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Alaca, Ayse,Alaca, Saban,Ntienjem, Ebenezer Department of Mathematics 2019 Kyungpook mathematical journal Vol.59 No.3
We evaluate the convolution sum $W_{a,b}(n):=\sum_{al+bm=n}{\sigma}(l){\sigma}(m)$ for (a, b) = (1, 28),(4, 7),(2, 7) for all positive integers n. We use a modular form approach. We also re-evaluate the known sums $W_{1,14}(n)$ and $W_{1,7}(n)$ with our method. We then use these evaluations to determine the number of representations of n by the octonary quadratic form $x^2_1+x^2_2+x^2_3+x^2_4+7(x^2_5+x^2_6+x^2_7+x^2_8)$. Finally we express the modular forms ${\Delta}_{4,7}(z)$, ${\Delta}_{4,14,1}(z)$ and ${\Delta}_{4,14,2}(z)$ (given in [10, 14]) as linear combinations of eta quotients.
ON FIXED POINT THEOREMS IN INTUITIONISTIC FUZZY METRIC SPACES
Alaca, Cihangir Korean Mathematical Society 2009 대한수학회논문집 Vol.24 No.4
In this paper, we give some new fixed point theorems for contractive type mappings in intuitionistic fuzzy metric spaces. We improve and generalize the well-known fixed point theorems of Banach [4] and Edelstein [8] in intuitionistic fuzzy metric spaces. Our main results are intuitionistic fuzzy version of Fang's results [10]. Further, we obtain some applications to validate our main results to product spaces.
ON COMPATIBLE MAPPINGS OF TYPE (I) AND (II) IN INTUITIONISTIC FUZZY METRIC SPACES
Alaca, Cihangir,Altun, Ishak,Turkoglu, Duran Korean Mathematical Society 2008 대한수학회논문집 Vol.23 No.3
In this paper, we give some new definitions of compatible mappings in intuitionistic fuzzy metric spaces and we prove a common fixed point theorem for four mappings under the condition of compatible mappings of type (I) and of type (II) in complete intuitionistic fuzzy metric spaces.
REPRESENTATIONS BY QUATERNARY QUADRATIC FORMS WITH COEFFICIENTS 1, 2, 5 OR 10
Alaca, Ayse,Altiary, Mada Korean Mathematical Society 2019 대한수학회논문집 Vol.34 No.1
We determine explicit formulas for the number of representations of a positive integer n by quaternary quadratic forms with coefficients 1, 2, 5 or 10. We use a modular forms approach.
A New Version of Mazur-Ulam Theorem Under Weaker Conditions in Linear n-Normed Spaces
Park, C.,Alaca, C. Eudoxus Press LLC 2014 Journal of computational analysis and applications Vol.16 No.5
The purpose of this paper is to prove a new result of Mazur-Ulam theorem for n-isometry without any other conditions in linear n-normed spaces.
COMMON FIXED POINT THEOREMS IN INTUITIONISTIC FUZZY METRIC SPACES
Turkoglu, D.,Alaca, C.,Cho, Y.J.,Yildiz, C. 한국전산응용수학회 2006 Journal of applied mathematics & informatics Vol.22 No.1
The purpose of this paper, using the idea of intuitionistic fuzzy set due to Atanassov [2], we define the notion of intuitionistic fuzzy metric spaces (see, [1]) due to Kramosil and Michalek [17] and Jungck's common fixed point theorem ([11]) is generalized to intuitionistic fuzzy metric spaces. Further, we first formulate the definition of weakly commuting and R-weakly commuting mappings in intuitionistic fuzzy metric spaces and prove the intuitionistic fuzzy version of Pant's theorem ([21]).
Common fixed point theorems in intuitionistic fuzzy metric spaces
D. Turkoglu,C. Alaca,Y. J. Cho,C. Yildiz 한국전산응용수학회 2006 Journal of applied mathematics & informatics Vol.22 No.1-2
The purpose of this paper, using the idea of intuitionistic fuzzy set due to Atanassov [2], we define the notion of intuitionistic fuzzy metric spaces (see, [1]) due to Kramosil and Michalek [17] and Jungck’s common fixed point theorem ([11]) is generalized to intuitionistic fuzzy metric spaces. Further, we first formulate the definition of weakly commuting and R-weakly commuting mappings in intuitionistic fuzzy metric spaces and prove the intuitionistic fuzzy version of Pant’s theorem ([21]).