Browsing by Author "Ege, O"

Now showing 1 - 16 of 16
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    Digital Fibrations
    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.
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    Banach fixed point theorem for digital images
    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. (C) 2015 All rights reserved.
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    Some fixed point results on complex valued Gb-metric spaces
    Ansari, AH; Ege, O; Radenovic, S
    In this paper, we prove some fixed point theorems for new type generalized contractive mappings involving -class function in complex valued -metric spaces. The obtained results generalize and improve some fixed point results in the literature.
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    SOME RESULTS OF THE NILPOTENCE IN THE MOD P STEENROD ALGEBRA
    Ege, O; Karaca, I
    In this paper, we deal with a collection of left and right ideals of A(p) which is the mod p Steenrod algebra. We also prove that for all odd prime numbers p, the nilpotence heights of P-2P and P2P+1 are p and p - 1, respectively.
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    Digital homotopy fixed point theory
    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. (C) 2015 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
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    Applications of the Lefschetz Number to Digital Images
    Ege, O; Karaca, I
    The goal of this paper is to develop some applications of the Lefschetz fixed point theorem to digital images. We also deal with relative and reduced Lefschetz fixed point theorem for digital complexes. We give some examples related to the topic. We calculate the degree of the antipodal map for sphere-like digital images using fixed point properties.
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    Cohomology Theory for Digital Images
    Ege, O; Karaca, I
    In this paper we propose a mathematical framework that can be used for de fining cohomology of digital images. We state the Eilenberg-Steenrod axioms and the Universal Coefficient Theorem for this cohomology theory. We show that the Kunneth formula doesn't hold. A cup product is defined and its main properties are proved.
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    GRAPH TOPOLOGY ON FINITE DIGITAL IMAGES
    Ege, O; Karaca, I
    The main goal of this work is to present a topology, called a graph topology, on finite digital images. We deal with some properties of this topology such as k-connectivity and digital continuous mapping. We finally show that the property of being graph topology is a topological invariant between digital isomorphic finite digital images.
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    Lefschetz fixed point theorem for digital images
    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.
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    Complex Valued Gb-Metric Spaces
    Ege, O
    In this paper, we introduce the concept of complex valued Gb-metric spaces. We also prove Banach contraction principle and Kaim an's fixed point theorem in this space. Our result generalizes some well-known results in the fixed point theory.
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    Complex valued rectangular b-metric spaces and an application to linear equations
    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. (C) 2015 All rights reserved.
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    SOME FIXED POINT THEOREMS IN COMPLEX VALUED Gb-METRIC SPACES
    Ege, O
    In this study, we prove a common fixed point theorem in the complex valued G(b)-metric spaces using a concept of alpha-series. We also introduce alpha - psi-contractive mapping and prove a fixed point theorem in this space.
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    Digital fixed points, approximate fixed points, and universal functions
    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).
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    Nielsen fixed point theory for digital images
    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.
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    Fixed point theorems and an Application in Parametric Metric Spaces
    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.
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    Relative Homology Groups of Digital Images
    Ege, O; Karaca, I; Ege, ME
    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.