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    A Note on Representation Variety of Abelian Groups and Reidemeister Torsion
    (Springer, 2021) Hezenci, F.; Sozen, Y.
    Let S and G denote respectively the 2 - torus and one of the Lie groups GL (n, C), SL (n, C), SO (n, C), Sp (2 n, C). In the present article, we consider the smooth part of the representation variety Rep (S, G) consisting of conjugacy classes of homomorphisms from fundamental group ?1(S) to G. We show the well definiteness of Reidemeister torsion for such representations. In addition, we establish a formula for computing the Reidemeister torsion of such representations in terms of the symplectic structure on Rep (S, G) [51]. This symplectic form is analogous to Atiyah–Bott–Goldman symplectic form of higher genera for the Lie group G. © 2021, Springer Nature Switzerland AG.
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    On bitsadze-samarskii type elliptic differential problems on hyperbolic plane
    (Academic Publications Ltd., 2021) Ashyralyev, A.; Sozen, Y.; Hezenci, F.
    In the present article, we consider nonlocal boundary value problems (NBVP) of elliptic type on relatively compact domains in the hyperbolic plane. We establish the wellposedness of Neumann-Bitsadze-Samarskii type and also Dirichlet-Bitsadze-Samarskii type on such domains. Furthermore, we establish new coercivity inequalities for solutions of such elliptic NBVP on relatively compact domains in the hyperbolic plane with various H¨older norms. © 2021
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    On new versions of Hermite-Hadamard-type inequalities based on tempered fractional integrals
    (Univ Nis, Fac Sci Math, 2024) Budak, H.; Hezenci, F.; Tunc, T.; Kara, H.
    This research is on the new versions of Hermite-Hadamard type inequalities. These inequalities established by means of convex mappings include tempered fractional integral operators. Obtaining these inequalities, well-known Holder inequality and power mean inequality are also utilized. The resulting Hermite-Hadamard type inequalities are a generalization of some of the studies on this subject, including Riemann-Liouville fractional integrals. What's more, new results are obtained through special choices.
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    A remark on elliptic differential equations on manifold
    (Karaganda State Univ, 2020) Ashyralyev, A.; Sozen, Y.; Hezenci, F.
    For elliptic boundary value problems of nonlocal type in Euclidean space, the well posedness has been studied by several authors and it has been well understood. On the other hand, such kind of problems on manifolds have not been studied yet. Present article considers differential equations on smooth closed manifolds. It establishes the well posedness of nonlocal boundary value problems of elliptic type, namely Neumann-Bitsadze-Samarskii type nonlocal boundary value problem on manifolds and also Dirichlet-Bitsadze-Samarskii type nonlocal boundary value problem on manifolds, in Holder spaces. In addition, in various Holder norms, it establishes new coercivity inequalities for solutions of such elliptic nonlocal type boundary value problems on smooth manifolds.
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    A remark on Schottky representations and Reidemeister torsion
    (Karaganda State Univ, 2023) Hezenci, F.; Sozen, Y.
    The present paper establishes a formula of Reidemeister torsion for Schottky representations. The theoretical results are applied to 3-manifolds with boundary consisting orientable surfaces with genus at least 2.
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    Simpson-Type Inequalities for Conformable Fractional Operators Concerning Twice-Differentiable Functions
    (Islamic Azad Univ, Shiraz Branch, 2023) Hezenci, F.; Budak, H.
    The authors of the paper propose a new method of investigation of an an equality for the case of twice-differentiable convex functions with respect to the conformable fractional integrals. With the help of this equality, we establish several Simpson-type inequalities for twice-differentiable convex functions by using conformable fractional integrals. Sundry significant inequalities are obtained by taking advantage of the convexity, the Holder inequality, and the power mean inequality. By using the specific selection of our results, we give several new and well-known results in the literature.