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Öğe Fixed Point Results for Mixed Multivalued Mappings of Feng-Liu Type on Mb-Metric Spaces(Springer International Publishing Ag, 2019) Şahin, Hakan; Altun, İshak; Türkoğlu, Duran[Abstract No tAvailable]Öğe Almost Picard Operators(Amer Inst Physics, 2019) Altun, Ishak; Hancer, Hatice AslanThe concept of Picard operator is one of the most important concept of fixed point theory. As known, a self mapping T of a metric space X is called Picard operator (PO) if it has unique fixed point and every Picard iteration sequence converges to this fixed point. There are some weaker forms of PO in the literature as weakly Picard operator (WPO) and pseudo Picard operator (PPO). In this study, we present a new kind of PO as almost Picard operator (APO) and we show the differences from the others. Then we show that every continuous P-contractive self mapping of a compact metric space is APO. Also we present some open problems.Öğe Tauberian theorems for the weighted mean method of summability of integrals(Amer Inst Physics, 2019) Canak, Ibrahim; Ozsarac, FiratLet q be a positive weight function on R+ := [0, infinity) which is integrable in Lebesgue's sense over every finite interval (0, x) for 0 < x < infinity, in symbol: q is an element of L-loc(1)(R+) such that Q(x) := integral(x)(0)(t)dt # 0 for each x > 0, Q(0) = 0 and Q(x) -> infinity as x -> infinity. Given a real or complex-valued function f is an element of L-loc(1)(R+), we define s(x) := integral(x)(0) f(t)dt and tau((0))(q)(x) := s(x), tau((m))(q)(x) := 1/Q(x) integral(x)(0) tau((m 1))(q)(t)q(t)dt (x > 0, m = 1, 2, ...), provided that Q(x) > 0. We say that integral(infinity)(0) f(x)dx is summable to L by the m-th iteration of weighted mean method determined by the function q(x), or for short, ((N) over bar, q, m) integrable to a finite number L if lim(x ->infinity) tau((m))(q)(x) = L. In this case, we write s(x) -> L((N) over bar, q, m). It is known that if the limit lim(x ->infinity) s(x) = L exists, then lim(x ->infinity) tau((m))(q)(x) = L also exists. However, the converse of this implication is not always true. Some suitable conditions together with the existence of the limit lim(x ->infinity) tau((m))(q)(x), which is so called Tauberian conditions, may imply convergence of lim(x ->infinity) s(x). In this paper, one- and two-sided Tauberian conditions in terms of the generating function and its generalizations for ((N) over bar, q, m) summable integrals of real- or complex-valued functions have been obtained. Some classical type Tauberian theorems given for Cesaro summability (C, 1) and weighted mean method of summability ((N) over bar, q) have been extended and generalized.Öğe Generalized Lupas Operators(Amer Inst Physics, 2018) Ilarslan, Hatice Gill Ince; Aral, Ali; Bascanbaz-Tunca, GulenIn this work, by taking a continuously differentiable, increasing and unbounded function rho, we consider an extension of the Lupas operator L-n in the form L-n (f o rho(-1)) o rho for convenient functions f on [0, infinity). We give weighted approximation, Voronovskaya type theorem, quantitative estimates for the local approximation.Öğe New Results for General Helix in Euclidean 3-space(Amer Inst Physics, 2018) Ilarslan, KazimFinding parametric equation of a space curve is not easy task when its curvature functions are given. It is well known that this problem is known as fundamental theorem of a space curve. If the curvature functions are functions of arc-length, the solution of this problem is usually impossible. In this study, we discuss the answer of the problem when the curve is a general helix in Euclidean 3-space. By using slope axis of general helix, we get parametric equations of a general helix. Also, we give some examples and their figures.Öğe An Extension of Some Lauricella Hypergeometric Functions(Amer Inst Physics, 2013) Sahin, RecepIn this paper, we present an extension of Lauricella hypergeometric functions, which is motivated by the extended Beta function.Öğe Lateral buckling of precast reinforced concrete girders(International Association for Bridge and Structural Engineering (IABSE), 2012) Kalkan, İlker; Lee, J.-H.; Kim, C.-H.; Kim, H.-B.The development of high-strength materials and new construction techniques enable engineers to design longer and deeper precast concrete bridge girders. The increase in the slenderness ratios of these girders causes the lateral stability to be a cause of concern in the design and during construction of bridges. This paper presents a study pertaining to the lateral torsional buckling of precast reinforced concrete beams with initial geometric imperfections. An analytical formula accounting for the material nonlinearities and non-homogenous nature of reinforced concrete and the contribution of longitudinal reinforcements is proposed to estimate the lateral torsional buckling moments of reinforced concrete beams with initial geometric imperfections. In the present study, standard AASHTO I-girders are analyzed using the proposed formula to determine the critical unbraced lengths and the maximum design spans of the girders. Considering the PCI girder sweep tolerances, this study determines the critical unbraced lengths, at which the lateral torsional buckling moment of the girders becomes equal to the ultimate flexural moment capacity, to prevent lateral instability of the girders. Furthermore, for the maximum design span lengths given by the PCI Bridge Design Manual, the critical initial sweeps are determined to ascertain that the girders are stable until they reach the ultimate flexural capacity. The results of the analyses are used for evaluating the girder sweep tolerances and the maximum span lengths of the PCI Manual.
