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In this paper, we deal with the uniqueness problem of two non-admissible functions sharing some values and sets in the unit disc, and also investigate the problem on an admissible function and a non-admissible function sharing some values and sets. Some theorems of this paper improve the results given by Fang. In addition, the results in this paper analogous version of the uniqueness theorems of meromorphic functions sharing some sets on the whole complex plane which given by Yi and Cao. [ABSTRACT FROM AUTHOR]

The main objective of the present paper is to obtain sufficient conditions for the univalence, starlikeness and convexity of a new integral operator defined on the space of normalized analytic functions in the open unit disk. Results presented in this paper may motivate further reserch in this fascinating field. [ABSTRACT FROM AUTHOR]

The "oldest quartic" functional equation was introduced and solved by the author of this paper (see: Glas. Mat. Ser. III 34 (54) (1999), no. 2, 243-252) which is of the form: f(x + 2y) + f(x - 2y) = 4[f(x + y) + f(x - y)] - 6f(x)+ 24f(y). Interesting results have been achieved by S.A. Mohiuddine et al., since 2009. In this paper, we are introducing new quartic functional equations, and establish fundamental formulas for the general solution of such functional equations and for "Ulam stability" of pertinent quartic functional inequalities. [ABSTRACT FROM AUTHOR]

The "oldest quartic" functional equation was introduced and solved by the author of this paper (see: Glas. Mat. Ser. III 34 (54) (1999), no. 2, 243-252) which is of the form: f(x + 2y) + f(x - 2y) = 4[f(x + y) + f(x - y)] - 6f(x)+ 24f(y). Interesting results have been achieved by S.A. Mohiuddine et al., since 2009. In this paper, we are introducing new quartic functional equations, and establish fundamental formulas for the general solution of such functional equations and for "Ulam stability" of pertinent quartic functional inequalities. [ABSTRACT FROM AUTHOR]

In the present paper, we aim to investigate a new q-integral inequality of Grüss type for the Saigo fractional q-integral operator. Some special cases of our main results are also provided. The results presented in this paper improve and extend some recent results. [ABSTRACT FROM AUTHOR]

In this paper, we consider the preconditioned generalized accelerated overrelaxation (GAOR) methods for solving weighted linear least squares problems. New type of preconditioners are proposed and the convergence rates of the new preconditioned GAOR methods are studied. Comparison results show the effectiveness of the proposed preconditioners in this paper. A numerical example is given to confirm our theoretical results. [ABSTRACT FROM AUTHOR]

In the present paper we establish several differential superordinations regarding the operator RDλ,αn defined by using Ruscheweyh derivative Rn f (z) andthe generalizedSălăgean operator Dλn f (z), RDλ,αn : A → A, RD RDλ,αn f (z) = (1 - α)Rn f (z) + αDλn f (z),z ∈ - U, where n ∈ ..., λ, α ≥ 0 and f ∈ A, A = {f ∈ H(U) : f (z) = z + ...,z ∈ U}. A number of interesting consequences of some of these superordination results are discussed. Relevant connections of some of the new results obtained in this paper with those in earlier works are also provided. [ABSTRACT FROM AUTHOR]

In this paper, we give some interesting identities of higher-order Bernoulli, Frobenius-Euler and Euler polynomials arising from umbral calculus. From our method of this paper, we can derive many interesting identities of special polynomials. [ABSTRACT FROM AUTHOR]

In the present paper, we obtain the Voronovaskaja-type results of approximation by a type of Bernstein-Stancu operators with shifted knots. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the second kind twisted q-Euler polynomials E(k) n;!;q(x) of order k. We also get interesting properties related to the second kind twisted q-Euler numbers and polynomials. Finally, we construct twisted q-zeta function of order which interpolates the second kind twisted q-Euler numbers of higher order at negative integer. [ABSTRACT FROM AUTHOR]

In this paper, we study about the q-exponential function which was introduced by Exton. We propose the addition theorem for this q-exponential function and also Continued fraction representation for this q{exponential function is given. [ABSTRACT FROM AUTHOR]

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

Our purpose in this paper, is to derive the main properties of the generalized moment functions defined on some types of white noise spaces. A new version of Wick product on some spaces of generalized functions is introduced. Applying the direct connection between the theory of construction for hypercomplex systems and white noise analysis, we setup a framework to construct a lot of spaces of generalized functions connected with different examples of hypercomplex systems. [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, we prove that a covering approximation space (U; C) is an Sr-covering approximation space if and only if {N(x) : x ∈ U} forms a partition of the universe of discourse U. Furthermore, we give some simple characterizations for Sr-space (U; C) by using only a single covering approximation operator and by using only elements of covering C. Results of this paper answer affirmatively an open problem posed by Z.Yun et al. in [16]. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study the random nonlinear variational inclusion problem with multi-valued random operators. We define a random iterative algorithm for finding the approximate solutions of class of random variational inclusions and establish the convergence of random iterative sequence generated by proposed algorithm in a uniformly smooth Banach space. Our result in this paper improves and generalizes some know corresponding results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we observe the behavior of real roots of the second kind q-Bernoulli polynomials Bn,q(x) for 0 < q < 1. By means of numerical experiments, we demonstrated a remarkably regular structure of the complex roots of the second kind q-Bernoulli polynomials Bn,q(x) for -1 < q < 0. The main purpose of this paper is to investigate the zeros of the second kind q-Bernoulli polynomials Bn,q(x) for -1 < q < 0. Furthermore, we give a table for the solutions of the second kind q-Bernoulli polynomials Bn,q(x) for -1 < q < 0. [ABSTRACT FROM AUTHOR]

A new representation for fuzzy systems in terms of additive and multiplicative subsystem inferences of single variable is proposed. This representation enables an approximate functional characterization of the inferred output. The form of the approximating function is dictated by the choice of polynomial, sinusoidal, or other designs of subsystem inferences. The paper is organized as follows. The first section gives a brief review on product sum fuzzy inference and introduces the concepts of additive and multiplicative decomposable systems. The second section presents the proposed subsystem inference representation. The third section focuses on subsystem inference of single variable. The sections 4 to 6 discuss the cases of polynomial, sinusoidal, orthonormal and other designs of subsystem inferences, and their applications. The section 7 presents some conclusions. The paper one finishes with its references. [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]

In this paper, we introduce and solve the following additive (ρ1, ρ2)-functional in-equalities (0.1) ∥f (x + y + z) - f(x) - f(y) - f(z)∥ ≥ ∥ρ1(f(x + y - z) - f(x) - f(y) + f(z))∥ + ∥ρ2 (f(x - y + z) - f(x) + f(y) - f(z))∥, where ρ1 and ρ2 are fixed complex numbers with |ρ1| ⋅ |ρ2| > 1, and (0.2) ∥f (x + y - z) - f(x) - f(y) + f(z)∥ ≥ ∥ρ1(f(x + y + z) - f(x) - f(y) f(z))∥ + ∥ρ2 (f(x - y + z) - f(x) + f(y) f(z))∥ where ρ1 and ρ2 are fixed complex numbers with |ρ1| > 1. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive (ρ1, ρ2)-functional inequalities (0.1) and (0.2) in complex Banach spaces. [ABSTRACT FROM AUTHOR]

In this paper, the concepts of differentiability and gradient for fuzzy mappings are presented and discussed using the characteristic theorem for generalized difference of n dimensional fuzzy numbers. The relationships of gradient, support-function-wise gradient and level-wise gradient are characterized. [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, 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]

Recently, stability results of set-valued functional equations on domain of cones in Banach spaces are obtained by several authors. In this paper, we present the refined stability results of set-valued functional equations which is stable in the sense of Aoki, Rassias and Găvrută on domain of cones. [ABSTRACT FROM AUTHOR]

In this paper, we would like to use umbral calculus in order to derive some properties, recurrence relations and identities related to r-Stirling numbers of second kind and r-Bell polynomials. In particular, we will express the r-Bell polynomials as linear combinations of many well-known families of special polynomials. [ABSTRACT FROM AUTHOR]

In this paper we discuss the concept of a Z-sequence and use it to define the Fibonacci Z-sequence. Based on Z-sequences one may define analogs of logarithm functions. The special case of the logarithm function associated with the Fibonacci Z-sequence is of interest, since the recursive property of this sequence permits a more detailed study of these functions. They are similar to ordinary logarithm functions which may be based onZ-sequences {an}nϵZ, where a > 1. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new idea of best proximity point of F-contraction on a closed ball and obtain new theorems in a complete metric space. That is why this outcome becomes useful for contraction of a mapping on a closed ball instead of the whole space. At the same time, some comparative examples are constructed which establish the superiority of our results. Our results that have come into being give a proof of extension as well as substantial generalizations and improvements of several well known results in the existing comparable literature. [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]

The purpose of this paper is to introduce the concept of a Menger probabilistic normed Riesz space. We study some properties of these spaces and compare normed Riesz spaces with Menger probabilistic normed Riesz spaces. Next, we investigate the Hyers-Ulam stability of lattice homomorphisms in Menger probabilistic normed Riesz spaces. [ABSTRACT FROM AUTHOR]

In this paper, some notions are introduced in modular metric spaces. Next some common fixed points are established in ω-orbitally complete modular metric spaces by employing C-class functions that extend and generalize the results of [10, 18]. Finally, for usibility of our results an application is provided to show the existence of solutions for certain system of integral equations. [ABSTRACT FROM AUTHOR]

Let A be the class of analytic functions in the open unit disc U with normalization ƒ(0) = ƒ'0 (0) - 1 = 0: The purpose of the present paper is to obtain several sufficient conditions of starlikeness and strongly starlikeness for some subclasses of A with fixed second coefficients that satisfy certain conditions for the quotient of the representations of convexity and starlikeness. [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]

Recently, Mihoubi and Taharbouchet gave some interesting method of obtain-ing certain identities for Appell polynomials of arbitrary orders starting from the given identities for Appell polynomials of fixed orders. In addition, they illustrated their method with several examples. The purpose of this paper is to note that their method can be gen-eralized so as to include any Sheffer polynomials. Also, we will provide many examples that illustrate our results. [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]

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, we give some necessary conditions on the existence of meromorphic solutions on Fermat type difference equations. We also consider the properties of transcendental entire solutions on the systems of Fermat type differential-difference equations. [ABSTRACT FROM AUTHOR]

In this paper, we study locally and globally small Riemann sums with respect to α for n-dimensional fuzzy number valued functions. And we prove that a fuzzy-number-valued functions in n-dimensional is Henstock-Stieltjes (HS) integrable on [a; b] if and only if it has (LSRS) with respect to α on [a, b]. Also we shall prove that a fuzzy number valued functions in n-dimensional is Henstock-Stieltjes (HS) integrable on [a, b] if and only if it has (GSRS) with respect to α on [a; b]. [ABSTRACT FROM AUTHOR]

In this paper we are interested to give the Hadamard inequality for n-times differentiable convex functions via Caputo fractional derivatives. We also find bounds of a difference of this inequality. [ABSTRACT FROM AUTHOR]

In this paper we introduce the notion of Fibonacci periodicity modulo n, denoting this period by the function ̂F(n). We note that ̂F(n) is an integral multiple of a fundamental frequency ̂f(n), where the ratio ̂F(n)= ̂f(n) is a power of 2 for a collection of observed values of n. It is demonstrated that if a, b are natural numbers with gcd(a, b) = 1, then ̂F(n) = lcmf ̂F(a), ̂F(b)g and thus that ̂F is a non-trivial example of a function which we refer to as radical. From observations it also seems clear that ̂F(ps+1)/̂F(ps) = p for primes p. [ABSTRACT FROM AUTHOR]

Recently, stability results of set-valued functional equations on domain of cones in Banach spaces are obtained by several authors. In this paper, we present the refined stability results of set-valued functional equations which is stable in the sense of Aoki, Rassias and Găvrută on domain of cones. [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 present new fixed point theorems for Kannan type Fp-contraction and Kannan type (α, η, GFp)-contraction on a closed ball contained in a complete partial metric space. Some comparative examples are constructed to illustrate the signifficance of these results. Our results provide substantial generalizations and improvements of several well known results existing in the comparable literature. [ABSTRACT FROM AUTHOR]

In a group decision making (GDM) situation with qualitative settings and complex environments, experts may require intervals with corresponding possibility values, rather than only intervalvalued hesitant fuzzy sets (IVHFSs) or probability-hesitant fuzzy sets (P-HFSs), to express their preferences. In this paper, in line with such situations, probability-interval valued hesitant fuzzy sets (P-IVHFSs) are presented to address GDM problems with hesitant fuzzy intervals and the corresponding possibility values. A P-IVHFS can serve as an extension of both a P-HFS and an IVHFS. As important tools in GDM, P-IVHFSs can describe the actual preferences of decisionmakers and better reflect their uncertainty, hesitancy, and inconsistency, thus enhancing the modeling abilities of HFSs. Firstly, the concept of P-IVHFSs is defined, and then some properties of P-IVHFSs are presented. Furthermore, probability-interval valued hesitant fuzzy preference relations (P-IVHFPRs) are defined and the consistency of P-IVHFPRs is discussed. Then, based on related research, a decomposition method is developed to deal with the consistency of P-IVHFPRs. Finally an example is provided to illustrate the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the stability of the Cauchy-Jensen and bi-quadratic functional equation 2f (x + y,z + w2) = f(x, z) + f(x,w) + f(y, z) + f(y,w), f(x + y, z + w) + f(x + y,z - w) + f(x - y, z + w) + f(x - y, z - w) = 4[f(x, z) + f(x,w) + f(y, z) + f(y,w)], respectively, in 2-Banach spaces. [ABSTRACT FROM AUTHOR]

Abstract. In this paper, we introduce and solve the following additive (ρ1; ρ2)-functional in- equalities ‖ (x + y + z) - f(x) - f(y) - f(z)‖ ≥ kρ,1(f(x + y - z) - f(x) - f(y) + f(z))‖ +‖ρ,2 (f(x - y + z) - f(x) + f(y) - f(z))‖ , (0.1) where ρ1 and ρ,2 are fixed complex numbers with |ρ1| • |ρ,2| > 1, and ‖ (x + y - z) - f(x) - f(y) + f(z)‖ ≥ ‖ρ,1(f(x + y + z) - f(x) - f(y) - f(z))‖ +‖ρ2 (f(x - y + z) - f(x) + f(y) - f(z))‖ (0.2) where ρ,1 and ρ,2 are fixed complex numbers with |ρ1| > 1. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive (ρ1, ρ,2)-functional inequalities (0.1) and (0.2) in complex Banach spaces. [ABSTRACT FROM AUTHOR]