Some properties of digital H-spaces(Turkiye Klinikleri Journal of Medical Sciences, 2016) Ege O.; Karaca I.In this paper, we study certain properties of digital H-spaces. We prove that a digital image that has the same digital homotopy type with any digital H-space is also a digital H-space. We show that the digital fundamental group of a digital H-space is abelian. We give examples that are related to a digital homotopy associative H-space and a κ -contractible digital H-space. Several important applications of digital H-spaces are given in computer vision and image processing. Finally, we deal with the importance of digital H-space in digital topology and image processing. We conclude that any κ-contractible digital image is a digital H-space. © TÜBİTAK.Item Complex valued Gb-metric spaces(Eudoxus Press, LLC, 2016) Ege O.In this paper, we introduce the concept of complex valued Gb-metric spaces. We also prove Banach contraction principle and Kannan’s fixed point theorem in this space. Our result generalizes some well-known results in the fixed point theory. © 2016 by Eudoxus Press,LLC,All rights reserved.Item Digital Fibrations(Springer India, 2017) Ege O.; Karaca I.In this paper, digital fibrations were introduced. Theorems related to digital fibrations were proved. Homology properties of digital fibrations with counter examples were studied and an application for digital fibrations was also described. © 2016, The National Academy of Sciences, India.Item Fixed point theorems and an application in parametric metric spaces(Azerbaijan Mathematical Society, 2017) Ege O.; Karaca I.In this paper, we give concepts of coupled fixed and coupled coincidence point in parametric metric spaces. We also prove a coupled fixed point theorem in this space and give a corollary and an example about the main result. Finally, we give an application to homotopy with proof. © 2010 AZJM All rights reserved.Item Nielsen fixed point theory for digital images(Eudoxus Press, LLC, 2017) Ege O.; Karaca I.In this paper, we introduce the Nielsen fixed point theory in digital images. We also deal with some important properties of the Nielsen number and calculate the Nielsen number of some digital images. We get some new results using digital covering maps and Nielsen number. © 2017 by Eudoxus Press,LLC,All rights reserved.Item Some fixed point theorems in complex valued Gb-metric spaces(Yokohama Publications, 2017) Ege O.In this study, we prove a common fixed point theorem in the complex valued Gb,-metric spaces using a concept of a-series. We also introduce α - ψ-contractive mapping and prove a fixed point theorem in this space. © 2017.Item Some fixed point results on complex valued Gb -metric spaces(Springer-Verlag Italia s.r.l., 2018) Ansari A.H.; Ege O.; Radenović S.In this paper, we prove some fixed point theorems for new type generalized contractive mappings involving C-class function in complex valued Gb-metric spaces. The obtained results generalize and improve some fixed point results in the literature. © 2017, Springer-Verlag Italia.Item Fixed point theorems for various contraction conditions in digital metric spaces(Eudoxus Press, LLC, 2019) Park C.; Ege O.; Kumar S.; Jain D.; Lee J.R.In this paper, we prove the existence of fixed points for Kannan contraction, Chatterjea contraction and Reich contraction in setting of digital metric spaces. These digital contractions are the applications of metric fixed point theory contractions. © 2019 by Eudoxus Press, LLC,all rights reserved.