Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Conference Object Citation - WoS: 13Citation - Scopus: 12On Admissible Hybrid Geraghty Contractions(North Univ Baia Mare, 2020) Karapinar, Erdal; Karapınar, Erdal; Petrusel, Adrian; Petrusel, Gabriela; MatematikIn this manuscript, we introduce the notion of admissible hybrid Geraghty contraction and we investigate the existence of fixed points of such mappings in the setting of complete metric spaces. Our results not only extend and generalize several results in the fixed point theory literature, but also unify most of them. We give some corollaries to illustrate the novelty of the main result.Book Part Introduction(Springer Nature, 2022) Karapınar, Erdal; Agarwal, Ravi P.Fixed point theory can be described as a framework for researching and investigating the existence of the solution of the equation f(p) = p for a certain self-mapping f that is defined on a non-empty set X. As is expected, here, p is called the fixed point of the mapping f. On the other side, we may re-consider the fixed point equation f(p) = p as T(p) = f(p) - p= 0 and, accordingly, finding the zeros of the mapping T and finding the fixed point of f becomes an equivalent statement. This equivalence, not only enriches the fixed point theory but also, opens the doors to a wide range of potential applications in the setting of almost all quantitative sciences. For example, let us consider one of the classical open problems of number theory, finding perfect numbers: Let p be a self-mapping on a natural number such that p(n) is the sum of all divisors of n for n> 1. Thus, any fixed points of the function p give a perfect number. In particular, 6 is the smallest perfect numbers, and 2 74207280× (2 74207281- 1 ), with 44, 677, 235 digits, is the biggest known perfect number. © 2022 Elsevier B.V., All rights reserved.Article Common fixed point theorems in cone Banach spaces(Hacettepe Univ, FAC Sci, 2011) Abdeljawad, Thabet; Karapınar, Erdal; Taş, Kenan; Tas, Aysegul; Kumar, AnilRecently, E. Karapınar (Fixed Point Theorems in Cone Banach Spaces, Fixed Point Theory Applications, Article ID 609281, 9 pages, 2009) presented some fixed point theorems for self-mappings satisfying certain contraction principles on a cone Banach space. Here we will give some generalizations of this theorem.Article Generalized (C)-conditions and related fixed point theorems(Pergamon-Elsevier Science Ltd, 2011) Karapınar, Erdal; Taş, Kenan; Karapnar, ErdalIn this manuscript, the notion of C-condition [K. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal. Appl. 340 (2008) 1088-1095] is generalized. Some new fixed point theorems are obtained.