Yazar "Unal, Cihan" seçeneğine göre listele

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    A study on error bounds for Newton-type inequalities in conformable fractional integrals
    (Walter De Gruyter Gmbh, 2024) Budak, Huseyin; Unal, Cihan; Hezenci, Fatih
    The authors of the paper suggest a novel approach in order to examine an integral equality using conformable fractional operators. By using this identity, some Newton-type inequalities are proved for differentiable convex functions by taking the modulus of the newly established equality. Moreover, we prove some Newton-type inequalities by using the H & ouml;lder and power-mean inequality. Furthermore, some new results are presented by using special choices of obtained inequalities. Finally, we give some conformable fractional Newton-type inequalities for functions of bounded variation.
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    Compact embeddings of weighted variable exponent Sobolev spaces and existence of solutions for weighted p(•)-Laplacian
    (Taylor & Francis Ltd, 2021) Unal, Cihan; Aydin, Ismail
    In this study, we define double weighted variable exponent Sobolev spaces W-1,W-q(.),W-p(.) (Omega, theta(0),theta) with respect to two different weight functions. Also, we investigate the basic properties of this spaces. Moreover, we discuss the existence of weak solutions for weighted Dirichlet problem of p(center dot)-Laplacian equation -div(theta(x) vertical bar del f vertical bar p(x)(-2)del f) = theta(0)(x) vertical bar f vertical bar(q(x)-2) f x is an element of Omega f = 0 x is an element of partial derivative Omega under some conditions of compact embedding involving the double weighted variable exponent Sobolev spaces.
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    COMPACT EMBEDDINGS ON A SUBSPACE OF WEIGHTED VARIABLE EXPONENT SOBOLEV SPACES
    (Springer Basel Ag, 2019) Unal, Cihan; Aydin, Ismail
    In this paper, we define an intersection space between weighted classical Lebesgue spaces and weighted Sobolev spaces with variable exponent. We consider the basic properties of the space. Also, we investigate some inclusions, continuous embeddings, and compact embeddings under some conditions.
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    Conformable fractional Newton-type inequalities with respect to differentiable convex functions
    (Springer, 2023) Unal, Cihan; Hezenci, Fatih; Budak, Huseyin
    The authors propose a new method of investigation of an integral identity according to conformable fractional operators. Moreover, some Newton-type inequalities are considered for differentiable convex functions by taking the modulus of the newly established equality. In addition, we prove several Newton-type inequalities with the aid of Holder and power-mean inequalities. Furthermore, several new results are given by using special choices of the obtained inequalities. Finally, we give several inequalities of conformable fractional Newton-type for functions of bounded variation.
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    Existence and multiplicity of weak solutions for eigenvalue Robin problem with weighted p(.)-Laplacian
    (Springer-Verlag Italia Srl, 2023) Aydin, Ismail; Unal, Cihan
    By applying Mountain Pass Lemma, Ekeland's variational principle and Fountain Theorem, we prove the existence and multiplicity of solutions for the following Robin problem {-div(a(x) vertical bar del u vertical bar(p(x)-2) del u) =lambda b(x)vertical bar u vertical bar(q(x)-2) u, x is an element of Omega a(x) vertical bar del u vertical bar(p(x)-2) partial derivative u/partial derivative u + beta(x)vertical bar u vertical bar(p(x)-2) u = 0, x is an element of partial derivative Omega, under some appropriate conditions in the space W-a,b(1, p(.)) (Omega).
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    Existence of Weak Solutions for Weighted Robin Problem Involving p(.)-biharmonic operator
    (Springer India, 2024) Kulak, Oznur; Aydin, Ismail; Unal, Cihan
    Using Mountain Pass Theorem, we consider the existence of weak solutions of weighted Robin problem involving p(.)-biharmonic operator { a(x)Delta(2)(p(x)) u = lambda b(x)vertical bar u vertical bar(q(x)-2)u, in Omega a(x)vertical bar Delta u vertical bar(p(x)-2)partial derivative u/partial derivative v + beta(x) vertical bar u vertical bar(p(x)-2) u = 0, on partial derivative Omega under some conditions in the space W-a,b(2,p(.)) (Omega).
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    On existence and multiplicity of solutions for a biharmonic problem with weights via Ricceri's theorem
    (De Gruyter Poland Sp Z O O, 2024) Unal, Cihan
    In this work, we consider a special nondegenerate equation with two weights. We investigate multiplicity result of this biharmonic equation. Mainly, our purpose is to obtain this result using an alternative Ricceri's theorem. Moreover, we give some compact embeddings in variable exponent Sobolev spaces with second order to prove the main idea.
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    On some compact embeddings of a weighted space
    (Tbilisi Centre Math Sci, 2019) Unal, Cihan; Aydn, Ismail
    In this paper, we define an intersection spaces between weighted classical Lebesgue spaces and an amalgam space with two weight functions on a locally compact abelian group with Haar measure. We consider the basic properties of the space such as Banach algebra, translation invariant, Banach module, a generalized type of Segal algebra etc. Also, we investigate some inclusions, compact embeddings in sense to weights and further discuss multipliers of this space.
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    Some properties of thinness and fine topology with relative capacity
    (Springer-Verlag Italia Srl, 2023) Unal, Cihan; Aydin, Ismail
    In this paper, we introduce a thinness in sense to a type of relative capacity for weighted variable exponent Sobolev space. Moreover, we reveal some properties of this thinness and consider the relationship with finely open and finely closed sets. We discuss fine topology and compare this topology with Euclidean one. Finally, we give some information about importance of the fine topology in the potential theory.
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    Some remarks on parameterized inequalities involving conformable fractional operators
    (Tubitak Scientific & Technological Research Council Turkey, 2023) Unal, Cihan; Hezenci, Fatih; Budak, Hueseyin
    In this paper, we prove an identity for differentiable convex functions related to conformable fractional integrals. Moreover, some parameterized inequalities are established by using conformable fractional integrals. To be more precise, parameterized inequalities are obtained by taking advantage of the convexity, the Holder inequality, and the power mean inequality. Furthermore, previous and new results are presented by using special cases of the obtained theorems.
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    THE INCLUSION THEOREMS FOR GENERALIZED VARIABLE EXPONENT GRAND LEBESGUE SPACES
    (Kangwon-Kyungki Mathematical Soc, 2021) Aydin, Ismail; Unal, Cihan
    In this paper, we discuss and investigate the existence of the inclusion L-p(.),L-theta (mu) subset of L-q(.),L-theta (nu), where mu and nu are two finite measures on (X, Sigma) Moreover, we show that the generalized variable exponent grand Lebesgue space L-p(.),L-theta (Omega) has a potential-type approximate identity, where Omega is a bounded open subset of R-d.
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    The Kolmogorov-Riesz theorem and some compactness criterions of bounded subsets in weighted variable exponent amalgam and Sobolev spaces
    (Springer-Verlag Italia Srl, 2020) Aydin, Ismail; Unal, Cihan
    We study totally bounded subsets in weighted variable exponent amalgam and Sobolev spaces. Moreover, this paper includes several detailed generalized results of some compactness criterions in these spaces.
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    THREE SOLUTIONS TO A ROBIN PROBLEM WITH TWO WEIGHTED GENERALIZED VARIABLE EXPONENT SOBOLEV SPACES
    (Rocky Mt Math Consortium, 2024) Unal, Cihan
    By applying Ricceri's variational principle, we demonstrate the existence of solutions for a double weighted Robin problem in weighted variable exponent Sobolev spaces under some appropriate conditions.
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    THREE SOLUTIONS TO A STEKLOV PROBLEM INVOLVING THE WEIGHTED p(.)-LAPLACIAN
    (Rocky Mt Math Consortium, 2021) Aydin, Ismail; Unal, Cihan
    We study a nonlinear Steklov boundary-value problem involving the weighted p(.)-Laplacian. Using the Ricceri's variational principle, we obtain the existence of at least three weak solutions in double weighted variable exponent Sobolev space.
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    Weighted stochastic field exponent Sobolev spaces and nonlinear degenerated elliptic problem with nonstandard growth
    (Hacettepe Univ, Fac Sci, 2020) Aydin, Ismail; Unal, Cihan
    In this study, we consider weighted stochastic field exponent function spaces L-v(p(.,.))(D x Omega) and W-v(k,p(.,.))( (D x Omega). Also, we study some basic properties and embeddings of these spaces. Finally, we present an application for defined spaces to the stochastic partial differential equations with stochastic field growth.
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    WEIGHTED VARIABLE EXPONENT SOBOLEV SPACES WITH ZERO BOUNDARY VALUES AND CAPACITY ESTIMATES
    (Yildiz Technical Univ, 2018) Unal, Cihan; Aydin, Ismail
    In this paper, we define weighted variable exponent Sobolev space with zero boundary values and investigate some properties of this space with weighted variable Sobolev capacity. We obtain Poincare inequality with respect to zero boundary values. We will introduce a capacity in sense to this defined space and, also, give several estimates.