Search

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 prove some new characterizations of weights in some Hardy-type inequalities on time scales. The results as special cases contain the results due to Beesack and Heinig, Leindler and Bloom and Kerman. Some new integral and discrete inequalities related to Copson's, Flett's, Bliss's and Bennett's will be formulated. The main results will be proved by using new generalizations of Opial's type inequalities, Hölder's inequality, Minkowski's inequality and the chain rule on time scales. [ABSTRACT FROM AUTHOR]

In this paper, we solve the additive ρ-functional inequalities ... where ρ is a fixed non-Archimedean number with |ρ| < 1, and where ρ is a fixed non-Archimedean number with |ρ} < |2|. Furthermore, we prove the Hyers-Ulam stability of the additive ρ-functional inequalities (0.1) and (0.2) in non-Archimedean Banach spaces. [ABSTRACT FROM AUTHOR]

In this paper we introduce an argument property which gives an interesting relation between the classes of strongly convex and strongly starlike functions of order α and type β in the open unit disk. Also, the sufficient condition of starlikeness under cer-tain restrictions is obtained. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study a class of new general iteration processes for two finite families of total asymptotically nonexpansive mappings in hyperbolic spaces, which includes asymptotically nonexpansive mapping, (generalized) nonexpansive mapping of all normed linear spaces, Hadamard manifolds and CAT(0) spaces as special cases. Some important related properties to the new general iterative processes are also given and analyzed, and Δ-convergence and strong convergence of the iteration in hyperbolic spaces are proved. Furthermore, some meaningful illustrations for clarifying our results and two open questions are proposed. The results presented in this paper extend and improve the corresponding results announced in the current literature. [ABSTRACT FROM AUTHOR]

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]

In this paper, the weighted boundedness for θ-type Calderón-Zygmund operators Tθ is established on the λ-central Morrey space. Futhermore, the weighted norm inequalities for commutators of [b; Tθ] generated by Tθ and BMO functions on the weighted λ-central Morrey space is also given. [ABSTRACT FROM AUTHOR]

In this paper we investigate some interesting symmetric identities for multiple twisted (h, q)-l-function and higher-order generalized twisted (h, q)-Euler polynomials in complex field. [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, a weak Galerkin (WG) finite element method is proposed for solving the convection-diffusion-reaction problems. The main idea of WG finite element methods is the use of weak functions and their corresponding discrete weak derivatives in standard weak form of the model problem. We show that the continuous time WG finite element method preserves the energy conservation law as well the optimal order error estimate in L² norm. Numerical experiment is conducted to confirm the theoretical results. [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]

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]

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, we consider three types of functions given by sums of products of higher-order Euler functions and derive their Fourier series expansions. Moreover, we express each of them in terms of Bernoulli functions. [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 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]

In the present paper, second order duality for multiobjective nonlinear programming are investigated under the second order generalized (F, b, ϕ, ρ, θ)- univex functions. The weak, strong and converse duality theorems are proved. Further, we also illustrated an example of (F, b, ϕ, ρ, θ)- univex functions. Results obtained in this paper extend some previously known results of multiobjective nonlinear programming in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we consider the uniqueness problem of admissible functions and non-admissible functions sharing some values in the unit disc. We obtain: If f1 is admissible and f2 is inadmissible satisfying lim r→1- T(r,f2) = ∞, aj(j = 1, 2, ...;q) be q distinct complex numbers. Then (i) f1(z); f2(z) can share at most three values a1, a2, a3 IM; (ii) f1(z); f2(z) can share at most five values aj(j = 1, 2, ...; 5) with reduced weight 1. Our results of this paper are improvement of the uniqueness theorems of meromorphic functions sharing some values on the whole complex plane which given by Yi and Cao. [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]

In this paper, the notions of locally and globally small Riemann sums modifications with respect to a fuzzy-number-valued functions in En are introduced and studied. The basic properties and characterizations are presented. In particular, it is proved that a fuzzy-number-valued functions in En is Henstock (H) integrable on [a,b] if and only if it has (LSRS), and also it is proved that a fuzzy-number-valued functions in En is Henstock (H) integrable on [a,b] if and only if it has (GSRS). [ABSTRACT FROM AUTHOR]

In this paper, we introduce several extensions of Meir-Keeler contractive mappings in the structure of S-metric spaces. Then we investigate some existence, uniqueness, and generalized Ulam-Hyers stability results for the classes of MKC mappings via fixed point theory. Besides the the- oretical results, we also present some illustrative examples to verify the effectiveness and applicability of our main results. [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 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 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]

This paper proposes a pointwise approximation scheme on the unit sphere S2, which aims to handle spherical scattered data with high level noise by using a regularized moving least squares (RMLS) approximation with Laplace-Beltrami operator. The pointwise errors of approximation by the RMLS are estimated, and some numerical examples are designed to examine the obtained theoretical results. Also, the given numerical examples illustrate that the different choices for the order of Laplace-Beltrami operator and regularized parameter can provide different pointwise approximation results. [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 article, we investigate the uniqueness problems of differences of meromorphic functions and obtain some results which can be viewed as discrete analogues of the results given by Yi. An example is given to show the results in this paper are best possible. [ABSTRACT FROM AUTHOR]

In this paper, we will consider three types functions associated with poly-Genocchi polynomials and find their Fourier series expansions. In addition, we will express each of them in terms of Bernoulli functions. [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, 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]

This paper is mindful with the solution of the nonlinear di¤erence equation... where the initial conditions x-6; x-5; x-4; x-3; x-2; x-1; x0 are arbitrary non zero real numbers and we study the behaviors of the solutions: Also, we gained the equilibrium points of the previous equations. [ABSTRACT FROM AUTHOR]

Recently, some authors introduced poly-Genocchi polynomials as an analogy to poly-Bernoulli polynomials. In this paper, we will consider three types of sums of products of poly-Genocchi functions and derive their Fourier expansions. In addition, we will express each of them in terms of Bernoulli functions. [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 the paper, the authors establish several new inequalities of the Hermite-Hadamard type for functions whose derivatives are extended s-convex in the absolute value and present some applications to special means of positive real numbers. [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]

One purpose of this paper is to investigate the growth of analytic function represented by Laplace-Stieltjes transform which is of infinite order and converges in the half plane, and a necessary and sufficient conditions on the growth of Laplace-Stieltjes transforms of finite XU-order was obtained. Besiders, we further investigate the error in approximating on Laplace-Stieltjes transform of finite XU-order, and obtained some relations between the error and growth of Laplace-Stieltjes transforms of finite XU-order. [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]

Let Φ be an analytic self-map of unit disk D, H(D) the space of analytic functions on D, and g ξ H(D). For an analytic function... The boundedness and compactness of C[β] Φ,g from mixed-norm spaces H(p, q, µ) to Bloch-type spaces B! are discussed in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we prove the Hyers-Ulam stability of the following additive functional equations f (x+y/2 + z + w) = 1/2 f(x) + 1/2 f(y) + f(z) + f(w), f (x+y+z/3 + w) = 1/3 f(x) + 1/3 f(y) + 1/3 f(z) + f(w) in paranormed spaces. [ABSTRACT FROM AUTHOR]

In this paper, we prove the Hyers-Ulam stability of the following additive functional equation ... in fuzzy Banach spaces, where m is a positive integer greater than 3. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce and investigate two new subclasses of the function class Σ of bi-univalent functions of complex order defined in the open unit disk, which are associated with the one of the orthogonal polynomial namely Generalized Meixner-Pollaczek polynomials, and satisfying subordinate conditions. Taylor-MacLaurin coefficients |α2| and |α3| were estimated for functions in new subclass. Furthermore, several known consequences are also investigated. [ABSTRACT FROM AUTHOR]

In this paper, in order to solve a class of nonlinear bilevel programming problems, we equivalently transform the nonlinear bilevel programming problems into corresponding single level nonlinear programming problems by using the Karush-Kuhn-Tucker optimality condition. Then, based on penalty function theory, we construct a smooth approximation method for obtaining optimal solutions of classic l1-exact penalty function optimality problems, which is equivalent to the single level nonlinear programming problems. Furthermore, using ∈-approximate optimal solution theory, we prove convergence of a simple ∈-approximate optimal algorithm. Finally, through adding parameters in the constraint set of objective function, we prove some perturbation convergence results for solving the nonlinear bilevel programming problems. [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 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 consider three types of functions involving higher-order Euler polynomials and derive their Fourier series expansions. In addition, we express each of them in terms of Bernoulli functions. [ABSTRACT FROM AUTHOR]

In the present paper, we find the general solution of the inhomogeneous Euler-Cauchy dynamic equation ... on the time scale with the constant graininess function and the linear variable graininess function, respectively. And then, we study the Ulam stability problem of the forgoing equation on different types of time scales. Our results can be viewed as a unfication and extension of the results of Mortici et al. [C. Mortici, T.M. Rassias, S.M. Jung, The inhomogeneous Euler equation and its Hyers-Ulam stability, Appl. Math. Lett. 40 (2015) 23-28]. [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]