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The aim of this paper is to present, in the context of b-metric spaces, coupled coincidence point theorems under some contraction type conditions. The method is based on the application of some coincidence point theorems of Ran-Reurings type in ordered b-metric spaces. Some applications will illustrate the theory. The approach is new even for the case of usual metric spaces.

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.

The purpose of this paper is to present some fixed point results in b-metric spaces using a contractive condition of Hardy-Rogers type with respect to the functional H. The data dependence of the fixed point set, the well-posedness of the fixed point problem, as well as, the Ulam-Hyres stability are also studied.

In this paper, the authors investigate a majorization problem for certain subclasses of multivalent meromorphic functions defined in the punctured unit disk U* having a pole of order p at origin. The subclasses under investigation are defined through iterations and combinations of the Liu-Srivastava operator and a meromorphic analogue of the Cho-Kwon-Srivastava operator for normalized analytic function. Several consequences of the main results in form of corollaries are also pointed out.

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 propose a method based on generating functions for constructing q-analogues of some discrete type positive linear operators (e.g., q-Lupas, q-Bernstein, q-Meyer-Konig and Zeller and ¨ q-Bleimann-Butzer-Hahn operators etc.). In other words, general operators of the discrete type are constructed, and their respective formulae for central moments are thereby obtained. Finally, through the use of specific generating functions, we are able to provide some relevant exemplary applications of general operators.

In this paper, some additive properties of the pseudo Drazin inverse are obtained in a Banach algebra. In addition, we find some new conditions under which the pseudo Drazin inverse of the sum a + b can be explicitly expressed in terms of a, az, b, bz. In particular, necessary and sufficient conditions for the existence as well as the expression for the pseudo Drazin inverse of the sum a+b are obtained under certain conditions. Also, a result of Wang and Chen [Pseudo Drazin inverses in associative rings and Banach algebras, LAA 437(2012) 1332-1345] is extended.

In this paper we give a new family of numbers, called ??-Whitney numbers, which gives generalization of many types of Whitney numbers and Stirling numbers. Some basic properties of these numbers such as recurrence relations, explicit formulas and generating functions are given. Finally many interesting special cases are derived.

In this paper, based on some biological meaning, triple-negative T cells (TN) and the immature singlepositive T cells (CD3^{−}4^{+}8^{−} and CD3^{−}4^{−}8^{+}) have been introduced into well known Mehr’s non-linear differential equation which is used to describe proliferation, differentiation and death of T cells in the thymus (Modeling positive and negative selection and differentiation processes in the thymus, Journal of Theoretical Biology, 175 (1995) 103-126), and a class of improved nonlinear differential system with seven state variables and time delays has been proposed. Then, by using quasi-steady-state approximation and some classical analysis techniques of functional differential equations, the local and global asymptotic stability of the equilibrium of the system have been analysed. Finally, some numerical simulations are given to summarize the applications of the theoretical results.

In this paper, we obtain some new fixed point theorems for (?,?,?,?) -contractive multi-valued mappings in ?-?-T-complete Menger PM-spaces, which turn out to generalize many results in existing literatures. Some examples are also given to illustrate the definition and support our new results. Moreover, some interesting fixed point results endowed with binary relations or graphs are derived as applications of our main results.

In this paper, some fixed point results of Ciric type in partial b-metric spaces are complemented and generalized. An example is given to support the obtained results.

In this paper, inspired the very interesting results of Ciric [20], we investigate the existing non-unique fixed points of certain operators in the context of b-metric spaces. Our main results unify and cover several existing results on the topic in the literature.

In the present paper, we introduce the notion of ?-type F-?-contraction and establish related fixed point results in metric spaces. An example is also given to illustrate our main results and to show that our results are proper generalization of Altun et al. (2015), Miank et al. (2015), Altun et al. (2016) and Olgun et al. (2016). We also obtain fixed point results in the setting of partially ordered metric spaces. Finally, an application is given to set up the existence of positive definite solution of non-linear matrix equation.

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.

iscan, imdat/0000-0001-6749-0591 WOS: 000428735200005 In this paper, we give a new concept which is a generalization of the concepts quasi-convexity and harmonically quasi-convexity and establish a new identity. A consequence of the identity is that we obtain some new general inequalities containing all of the Hermite-Hadamard and Simpson-like type for functions whose derivatives in absolute value at certain power are p-quasi-convex. Some applications to special means of real numbers are also given.

The classical power sum and alternating power sum identities can be stated as ?m,i=0 sn(i)= 1/n+1 (Bn+1(m+1)- Bn+1), ?m,i=0(-1)i sn (i) = 1/2 ((-1)m En(m+1) + En), where sn(x)=xn is the simplest possible Appell polynomial for the Sheffer pair (1,t). The impetus for this research starts from the question that what if we replace sn(x)=xn by any Appell polynomial. In this paper, we give a generalization of power and alternating power sums to any Appell polynomials.

In this paper, we establish some fixed point theorems in G-metric spaces involving generalized cyclic contractions. Some subsequent results are derived. The presented results generalize many well known results in the literature. Moreover, we provide some concrete examples and an application on the existence and uniqueness of solutions to a class of nonlinear integral equations.

In this paper existence and uniqueness of fixed points for a general class of contractive and nonexpansive mappings on modular metric spaces is discussed. As an application of the theoretical results, the existence of a solution of anti-periodic boundary value problems for nonlinear first order differential equations of Carath?odory?s type is considered in the framework of modular metric spaces.

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 this paper we establish a common fixed point theorem for two maps under the generalized contractive condition in a complete metric spaces.

The main purpose of this paper is to introduce and investigate the concepts of lacunary strong summability of order and lacunary statistical convergence of order of real-valued functions which are measurable (in the Lebesgue sense) in the interval (1,∞). Some relations between lacunary statistical convergence of order and lacunary strong summability of order are also given.

In this paper, we study the following gradient system on a complete Riemannian manifold M, {-x?(t) = grad'(x(t)) x(0) = x0, where ? : M ? R is a C1 function with Argmin ? ? ?. We prove that the gradient flow x(t) converges to a critical point of ? if ? is pseudo-convex, or if ? is quasi-convex and M is Hadamard. As an application to minimization, we consider a discrete version of the system to approximate a minimum point of a given pseudo-convex function ?.

In this paper, the concept of (?-?)-generalized rational contraction multivalued operator is introduced and then the existence of common fixed points of such mapping in complete dislocated quasi bmetric spaces is obtained. Some examples are presented to show that the results proved herein are potential generalization and extension of comparable existing results in the literature. We also study Ulam-Hyers stability of fixed point problems of (?-?)-generalized rational contraction multivalued operator. We also obtain some common fixed point results for single and multivalued mappings in a complete dq b-metric space endowed with a partial order. As an application, the existence of a continuous solution of an integral equation under appropriate assumptions is obtained.

In the present paper, utilizing the techniques of suitable measures of noncompactness in Banach algebra, we prove an existence theorem for nonlinear functional-integral equation which contains as particular cases several integral and functional-integral equations that appear in many branches of nonlinear analysis and its applications. We employ the fixed point theorems such as Darbo?s theorem in Banach algebra concerning the estimate on the solutions. We also provide a nontrivial example that explains the generalizations and applications of our main result.

This paper concerns the relationship between uniform boundedness and convergence of various generalized inverses. Using the stable perturbation for generalized inverse and the gap between closed linear subspaces, we prove the equivalence of the uniform boundedness and convergence for generalized inverses. Based on this, we consider the cases for the Moore-Penrose inverses and group inverses. Some new and concise expressions and convergence theorems are provided. The obtained results extend and improve known ones in operator theory and matrix theory.

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 introduce and study H-invex functions including the classes of convex, ?-invex, (F,G)-invex, c-strongly convex, ?-uniformly convex and superquadratic functions, respectively. Each Hinvex function attains its global minimum at an H-stationary point. For H-invex functions we prove Jensen, Sherman and Hardy-Littlewood-P?lya-Karamata type inequalities, respectively. We also analyze such inequalities when the control function H is convex. As applications, we give interpretations of the obtained results for uniformly convex and superquadratic functions, respectively.

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.

In this paper, we establish some new inequalities of Simpson?s type based on s-convexity via fractional integrals. Our results generalize the results obtained by Sarikaya et al. [1].

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).

The aim of this paper is to generalize celebrated results due to Boyd and Wong [2] and Matkowski [9] and also to provide yet new solutions to the once open problem on the existence of a contractive mapping which possesses a fixed point but is not continuous at the fixed point. Besides continuous mappings our results also apply to discontinuous mappings which include threshold operations that are integral part of many a phenomena.

In this paper we prove the local uniqueness of the fixed point of the probabilistic q-contraction in fuzzy metric space.

In this paper, we present a new classes of ideals: called n-ideal. Let R be a commutative ring with nonzero identity. We define a proper ideal I of R as an n-ideal if whenever ab is an element of I with a is not an element of root 0, then b is an element of I for every a, b is an element of R. We investigate some properties of n-ideals analogous with prime ideals. Also, we give many examples with regard to n-ideals.

In this paper, we consider perturbation analysis for the generalized Drazin inverse of an operator in Banach space. An necessary and sufficient condition for the generalized Drazin invertible is given. The upper bound is given under some certain conditions, and a relative perturbation bound is also considered.

The aim of the present paper is to show the significance of the concept of orbital continuity introduced by Ciric. We prove that orbital continuity of a pair of R-weak commuting self-mappings of type Af or of type A1 of a complete metric space is equivalent to fixed point property under Jungck type contraction. We also establish a situation in which orbital continuity is a necessary and sufficient condition for the existence of a common fixed point of a pair of mappings yet the mappings are necessarily discontinuous at the fixed point.

In this note, we point out several gaps in the paper ?On the lower bound for a class of harmonic functions in the half space? by Zhang, Deng and Kou (Acta Math. Sci. Ser. B Engl. Ed., 32(4), 2012) and give the main results under weaker conditions.

In this paper, we consider the various sets of comultiplications of a wedge of spheres and provide some methods to calculate many kinds of comultiplications with different properties. In particular, we concentrate on studying to compute the number of comultiplications, associative comultiplications, commutative comultiplications, and comultiplications which are both associative and commutative of a wedge of spheres. The more spheres that appear in a wedge, the more complicate the proofs and computations become. Our methods involve the basic Whitehead products in a wedge of spheres and the Hopf-Hilton invariants.

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.

In this paper, the Mannheim mate curves of the proper biharmonic curves in Cartan-Vranceanu 3-dimensional spaces (M,ds2l,m), with l2 ? 4m and m ? 0 are studied. We give the definition of the Mannheim mate of a proper biharmonic curve and give the explicit parametric equations of that Mannheim mate curve in Cartan-Vranceanu 3-dimensional space. Moreover, we show that the distance between corresponding points of the Mannheim pairs is constant in Cartan-Vranceanu 3-dimensional spaces.

In this paper, we extend the definition of weakly second submodule of a module over a commutative ring to a module over an arbitrary ring. First, we investigate some properties of weakly second submodules. We define the notion of weakly second radical of a submodule and determine the weakly second radical of some modules. We also define the notion of weak m*-system and characterize the weakly second radical of a submodule in terms of weak m*-systems. Then we introduce and study a topology on the set of all weakly second submodules of a module. We give some results concerning irreducible subsets, irreducible components and compactness of this topological space. Finally, we investigate this topological space from the point of view of spectral spaces.

Aktu?lu and H. Gezer [Central European J. Math. 7 (2009), 558-567] introduced the concepts of lacunary equistatistical convergence, lacunary statistical pointwise convergence and lacunary statistical uniform convergence for sequences of functions. In this paper, we apply the notion of lacunary equistatistical convergence to prove a Korovkin type approximation theorem by using test functions 1, x/1-x,(x/1-x)2.

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

In this paper, we examine the stability of several spectral properties under commuting perturbations. In particular, we show that if T ( L(X) is an isoloid operator satisfying generalized Weyl?s theorem and if F ( L(X) is a power finite rank operator that commutes with T, then generalized Weyl?s theorem holds for T + F. In addition, we consider the permanence of Bishop?s property (?), at a point, under commuting perturbation that is an algebraic operator.

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.

An operator T is said to be k-quasi-∗-paranormal if ||Tk+2x||||Tkx|| ≥ ||T∗Tkx||2for all x ∈ H, where k is a natural number. In this paper, we give the inclusion relation of k-quasi-∗-paranormal operators and k-quasi-∗-A operators. And we prove that if T is an algebraically k-quasi-∗-paranormal operator, then T is polaroid and has SVEP. We also show that if T is an algebraically k-quasi-∗-paranormal operator, then Weyl type theorems hold for T.

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.

iscan, imdat/0000-0001-6749-0591; SET, ERHAN/0000-0003-1364-5396; Kara, Hasan Huseyin/0000-0002-4701-8545 WOS: 000393218000001 In this paper, we established Hermite-Hadamard-Fejer type inequalities for s-convex functions in the second sense via fractional integrals. The some results presented here would provide extansions of those given in earlier works.

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.

The purpose of this paper is to give some new symmetric identities for the higher-order q-Euler polynomials of the first kind related to symmetry group S3 arising from p-adic q-fermionic integrals on Zp.