Yazar "Altun, İshak" seçeneğine göre listele
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Öğe A new approach to fractals via best proximity point(Pergamon-Elsevier Science Ltd, 2021) Altun, İshak; Şahin, Hakan; Aslantaş, 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) Aslantaş, Mustafa; Şahin, Hakan; Altun, İshakIn 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 Presic Type Theorems with Applications to Second Order Boundary Value Problems(Univ Nis, Fac Sci Math, 2021) Altun, İshak; 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 An Existence Result for Second-Order Boundary-Value Problems via New Fixed-Point Theorems on Quasi-Metric Space(Mdpi, 2024) Güngör, Gonca Durmaz; Altun, İshakWe 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 Application of the Leray-Schauder alternative to nonlinear singular operator equations(Pergamon-Elsevier Science Ltd, 2009) Altun, İshak; Koca, KerimIn this paper, we study the problem of existence of solution of nonlinear singular integral equations of the form {w(z) = Phi(z) + T(G)F (., w (.), h (.)) (z) h(z) = Phi'(z) + Pi(G)F (., w (.), h (.)) (z), z is an element of G subset of C. (C) 2009 Elsevier Ltd. All rights reserved.Öğe Best proximity and best periodic points for proximal nonunique contractions(Springer Basel Ag, 2021) Şahin, Hakan; Aslantaş, Mustafa; Altun, İshakTaking into account nonunique fixed point and periodic point results of Ciric (Institut Mathematique 17, 52-58, 1974) and best proximity point results in the literature, we introduce the concept of proximal nonunique contraction for nonself mappings. Then, we obtain some nonunique best proximity point theorems. Further, we describe the concept of best periodic point of nonself mappings and we present some nonunique best periodic point results. We also provide many examples to show that our new concepts are meaningful and to support our theorems. Additionally, we present a new notion for the nonself mapping H called property P-b, and then we provide some results including sufficient conditions to guarantee that H has the property P-b.Öğe A common fixed point theorem for multivalued Ćirić type mappings with new type compatibility(Ovidius Univ Press, 2009) Altun, İshakKaneko and Sessa defined the concept of compatibility for multivalued mappings with Hausdorff metric and proved a coincidence point theorem. After then, Pathak defined the concept of weak compatibility and proved a coincidence theorem. In the present work, we define a new type compatibility for multivalued mappings with Hausdorff metric. This new type compatibility is different from compatibility and weak compatibility. We give a common fixed point theorem for multivalued mappings using the new type compatibility.Öğe A common fixed point theorem for weakly compatible mappings in symmetric spaces satisfying an implicit relation(Soc Matematica Mexicana, 2007) Türkoğlu, Duran; Altun, İshakIn this paper, we prove a common fixed point theorem for weakly compatible mappings in symmetric spaces satisfying an implicit relation and a fixed point thorems under strict contractive conditions, J. Math. Anal. Appl. 270 (2002) 181-188]. Our theorem generalizes Theorem 1 of [A. Aliouche, A common fixed point theorem for weakly compatible mappings in symmetric spaces satisfying a contractive condition of integral type Theorem 2.2 of [M. Aamri, D. El Moutawakil, Common fixed points under contractive conditions in symmetric spaces, Appl. Math. E-Notes 3 (2003) 156-162] and Theorem 2 of [M. Aamri, D. El Moutawakil, Some new common fixed point thorems under strict contractive conditions, J. Math. Anal. Appl. 270 (2002) 181-188].Öğe Common fixed points of Ciric-type contractions on partial metric spaces(Kossuth Lajos Tudomanyegyetem, 2013) Abbas, Mujahid; Altun, İshak; Romaguera, SalvadorWe obtain a common fixed point theorem of Boyd-Wong type for four mappings satisfying a Ciric-type contraction on a complete partial metric space. Our result generalizes and unifies, among others, the very recent results of L. CIRIC, B. SAMET, H. AYDI and C. VETRO [Common fixed points of generalized contractions on partial metric spaces and an application, Appl. Math. Comput., 218 (2011), 2398-2406], S. ROMAGUERA [Fixed point theorems for generalized contractions on partial metric spaces, Topology Appl., 159 (2012), 194-199], T. ABDELJAWAD, E. KARAPINAR and K. TAS [Existence and uniqueness of a common fixed point on partial metric spaces, Appl. Math. Lett. 24 (2011), 1900-1904], and D. ILIC, V. PAVLOVIC and V. RAKOCEVIC [Some new extensions of Banach's contraction principle to partial metric space, Appl. Math. Lett. 24 (2011), 1326-1330].Öğe A fixed fuzzy point for fuzzy mappings in complete metric spaces(Univ Osijek, Dept Mathematics, 2008) Sedghi, Shaban; Shobe, Nabi; Altun, İshakIn this paper we prove a fixed point theorem for fuzzy mappings over a complete metric space.Öğe Fixed Point Results for Mixed Multivalued Mappings of Feng-Liu Type on Mb-Metric Spaces(Springer International Publishing Ag, 2019) Şahin, Hakan; Altun, İshak; Türkoğlu, Duran[Abstract No tAvailable]Öğe A Fixed Point Theorem for Multivalued Mappings with δ-Distance(Hindawi Publishing Corporation, 2014) Acar, Özlem; Altun, İshakWe mainly study fixed point theorem for multivalued mappings with delta-distance using Wardowski's technique on complete metric space. Let (X, d) be a metric space and let B(X) be a family of all nonempty bounded subsets of X. Define delta : B(X) x B(X) -> R by delta(A, B) = sup {d(a, b): a is an element of A, b is an element of B}. Considering delta-distance, it is proved that if (X, d) is a complete metric space and T : X -> B(X) is a multivalued certain contraction, then T has a fixed point.Öğe A Fixed Point Theorem for New Type Contractions on Weak Partial Metric Spaces(Springer Singapore Pte Ltd, 2015) Acar, Özlem; Altun, İshak; Durmaz, GoncaRecently, Karapinar and Romaguera (Filomat 27: 1305-1314, 2013) have introduced a new type contraction on partial metric spaces, and they have obtained a nonunique fixed point result. Then Romaguera (Math. Sci. Appl. E-Notes 1: 1-8, 2013) used this contraction to obtain some multivalued fixed point results on partial metric spaces. In the present work, we give a fixed point result on weak partial metric spaces using this new idea.Öğe Fixed point theorem for sequences of maps(Walter de Gruyter GmbH, 2005) Turkoglu, D.; Altun, İshak; Fisher, B.In this paper, we prove a common fixed point theorem for sequences of maps under the condition of compatible mappings on complete metric space. We extend and generalize several fixed point theorems on complete metric space. © 2005 Warsaw University. All rights reserved.Öğe Fixed Point Theorems for Generalized Weakly Contractive Condition in Ordered Metric Spaces(Springer International Publishing Ag, 2011) Nashine, Hemant Kumar; Altun, İshakFixed point results with the concept of generalized weakly contractive conditions in complete ordered metric spaces are derived. These results generalize the existing fixed point results in the literature.Öğe Fixed Point Theorems for Monotone Mappings on Partial Metric Spaces(Springer International Publishing Ag, 2011) Altun, İshak; Erduran, AliMatthews (1994) introduced a new distance p on a nonempty set X, which is called partial metric. If (X,p) is a partial metric space, then p(x,x) may not be zero for x is an element of X. In the present paper, we give some fixed point results on these interesting spaces.Öğe Fixed point theorems for weak contractions in the sense of Berinde on partial metric spaces(Elsevier Science Bv, 2012) Altun, İshak; Acar, ÖzlemIn this paper, we introduce the notion of (delta . L) weak contraction and (phi . L) weak contraction in the sense of Berinde in partial metric space. Then we give some fixed point results in partial metric space using these new concepts. (C) 2012 Elsevier B.V. All rights reserved.Öğe Fixed Point Theorems on Complete Quasi Metric Spaces Via C-class and A-Class Functions(UNIV MARAGHEH, 2020) Yalçın, M. Tugba; Şimşek, Hakan; Altun, İshakIn this paper, we present some fixed point theorems for single valued mappings on K-complete, M-complete and Symth complete quasi metric spaces. Here, for contractive condition, we consider some altering distance functions together with functions belonging to C-class and A-class. At the same time, we will consider two different type M functions in contractive conditions because the quasi metric does not provide the symmetry property. Finally, we show that our main results includes many fixed point theorems presented on both complete metric and complete quasi metric spaces in the literature. We also provide an illustrative example to show importance of our results.Öğe Fixed points of weakly compatible maps satisfying a general contractive condition of integral type(Springer, 2007) Altun, İshak; Türkoğlu, Duran; Rhoades, Billy E.We prove a fixed point theorem for weakly compatible maps satisfying a general contractive condition of integral type. Copyright (C) 2007.Öğe Generalized contractions on partial metric spaces(Elsevier Science Bv, 2010) Altun, İshak; Sola, Ferhan; Şimşek, HakanIn the present paper, we give some fixed point theorems for generalized contractive type mappings on partial metric space. Also, a homotopy result is given. (C) 2010 Elsevier B.V. All rights reserved.
