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    Generalized k-Cesàro Polynomials
    (Padova Univ Press, 2025) Cin, Yahya; Ozmen, Nejla
    The main purpose of this study is to introduce k-analogue of the generalized Ces & agrave;ro polynomials and give their some properties. Firstly, generalized k-Ces & agrave;ro polynomials are defined with the help of a generating function relation. After getting the explicit form of these polynomials, various generating function relations, the Mellin transform formula, expressions in terms of k-hypergeometric function and some integral representations are obtained.
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    Hermite-Hadamard inequalities for left fractional conformable integral operator
    (Springer, 2025) Budak, Huseyin; Ozmen, Nejla
    In this paper, we first establish the Hermite-Hadamard inequality for left fractional conformable integral operators. Then, we present an example and a graph to illustrate the obtained Hermite-Hadamard inequalities. Moreover, we also present several corresponding trapezoid and midpoint inequalities. For this aim, we first prove two identities for differentiable functions. By using these equalities, we establish some trapezoid- and midpoint-type inequalities for convex functions. Furthermore, we present several remarks to give the relation between the obtained results in this paper and earlier ones.
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    On generalized Pentanacci quaternions
    (Tbilisi Centre Math Sci, 2020) Soykan, Yuksel; Ozmen, Nejla; Gocen, Melih
    In this paper, we introduce the generalized Pentanacci quaternions and we present Binet's formulas, generating functions and the summation formulas for these quaternions and as special case for Pentanacci and Pentanacci-Lucas quaternions. Furthermore, we present matrices related to generalized Pentanacci quaternions.
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    On properties of generalized Tridovan numbers
    (Bulgarian Acad Science, 2023) Soykan, Yuksel; Ozmen, Nejla; Okumus, Inci
    In this paper, we examine generalized Tridovan sequences and treat in detail two cases called Tridovan sequences and Tridovan-Lucas sequences. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these sequences. In addition, we give some identities and matrices related to these sequences.