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In this paper, we establish the generalized viscosity implicit rules of asymptotically nonexpansive mappings in CAT(0) spaces. The strong convergence theorems of the implicit rules proposed are proved under certain assumptions imposed on the control parameters. The results presented in this paper improve and extend some recent corresponding results announced. [ABSTRACT FROM AUTHOR]

In this paper, we present a explicit viscosity technique of nonexpansive mappings in the framework of CAT(0) spaces. The strong convergence theorem of the proposed technique is proved under certain assumptions imposed on the sequence of parameters. The results presented in this paper extend and improve some recent announced in the current literature. [ABSTRACT FROM AUTHOR]

In this paper, we establish two versions of the existence theorems of solutions set of generalized vector variational-like inequalities in fuzzy environment by using two different notions; the first one by using affineness and the second by using the notion of vector O-diagonally convexity. Moreover, an example is established in order to illustrate the main problem. The results of this paper can be viewed as a significant improvement and refinement of several other previously existing known results. [ABSTRACT FROM AUTHOR]

In this paper, we prove the generalized Hyers-Ulam stability for the following cubic functional equation with involution f(2x + y) + f(2x + σ(y)) - 2f(x + y) - 2f(x + σ(y)) - 12f(x) = 0 in modular spaces by using a fixed point theorem. [ABSTRACT FROM AUTHOR]

In this paper, for any smooth function on [0, 1]², we give an asymptotic representation of hyperbolic cross approximations of its Fourier series whose principal part is determined by the values of the function at vertexes of [0, 1]² and present a novel approach to estimates of the upper bounds of approximation errors. At the same time, we also give an asymptotic formula of partial sum approximations whose principal part is determined by not only partial derivatives at vertexes of [0, 1]², but also mean values on each side. Comparing asymptotic representations of these two kinds of approximation, we find that although in general the hyperbolic cross approximation is better than the partial sum ap- proximation, the partial sum approximation possibly work better under some cases, and we also give the corresponding necessary and sufficient condition to characterize these cases. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to investigate the global stability of the solutions, the boundedness and the periodic character of the nonlinear difference equation xn+1 = αxn+βxn-l+γxn-k + axnxn-k/bxn + cxn-l + dxn-k, n = 0, 1, ..., where the parameters α, β, γ, a, b, c and d are positive real numbers and the initial conditions x-s, x-s+1, ..., x-1, x0 are positive real numbers where s = max{l, k}. Some numerical examples will be given to explicate our results. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the form of the solutions and the periodicity character of the following systems of nonlinear difference equations of order two zn+1=zn+tn-l/±tn±tn-1,tn+1=tnzn-l/±zn±zn-l where the initial conditions z-1, z0, t-1 and t0 are nonzero real numbers. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new extragradient method with regularization for finding a common element of the solution set Γ of the split feasibility problem and the set Fix(S) of fixed points of a nonexpansive mapping S in infinitedimensional Hilbert spaces, combining the regularization method and the technique of averaged operator, we prove the sequences generated by the proposed algorithm converge weakly to an element of Fix(S)∩Γ under mild conditions. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of analytic functions associated with Mittag-Leffler fuction in the open unit disk. Several properties of functions belonging to this class are derived. [ABSTRACT FROM AUTHOR]

The object of the present paper is to obtain subordination, superordination and sandwich-type results related to a certain family of integral operators defined on the space of multivalent functions in the open unit disk. Also we point out relevant connections of the results presented here with those obtained in earlier. [ABSTRACT FROM AUTHOR]

The stabilization problem of state observer based for linear discrete-time periodic (LDP) system and its robust consideration are discussed in this paper. It is proved that the periodic controller and the full-dimensional periodic state observer can be designed separately. Based on the well-known CGalgorithm for matrix equation Ax = b as well as applying the lifting technique and algebraic operations, an iterative algorithm for both periodic observer gains and periodic state feedback gains can be generated simultaneously. By optimizing the free parameter matrix in the proposed algorithm, a robust stabilization algorithm based on periodic observer for LDP systems is presented. One numerical example is worked out to illustrate the effect of the proposed approaches. [ABSTRACT FROM AUTHOR]

In this paper we study that the second kind q-Euler numbers En,q and q-Euler Euler polynomials En,q(x) are analytic continued to Eq(s) and Eq(s,w). We investigate the new concept of dynamics of the zeros of analytic continued polynomials. Finally, we observe an interesting phenomenon of 'scattering' of the zeros of Eq(s,w). [ABSTRACT FROM AUTHOR]

In this paper, we prove several fixed point results for mappings of Caristi type in the setting of G-metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we mainly investigate the problem of normal families of meromorphic functions concerning shared functions, and obtain some normality criteria of meromorphic functions sharing a holomorphic function. Our results generalize or extend the previous theorems given by Ding J. J., Ding L. W. and Yuan W. J.. [ABSTRACT FROM AUTHOR]

This paper deals with the existence of continuous selection of a multivalued mapping in product space. Many authors provided existence of continuous map for lower semicontinuous. We provide continuous selection for weakly lower semicontinuous. Rhybinski [9] proved the existence for contraction type mapping. We prove the existence for some general type of mapping different from contraction mapping. [ABSTRACT FROM AUTHOR]

In this paper we establish some equalities and inequalities for K-g-frames. Our results generalize the remarkable results obtained by Balan et al. and Găvruţa. We also give several new inequalities for K-g-frames by using operator theory methods, which differ in structure from those for frames. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to study the existence of solution of a system of differential equations using fixed point technique. In this regard, in the first part of this article, along with some properties of partial b-metric topology, we prove a common fixed point theorem for generalized Geraghty type contraction mappings in a complete partial b-metric spaces. Then in second part we apply this result to show the existence of the solution of a system of ordinary differential equations. [ABSTRACT FROM AUTHOR]

In the paper, the authors established two best approximation formulas for the Bateman's G-function. Also, they studied the completely monotonicity of some functions involving G(x). Some new inequalities are deduced for the function and its derivative such as 1/2 ln [1 + 2x + a/x2 + 2x + 4/3 ] < G(x + 2) < 1/2 ln [ 1 + 2x + b/x2 + 2x + 4/3 ], x > 0 where a = 3 and b = e4-16/12 are the best possible constants. Our results improve some recent inequalities about the function G(x). [ABSTRACT FROM AUTHOR]

In this paper, we discuss two quotient BI-algebras induced by fuzzy normal subalgebras and induced by fuzzy congruence relations, which are useful in the study of the structural theory of fuzzy quotient BI-algebras. [ABSTRACT FROM AUTHOR]

In this paper, we apply umbral calculus techniques in order to derive explicit exprissions, some properties, recurrence relations and identities for degenerate poly-Genocchi polynomials. Further-more, we derive several explicit expressions of degenerate poly-Genocchi polynomials as linear combinations of some of the well-known families of special polynomials. [ABSTRACT FROM AUTHOR]

In this paper, we consider three types of functions given by the sums of products of poly-Genocchi and poly-Bernoulli functions and derive their Fourier series expansions. Moreover, we will express each of them in terms of Bernoulli functions. [ABSTRACT FROM AUTHOR]

In this paper, we, motivated by Mihet [2], give the concept of two nonlinear contractions ((φ, ε-λ)-contraction and (f, bn)-contraction) in KM-fuzzy metric spaces, and obtained some fixed point theorems. We answer the open question posed by Mihet in [2, open question 2]. Finally, an example can be used to be exemplify our results. [ABSTRACT FROM AUTHOR]

The objective of this paper is to investigate and extend some Pachpatte type dynamic inequalities on time scales in three independent variables which provide explicit bounds on unknown functions and their derivatives. Some applications are also discussed here in order to illustrate the usefulness of our results. [ABSTRACT FROM AUTHOR]

In this paper, we study differential equations arising from the generating functions of generalized degenerate tangent polynomials. We give explicit identities for the generalized degenerate tangent polynomials arising from differential equations. [ABSTRACT FROM AUTHOR]

In this paper, we would like to exploit umbral calculus in order to derive explicit expressions, some properties, recurrence relations and identities for poly-Genocchi polynomials. [ABSTRACT FROM AUTHOR]

In this paper we introduce a generalized form of the well known ToDD's difference equation and give the closed form expressions for this generalized form . In other words , we have the following nonlinear rational partial difference equation T ‹X1,X2,X3, …,Xn› = 1 + T ‹X1 - 1,X2 - 1, …,Xn - 1› + T ‹X1 - 2,X2 - 2, …,Xn - 2› T ‹X1 - 3,X2 - 3,X3 - 3, …,Xn - 3› where X1,X2, …:,Xn ∊ ℕ,and the initial values T ‹p1, p2, …:, pn› ,T ‹p2, p1, p3, p4, …, pn› ,T ‹p2, p3, p1, p4, …, pn›,… …,T ‹p2, p3, p4, …p1, pn›,T ‹p2 - 3, p3 - 3, p4 - 3, …pn - 3, p1› are real numbers with p1 ∊ {0,-1,-2} and p2, p3, …, pn ∊ ℕ such that T ‹p1, p2, …:, pn› ≠ 0 ,T ‹p2, p1, p3, p4, …, pn› ≠ 0 , T ‹p2, p3, p1, p4, …, pn› ≠ 0,…,T ‹p2 - 3, p3 - 3, p4 - 3, …pn - 3, p1› ≠ 0. We will use a novel technique to prove the results by using what we call 'piecewise n-dimensional mathematical induction' which we intro- duce here for the first time . We will obvious that this new concept represents generalized form for many types of mathematical induction . As a direct consequences , we investigate and drive the explicit solutions for the well known ordinary ToDD's difference Equation . [ABSTRACT FROM AUTHOR]

The Changhee polynomials and numbers are introduced in [3], and some interesting identities and properties of these polynomials are found by many researcher. In this paper, we consider the q-analogue of modified degen-erated Changhee polynomials and derive some new and interesting identities and properties of those polynomials. [ABSTRACT FROM AUTHOR]

In this paper, we develop some fixed point theorems by using auxiliary functions for maps satisfying a rational type contractive condition in partially ordered S-metric spaces. Conditions for uniqueness of fixed point are also discussed. Our results generalize some existing results in the literature of S-metric spaces. [ABSTRACT FROM AUTHOR]

Recently, several researchers have studied for Appell-type of various polynomials (see [18-20,22]). In this paper, we consider some families of Appell-type q-Bernoulli polynomials and numbers. In particular, we derive some interesting identities for the Appell-type degenerate q-Bernoulli polynomials by using the some properties of those polynomials. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and solve the following quadratic (ƿ1, ƿ2)-functional inequalities... where ƿ1 and ƿ2 are fixed nonzero complex numbers with... where ƿ1 and ƿ2 are fixed nonzero complex numbers with... Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic (ƿ1; ƿ2)- functional inequalities (0.1) and (0.2) in complex Banach spaces. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the existence of positive solutions of the fully third-order boundary value problem... is continuous. Some inequality conditions on f to guarantee the existence of positive solution are presented. These inequality conditions allow that ƒ(t; x; y; z) may be superlinear or sublinear growth on x, y and z as |(x; y; z)| → 0 and |(x; y; z)| → ∞. [ABSTRACT FROM AUTHOR]

In this paper, some qualitative properties are discussed such as the boundedness, the periodicity and the global stability of the positive solutions of the nonlinear difference equation... where the coefficients A; αi; βi 2 (0,1), i = 1,...., 5; while the initial conditions y-5,y-4,y-3,y-2; y-1; y0 are arbitrary positive real numbers. Some numerical examples will be given to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we consider three types of functions related to higher-order Genocchi functions and derive their Fourier series expansions. In addition, we express each of them in terms of Bernoulli functions. [ABSTRACT FROM AUTHOR]

In this paper we study certain strong differential superordinations, obtained by using a new integral operator introduced in [13]. [ABSTRACT FROM AUTHOR]

In this paper we derive the famous Fekete-Szegö inequality for the class of p-valent non-bazilevič function using differential operator. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to study the existence of solution of a system of differential equations using fixed point technique. In this regard, in the first part of this article, along with some properties of partial b-metric topology, we prove a common fixed point theorem for generalized Geraghty type contraction mappings in a complete partial b-metric spaces. Then in second part we apply this result to show the existence of the solution of a system of ordinary differential equations. [ABSTRACT FROM AUTHOR]

This paper proposes the concept of trapezoidal interval type-2 hesitant fuzzy set (TIT2HFS), which is a generalization of trapezoidal interval type-2 and hesitant fuzzy set. Also, we study some of its operation laws and corresponding proprties are discussed. [ABSTRACT FROM AUTHOR]

New iterative algorithms are introduced to solve periodic Sylvester matrix equations in this paper. The iterative algorithms are based on the principle of matrix splitting and gradient iteration method. Detailed iterative steps for solving equations are presented and their convergence property are strictly verified. A numerical test is employed to prove the correctness and effectiveness of the iterative algorithms. [ABSTRACT FROM AUTHOR]

In this paper, motivated by some results of Dyakonov, we give an inner-outer factorization on Besov-type spaces. [ABSTRACT FROM AUTHOR]

In this paper, we solve the following additive-quadratic ρ-functional inequalities ‖f(x + y) + f(x - y) - 2f(x) - f(y) - f(-y)‖ (0.1) ⩽ ǁρ 2f ( x + y 2 ) + 2f ( x - y 2 ) - 3/2 f(x) + 1 2 f(-x) - 1/2 f(y) - 1/2 f(-y)ǁ ; where ρ is a fixed complex number with ǀρǀ < 1, and ǁ2f ( x + y 2 ) + 2f (-x - y 2) - 3/2 f(x) + 1 2 f(-x) - 12 f(y) - 1/2 f(-y)ǁ ⩽‖ρ(f(x + y) + f(x - y) - 2f(x) - f(y) - f(-y)ǁk; (0.2) where ρ is a fixed complex number with ǀρǀ < 1 2 , and prove the Hyers-Ulam stability of the additivequadratic ρ-functional inequalities (0.1) and (0.2) in β-homogeneous complex Banach spaces and prove the Hyers-Ulam stability of additive-quadratic ρ-functional equations associated with the additive-quadratic β-functional inequalities (0.1) and (0.2) in β-homogeneous complex Banach spaces. [ABSTRACT FROM AUTHOR]

In this paper, we prove some fixed point results for generalized contractive multimaps with respect to generalized distance. Consequently, several known fixed point results either generalized or improved including the corresponding recent fixed point results of Ciric, BinDehaish-Latif, Latif-Albar, Klim-Wardowski, Feng-Liu. [ABSTRACT FROM AUTHOR]

In this paper, the concept of fuzzy share functions of cooperative fuzzy games with fuzzy characteristic functions is proposed. Players in the proposed cooperative fuzzy game do not need to know precise information about the payoff value. We generalize the axiom of additivity by introducing a positive fuzzy value function ∼μ on the class of cooperative fuzzy games in fuzzy characteristic function form. The so-called axiom of ∼μ-additivity generalizes the classical axiom of additivity by putting the weight ∼μ(∼υ) on the value of the game ∼υ. We show that any additive function ∼μ- determines a unique fuzzy share function satisfying the axioms of effcient shares, null player property, symmetry and ∼μ-additivity on the subclass of games on which ∼μ is positive and which contains all positively scaled unanimity games. Finally, we introduce the fuzzy Shapley share functions and fuzzy Banzhaf share functions for the cooperative fuzzy games with fuzzy characteristic functions. [ABSTRACT FROM AUTHOR]

In this paper, we study the behavior of the solutions of the following rational difference equation with big order xn+1 = axn-l + bxn-k + cxn-s + dxn-t/exn-s + fxn-t where the parameters a; b; c; d; e and f are positive real numbers and the initial conditions x-r, x-r+1, x-1 and x0 are positive real numbers where r = max(l, k, s, t). [ABSTRACT FROM AUTHOR]

In this paper we use the differential subordinations techniques to obtain some properties of functions belonging to the class of analytic functions in the open unit disc U. Also, some properties of the class of two fixed points in U; are also discussed. Furthermore, some interesting results of Hurwitz Lerch Zeta function and Digamma function are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we solve the following cubic ρ-functional inequality ‖f(2x + y) + f(2x - y) - 2f(x + y) - 2f(x - y) - 12f(x)‖ ⩽ ǁ ρ 4f (x + y/2 )+ 4f (x - y/2) - f(x + y) - f(x - y) - 6f(x))ǁ ; (0.1) where ρ is a ρ xed complex number with ǀρǀ < 2, and the quartic ρ-functional inequality ‖f(2x + y) + f(2x - y) - 4f(x + y) - 4f(x - y) - 24f(x) + 6f(y)‖ (0.2) ⩽ ǁ ρ(8f x + y/2( + 8f (x - y/2) - 2f(x + y) - 2f(x - y) - 12f(x) + 3f(y) ǁ ; where ρ is a fixed complex number with ǀρǀ <2. Using the direct method, we prove the Hyers-Ulam stability of the cubic ρ-functional in- equality (0.1) and the quartic ρ-functional inequality (0.2) in complex Banach spaces. [ABSTRACT FROM AUTHOR]

In this paper, first, we consider the distribution and survival functions and we define intuitionistic random Lie C-algebras. As an application, using the fixed point method, we approximate the derivations on intuitionistic random Lie C-algebras for the the following additive functional equation∑m i=1 f ( mxi + ∑m j=1; j≠i xj ) + f (∑m i=1 xi ) = 2f (∑m i=1 mxi ) for all m ∊N with m ⩾ 2. [ABSTRACT FROM AUTHOR]

Topology and rough set theory are widely used in research field of computer science. In this paper, we study properties of topologies induced by binary relations, investigate a particular type of topological spaces which associate with some equivalence relation (i.e., approximating spaces) and obtain some characteristic conditions of approximating spaces. [ABSTRACT FROM AUTHOR]

In this paper, some new mixed type Riemann-Liouville and Hadamard fractional integral inequalities are established, in the case where the functions are bounded by integrable functions. Moreover, mixed type Riemann-Liouville and Hadamard fractional integral inequalities of Chebyshev type are presented. [ABSTRACT FROM AUTHOR]

An IF rough set, which is the result of approximation of an IF set with respect to an IF approximation space, is an extension of fuzzy rough sets. This paper studies rough set theory within the context of lattices. First, we introduce the concepts of IF rough sets and IF rough approximation operators based on lattices. Then, we give some properties on IF rough approximations of IF sublattices such as IF ideals and IF filters. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze a viral infection model with humoral immunity. The incidence rate is given by Hill type infection rate. We have derived two threshold parameters, R0 and R1 which completely determined the global properties of the model. By constructing suitable Lyapunov functions and applying LaSalle's invariance principle we have established the global asymptotic stability of all steady states of the model. We have proven that, if R0 ⩽ 1, then the infection-free steady state is globally asymptotically stable (GAS), if R1 ⩽ 1 < R0, then the chronic-infection steady state without humoral immune response is GAS, and if R1 > 1, then the chronic-infection steady state with humoral immune response is GAS. [ABSTRACT FROM AUTHOR]