WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 16Citation - Scopus: 22Some Fixed Point Results for Tac-Type Contractive Mappings(Hindawi Ltd, 2016) Tas, Kenan; Ansari, Arslan Hojat; Chandok, SumitWe prove some fixed point results for new type of contractive mappings using the notion of cyclic admissible mappings in the framework of metric spaces. Our results extend, generalize, and improve some well-known results from literature. Some examples are given to support our main results.Article Citation - WoS: 59Citation - Scopus: 68Generalized (c)-Conditions and Related Fixed Point Theorems(Pergamon-elsevier Science Ltd, 2011) Karapinar, Erdal; Tas, KenanIn 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. (C) 2011 Elsevier Ltd. All rights reserved.Article Further Results on the Neutrix Composition of Distributions Involving the Delta Function and the Function Cosh+<sup>-1</Sup> (x<sup>1/R<(de Gruyter Poland Sp Z O O, 2019) Tas, Kenan; Fisher, BrianThe neutrix composition F(f(x)) of a distribution F(x) and a locally summable function f(x) is said to exist and be equal to the distribution h(x) if the neutrix limit of the sequence {F-n(f(x))) is equal to h(x), where F-n(x) = F(x) * delta(n)(x) and {delta(n)(x)} is a certain sequence of infinitely differentiable functions converging to the Dirac delta-function delta(x). The function cosh(+)(-1)(x + 1) is defined by cosh(+)(-1)(x+ 1) = H(x) cosh(-1)(vertical bar x vertical bar + 1), where H(x) denotes Heaviside's function. It is then proved that the neutrix composition delta((s))[cosh(+)(-1)(x(1/r) + 1)] exists and delta((s))[cosh(+)(-1)(x(1/r) + 1] = Sigma(s-1)(k=0) Sigma(kr+r-1)(j=0) Sigma(j)(i=0) (-1)(kr+r+s-j-1)r/2(j+2) ((kr + r -1)(j)) ((j)(i)) [(j - 2i + 1)(s) - (j - 2i -1)(s)]delta((k))(x) for r, s = 1, 2, .... Further results are also proved. Our results improve, extend and generalize the main theorem of [Fisher B., Al-Sirehy F., Some results on the neutrix composition of distributions involving the delta function and the function cosh(+)(-1) (x + 1), Appl. Math. Sci. (Ruse), 2014, 8(153), 7629-7640].Article Citation - WoS: 6Citation - Scopus: 6On Square Integrable Solutions of a Fractional Differential Equation(Elsevier Science inc, 2018) Ugurlu, Ekin; Baleanu, Dumitru; Tas, KenanIn this paper we construct the Weyl-Titchmarsh theory for the fractional Sturm-Liouville equation. For this purpose we used the Caputo and Riemann-Liouville fractional operators having the order is between zero and one. (C) 2018 Elsevier Inc. All rights reserved.Article Citation - WoS: 5Citation - Scopus: 4Regular Fractional Differential Equations in the Sobolev Space(Walter de Gruyter Gmbh, 2017) Ugurlu, Ekin; Baleanu, Dumitru; Tas, KenanIn this paper regular fractional Sturm-Liouville boundary value problems are considered. In particular, new inner products are described in the Sobolev space and a symmetric operator is established in this space.Article Citation - WoS: 11Citation - Scopus: 15Fixed Points for Cyclic Orbital Generalized Contractions on Complete Metric Spaces(de Gruyter Open Ltd, 2013) Tas, Kenan; Karapinar, Erdal; Romaguera, SalvadorWe prove a fixed point theorem for cyclic orbital generalized contractions on complete metric spaces from which we deduce, among other results, generalized cyclic versions of the celebrated Boyd and Wong fixed point theorem, and Matkowski fixed point theorem. This is done by adapting to the cyclic framework a condition of Meir-Keeler type discussed in [Jachymski J., Equivalent conditions and the Meir-Keeler type theorems, J. Math. Anal. Appl., 1995, 194(1), 293-303]. Our results generalize some theorems of Kirk, Srinavasan and Veeramani, and of Karpagam and Agrawal.Article Citation - WoS: 79Citation - Scopus: 82A Generalized Contraction Principle With Control Functions on Partial Metric Spaces(Pergamon-elsevier Science Ltd, 2012) Abdeljawad, Thabet; Karapinar, Erdal; Tas, KenanPartial metric spaces were introduced by Matthews in 1994 as a part of the study of denotational semantics of data flow networks. In this article, we prove a generalized contraction principle with control functions phi and psi on partial metric spaces. The theorems we prove generalize many previously obtained results. We also give some examples showing that our theorems are indeed proper extensions. (C) 2011 Elsevier Ltd. All rights reserved.