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This paper is concerned with the existence of Siegel disks of the Cremona map $F_\alpha(x,y)=(x\cos\alpha -(y-x^2)\sin\alpha,\,\, x\sin\alpha+(y-x^2)\cos\alpha)$ with the parameter $\alpha\in [0,2\pi)$. This problem is reduced to the existence of local invertible analytic solutions to a functional equation with small divisors $\lambda^n+\lambda^{-n}-\lambda-\lambda^{-1}$. The main aim of this paper is to investigate whether this equation with $|\lambda|=1$ has such a solution under the Brjuno condition.

Recently, Filipovic et al. [M. Filipovic, L. Paunovic, S. Radenovic, M. Rajovic, Remarks on 'Cone metric spaces and fixed point theorems of T-Kannan and T-Chatterjea contractive mappings', Math. Comput. Modelling. 54 (2011) 1467-1472] proved several fixed and periodic point theorems for solid cones on cone metric spaces. In this paper several fixed and periodic point theorems for T-contraction of two maps on cone metric spaces with solid cone are proved. The results of this paper extend and generalize well-known comparable results in the literature.

The object of the present paper is to characterize Ricci semisymmetric almost Kenmotsu manifolds with its characteristic vector field ? belonging to the (k,?)'-nullity distribution and (k,?)-nullity distribution respectively. Finally, an illustrative example is given.

Recently, we have discussed the warped product pseudo-slant submanifolds of the type $M_\theta\times_fM_\perp$ of Kenmotsu manifolds. In this paper, we study other type of warped product pseudo-slant submanifolds by reversing these two factors in Kenmotsu manifolds. The existence of such warped product immersions is proved by a characterization. Also, we provide an example of warped product pseudo-slant submanifolds. Finally, we establish a sharp estimation such as $\|h\|^2\geq 2p\cos^2\theta\big(\|\vec\nabla\ln f\|^2-1\big)$ for the squared norm of the second fundamental form $\|h\|^2$, in terms of the warping function $f$, where $\vec\nabla\ln f$ is the gradient vector of the function $\ln f$. The equality case is also discussed.

In this paper, we generalized a known theorem dealing with absolute weighted arithmetic mean summability of infinite series by using a quasi-f-power increasing sequence instead of a quasi-?-power increasing sequence. And we applied it to the trigonometric Fourier series

In view of the relationship with the Kr\"{a}tzel function, we derive a new series representation for the $\lambda$-generalized Hurwitz-Lerch Zeta function introduced by H.M. Srivastava [Appl. Math. Inf. Sci. 8 (2014) 1485--1500] and determine the monotonicity of its coefficients. An integral representation of the Mathieu $\left(\textbf{a},\bm{\lambda}\right)$-series is rederived by applying the Abel's summation formula (which provides a slight modification of the result given by Pog\'{a}ny [Integral Transforms Spec. Funct. 16 (8) (2005) 685--689]) and this modified form of the result is then used to obtain a new integral representation for the $\lambda$-generalized Hurwitz-Lerch Zeta function. Finally, by making use of the various results presented in this paper, we establish two sets of two-sided inequalities for the $\lambda$-generalized Hurwitz-Lerch Zeta function.

In this paper, we investigate the existence of minimal nonnegative solution for a class of nonlinear fractional integro-differential equations on semi-infinite intervals in Banach spaces by applying the cone theory and the monotone iterative technique. An example is given for the illustration of main results.

The object of the present paper is to study Ricci semisymmetric contact metric manifolds. As a consequence of the main result we deduce some important corollaries. Besides these we study contact metric manifolds satisfying the curvature condition Q,R = 0, where Q and R denote the Ricci operator and curvature tensor respectively. Also we study the symmetric properties of a second order parallel tensor in contact metric manifolds. Finally, we give an example to verify the main result.

The main aim of this paper is to obtain a improved and generalized version of companion of Ostrowski type integral inequalities for mappings whose first derivatives are of bounded variation. Some previous results are also recaptured as special cases. New quadrature formulae are also provided.

In this paper, we investigate Ricci pseudo-symmetric and Ricci generalized pseudo-symmetric P-Sasakian manifolds. Next we study P-Sasakian manifolds satisfying the curvature condition S ? R = 0. Finally, we give an example of a 5-dimensional P-Sasakian manifold to verify some results.

In this paper, we obtain that if the metric of a three dimensional $(k,\mu)'$-almost Kenmotsu manifold satisfies the Miao-Tam critical condition, then the manifold is locally isometric to either the hyperbolic space $\mathbb{H}^3(-1)$ or the Riemannian product $\mathbb{H}^{2}(-4)\times\mathbb{R}$. Moreover, we also prove that if the metric of an almost Kenmotsu manifold with conformal Reeb foliation satisfies the Miao-Tam critical condition, then the manifold is either of constant scalar curvature or Einstein. Some corollaries of main results are also given.

In this paper we introduce the set of strictly quasi-Fredholm linear relations and we give some of its properties. Furthermore, we study the connection between this set and some classes of linear relations related to the notions of ascent, essentially ascent, descent and essentially descent. The obtained results are used to study the stability of upper semi-B-Fredholm and lower semi-B-Fredholm linear relations under perturbation by finite rank operators.

In this paper we obtain some results concerning the ascent and descent of a quasi-Fredholm relation in a Hilbert space and we analyze the behaviour of a polynomial in a quasi-Fredholm relation in a Hilbert space.

In this paper some new inequalities of Simpson-type are established for the classes of functions whose derivatives of absolute values are convex functions via Riemann-Liouville integrals. Also, by special selections of n;we give some reduced results. © 2017, University of Nis. All rights reserved., Firat University Scientific Research Projects Management Unit British Association for Psychopharmacology, 2010 Mathematics Subject Classification. Primary 26D15 Keywords. convex functions, Simpson-Type Inequalities,Riemann-Liouville fractional integrals Received: 10 March 2016; Accepted: 29 March 2016 Communicated by Dragan S. Djordjevi? This research is supported by Ordu University Scientific Research Projects Coordinations Unit (BAP). Project Number: YKD-280 Email addresses: erhanset@yahoo.com (Erhan Set), ahmetakdemir@agri.edu.tr (Ahmet Ocak Akdemir), mozdemirr@yahoo.com (M. Emin Özdemir)

In the present paper, we prove the inequality between the normalized scalar curvature and the generalized normalized ?-Casorati curvatures for the submanifolds of locally conformal Kaehler space form and also consider the equality case of the inequality.

In this paper, we derive a new integral identity for differentiable function. Using this new integral identity as an auxiliary result, we derive some new two point trapezoidal like inequalities for differentiable harmonic h-convex functions. These inequalities can also be viewed as Hermite-Hadamard type inequalities. We also discuss some new special cases which can be deduced from our main results.

Deniz, Emre/0000-0003-0546-4229 WOS: 000408376500026 In this paper we construct new integral type operators including heritable properties of Baskakov Durrmeyer and Baskakov Kantorovich operators. Results concerning convergence of these operators in weighted space and the hypergeometric form of the operators are shown. Voronovskaya type estimate of the pointwise convergence along with its quantitative version based on the weighted modulus of smoothness are given. Moreover, we give a direct approximation theorem for the operators in suitable weighted Lp space on [0; infinity).

ogur, oguz/0000-0002-3206-5330 WOS: 000376573900027 The object of this paper is to introduce generalized Lorentz sequence spaces L(f, v, p) defined by modulus function f. Also we study some topologic properties of this space and obtain some inclusion relations.

WOS: 000376574300020 In this paper, we have established Hermite-Hadamard type inequalities for fractional integrals depending on a parameter.

In the present paper, we obtain some characterizations for a certain generalized Bessel function of the first kind to be in the subclasses SpT(?,?), UCT(?,?), PT(?) and CPT(?) of normalized analytic functions in the open unit disk U. Furthermore, we consider an integral operator related to the generalized Bessel Function which we have characterized here.

In this paper, we consider the class of s-Godunova-Levin functions. We derive a new fractional integral identity for differentiable function. Using this new identity, we establish some new fractional Hermite-Hadamard type inequalities for the class of differentiable s-Godunova-Levin functions.

In this paper, a new identity for n-times differntiable functions is established and by using the obtained identity, some new inequalities Hermite-Hadamard type are obtained for functions whose nth derivatives in absolute value are convex and concave functions. From our results, several inequalities of Hermite-Hadamard type can be derived in terms of functions whose first and second derivatives in absolute value are convex and concave functions as special cases. Our results may provide refinements of some results already exist in literature. Applications to trapezoidal formula and special means of established results are given.

The aim of this paper is to further investigate properties of the local closure function, as a generalization of the ?-closure and the local function in ideal topological spaces. Similarities and differences between it and the local function are examined by varying several well-known ideals.

Suppose $S$ and $T$ are adjointable linear operators‎ ‎between Hilbert $C^*$-modules‎. ‎It is well known that an operator $T$ has closed range‎ ‎if and only if its Moore-Penrose inverse $T^\dagger$ exists‎. ‎In this paper‎, ‎we show that $(TS)^\dagger=S^\dagger T^\dagger $‎, ‎where $S$ and $T$ have closed ranges and $(\ker(T))^\perp=\rm {ran}(S)$‎. ‎Moreover‎, ‎we investigate some results related to the polar decomposition of $T$‎. ‎We also obtain‎ ‎the inverse of $1‎ - ‎T^{\dagger}T‎ + ‎T$‎, ‎when $T$ is a self-adjoint operator‎.

In this paper we determine some properties of pseudo-projective curvature tensor denoted by ?P on some Riemannian manifolds, especially on generalized quasi Einstein manifolds in the sense of Chaki. Firstly, we consider a pseudo-projectively Ricci semisymmetric generalized quasi Einstein manifold. After that, we study pseudo-projective flatness of this manifold. Moreover, we construct a non-trivial example for a generalized quasi Einstein manifold to prove the existence.

Recently Kiryakova and several other ones have investigated so-called multiindex Mittag-Leffler functions associated with fractional calculus. Here, in this paper, we aim at establishing a new fractional integration formula (of pathway type) involving the generalized multiindex Mittag-Leffler function E?,k[(?j,?j)m;z]. Some interesting special cases of our main result are also considered and shown to be connected with certain known ones.

In this paper, we prove strong convergence of a path for a convex combination of a pseudocontractive type of operators in a real reflexive Banach space having a weakly continuous duality mapping J? with gauge function ?. Using path convergency, we establish strong convergence of an implicit iterative algorithm for a pseudocontractive mapping combined with a strongly pseudocontractive mapping in the same Banach space.

In this paper, we introduce a new integrodifferential operator associated with the Hurwitz Lerch Zeta function in the puncture open disk of the meromorphic functions. We also obtain some properties of the third-order differential subordination and superordination for this integrodifferential operator, by using certain classes of admissible functions.

The aim of this paper is to propose a new space called partial cone b-metric space by using both the notions of cone b-metric spaces and partial metric spaces and by defining asymptotically regular maps and sequences. We also prove some fixed point theorems for such maps and sequences. Our results extend and generalize some interesting results of [11] and [21] in partial cone b-metric space. An example is also given to support the validity of our results.

In this paper, we define three types of lightlike hypersurfaces of an indefinite Kaehler manifold, which are called Hopf, recurrent and Lie recurrent lightlike hypersurfaces. After that we provide several new results on such three type lightlike hypersurfaces of an indefinite Kaehler manifold or an indefinite almost complex space form.

In this paper we study fundamental equations of holomorphically projective mappings of (pseudo-) K?hler manifolds with respect to the smoothness class of metrics Cr, r ? 1. We show that holomorphically projective mappings preserve the smoothness class of metrics.

In this paper we introduce new notions of hybrid rational Geraghty and Suzuki-Edelstein type contractive mappings and investigate the existence and uniqueness of PPF dependent fixed point for such mappings in the Razumikhin class, where domain and range of the mappings are not the same. As an application of our PPF dependent fixed point results, we deduce corresponding PPF dependent coincidence point results in the Razumikhin class. Our results extend and improve the results of Sintunavarat and Kumam [J. Nonlinear Anal. Optim.: Theory Appl., Vol. 4, (2013), 157-162], Bernfeld, Lakshmikantham and Reddy [Applicable Anal., 6(1977), 271-280] and others. As an application of our results, we establish PPF dependent solution of a periodic boundary value problem.

This paper is concerned with integral type boundary value problems of second order singular differential systems with quasi-Laplacian operators on whole lines. A Banach space and a nonlinear completely continuous operator are defined. By using the Banach space and the nonlinear operator, together with the Schauder?s fixed point theorem, sufficient conditions to guarantee the existence of at least one unbounded positive solution are established. Finally, we present a concrete example to illustrate the efficiency of the main theorem.

In this paper, we establish Hermite-Hadamard type inequalities for functions whose nth derivatives are m- and (?;m)-logarithmically convex functions. From our results, several results for classical trapezoidal and classical midpoint inequalities are obtained in terms second derivatives that are m- and (?,m)-logarithmically convex functions as special cases.

In this mainly review paper, we discuss connections between F. Gehring?s problem and some results of isoperimetric type. We also prove a few new results and give novelity at some places.

In this paper we deal with a pseudo-Riemannian Osserman curvature tensor whose reduced Jacobi operator is diagonalizable with exactly two distinct eigenvalues. The main result gives new insight into the theory of the duality principle for pseudo-Riemannian Osserman manifolds. We concern with special Osserman curvature tensor and propose new ways to exclude some additional duality principle conditions from its definition.

In this paper we give a generalization of the Lagrange mean value theorem via lower and upper derivative, as well as appropriate criteria of monotonicity and convexity for arbitrary function f : (a, b) ( R. Some applications to the neoclassical economic growth model are given (from mathematical point of view).

In this paper we consider equitorsion geodesic mappings of equiaffine spaces of the ?-kind, ? ? {0, ..., 5}. In the case when ? ? {0, 5}, vector ?i , which determines that mapping, is gradient, which doesn?t hold in general case. We found the condition when the vector ?i is gradient in the case of ? ? {1, ..., 4}. Some invariant geometric objects of such mappings are found. Anti-equiaffine spaces of ?-kind, ? ? {0, ..., 5} are introduced and discussed. Equitorsion geodesic mappings of such spaces are described and some invariants are found.