Search

In recent years, the two-dimensional (2D) quaternion Fourier and quaternion linear canonical transforms have been the focus of many research papers. In the present paper, based on the relationship between the quaternion Fourier transform (QFT) and the quaternion linear canonical transform (QLCT), we derive a version of the uncertainty principle associated with the QLCT. We also discuss the generalization of the Hausdorff-Young inequality in the QLCT domain. [ABSTRACT FROM AUTHOR]

Based on the concept of pseudocomplement, we introduce a new representation of preopenness of L -fuzzy sets in R L -fuzzy bitopological spaces. The concepts of pairwise R L -fuzzy precontinuous and pairwise R L -fuzzy preirresolute functions are extended and discussed based on the i , j - R L -preopen gradation. Further, we follow up with a study of pairwise R L -fuzzy precompactness in R L -fuzzy bitopological spaces of an L -fuzzy set. We find that our paper offers more general results since R L -fuzzy bitopology is a generalization of L -bitopology, R L -bitopology, and L -fuzzy topology. [ABSTRACT FROM AUTHOR]

In this paper, weighted norm inequalities for multilinear Fourier multipliers satisfying Sobolev regularity with mixed norm are discussed. Our result can be understood as a generalization of the result by Fujita and Tomita by using the L r -based Sobolev space, 1 < r ≤ 2 with mixed norm. [ABSTRACT FROM AUTHOR]

This paper uses the generalization of the Hukuhara difference for compact convex set to extend the classical notions of Carathéodory differentiability to multifunctions (set-valued maps). Using the Hukuhara difference and affine multifunctions as a local approximation, we introduce the notion of CH-differentiability for multifunctions. Finally, we tackle the study of the relation among the Fréchet differentiability, Hukuhara differentiability, and CH-differentiability. [ABSTRACT FROM AUTHOR]

The aim of this paper is to extend the notion of K -Riemann integrability of functions defined over a , b to functions defined over a rectangular box of ℝ n . As a generalization of step functions, we introduce a notion of K -step functions which allows us to give an equivalent definition of the K -Riemann integrable functions. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to establish a strong convergence of a new parallel iterative algorithm with mean errors to a common fixed point for two finite families of C'iric' quasi-contractive operators in normed spaces. The results presented in this paper generalize and improve the corresponding results of Berinde, Gu, Rafiq, Rhoades, and Zamfirescu. [ABSTRACT FROM AUTHOR]

We study, in this paper, a generalized viscoelastic equation which includes several interesting models considered in some recent papers. Many physically important nonlinear PDEs can be reduced to nonlinear ODEs by means of reduction techniques. So it is significant and very interesting to study, among all the closed-form solutions admitted by the model, the corresponding kink waves. A plot of the obtained solution is performed. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study properties of the third-order delay trinomial differential equation ((1/r(t))y"(t))' + p(t)y'(t) + q(t)y(σ(t)) = 0, by transforming this equation onto the second-/third-order binomial differential equation. Using suitable comparison theorems, we establish new results on asymptotic behavior of solutions of the studied equations. Obtained criteria improve and generalize earlier ones. [ABSTRACT FROM AUTHOR]

This paper deals with the higher-order nonlinear neutral delay differential equation (dn/dtn)[x(t) + ∑Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. pi(t)x(Ti(t))] + dn-1/dtn-1) f(t, x(α1(t)),…, x(α k(t)) + h(t, x(β1(t)),…, x(βk(t)) = g(t), t ≥ to, where n, m, k ∈ ℕ, pi, τi, βj, g ∈ C ([to,+∞),ℝ, αj ∈ Cn-1 ([to, +∞),ℝ, f ∈ Cn-1([to, + ∞) x ℝk,ℝ), h ∈ C ([to, + ∞) x ℝk,ℝ, and limt → + ∞ τi(t) = limt → + ∞ αj (t) = limt → + ∞ βj (t) = +∞, i ∈ {1, 2,…, m}, j ∈ {1, 2,…, k}. By making use of the Leray-Schauder nonlinear alterative theorem, we establish the existence of uncountably many bounded positive solutions for the above equation. Our results improve and generalize some corresponding results in the field. Three examples are given which illustrate the advantages of the results presented in this paper. [ABSTRACT FROM AUTHOR]

In this paper, the notion of generalized set-valued weak θ -contractions is introduced and a new fixed point theorem for such contractions is established in the setting metric spaces. The main result is a generalization of fixed point theorems in the literature. An example and an application to generalized differential equation are given to support the validity of the main theorem. [ABSTRACT FROM AUTHOR]

A new concept of the c-distance in conemetric space has been introduced recently in 2011. The aim of this paper is to extend and generalize some fixed point theorems on c-distance in cone metric space. [ABSTRACT FROM AUTHOR]

Wulan et al. (2009), Wulan et al. characterized the compactness of composition operators on the Bloch space in the unit disk by the nth power of the induced analytic function. This paper will generalize the result to the Bloch type space in the polydisk. [ABSTRACT FROM AUTHOR]

In this paper we prove a fixed-point theorem for a class of operators with suitable properties, in very general conditions. Also, we show that some recent fixed-points results in Brzdȩk et al., (2011) and Brzdȩk and Ciepliński (2011) can be obtained directly from our theorem. Moreover, an affirmative answer to the open problem of Brzdek and Ciepliński (2011) is given. Several corollaries, obtained directly from our main result, show that this is a useful tool for proving properties of generalized Hyers-Ulam stability for some functional equations in a single variable. [ABSTRACT FROM AUTHOR]

We study the behavior of Fourier integrals summed by the symbols of elliptic operators and pointwise convergence of Fourier inversion. We consider generalized localization principle which in classical Lp spaces was investigated by Sjölin (1983), Carbery and Soria (1988, 1997) and Alimov (1993). Proceeding these studies, in this paper, we establish sharp conditions for generalized localization in the class of finitely supported distributions. [ABSTRACT FROM AUTHOR]

We provide some new type of mappings associated with pseudocontractions by introducing some actual examples in smooth and strictly convex Banach spaces. Moreover, we also find the significant inequality related to the mappings mentioned in the paper and the mappings defined from generalized mixed equilibrium problems on Banach spaces. We propose an iterative shrinking projection method for finding a common solution of generalized mixed equilibrium problems and fixed point problems of closed and f-quasi-strict pseudo-contractions. Our results hold in reflexive, strictly convex, and smooth Banach spaces with the property (K). The results of this paper improve and extend the corresponding results of Zhou and Gao (2010) and many others [ABSTRACT FROM AUTHOR]

Lattice-valued fuzzy measures are lattice-valued set functions which assign the bottom element of the lattice to the empty set and the top element of the lattice to the entire universe, satisfying the additive properties and the property of monotonicity. In this paper, we use the lattice-valued fuzzy measures and outer measure definitions and generalize the Caratheodory extension theorem for lattice-valued fuzzy measures. [ABSTRACT FROM AUTHOR]

Using the equivalence relation between K-functional and modulus of smoothness, we establish a strong direct theorem and an inverse theorem of weak type for multivariate Bernstein-Durrmeyer operators with Jacobi weights on a simplex in this paper. We also obtain a characterization for multivariate Bernstein-Durrmeyer operators with Jacobi weights on a simplex. The obtained results not only generalize the corresponding ones for Bernstein-Durrmeyer operators, but also give approximation order of Bernstein-Durrmeyer operators. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to establish some new criteria for the classification of the sublinear differential equation as of the nonlinear limit circle type or of the nonlinear limit point type. The criteria presented here generalize some known results in the literature. [ABSTRACT FROM AUTHOR]

By using a generalized arithmetic-geometric mean inequality on time scales, we study the forced oscillation of second-order dynamic equations with nonlinearities given by Riemann-Stieltjes integrals of the form [p(t)Φα(xΔ(t))Δ + q(t)Φα(x(τ(t))) + ∫Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. r(t, s)Φγ(s) (x(g(t, s)))Δξ(s) = e(t), where t ∈ [t0,∞)픛T = [t0,∞) ∩ 픛, 픛 is a time scale which is unbounded from above; Φ*(u) = |u|*sgn u; γ : [a, b]픛1 → ℝ is a strictly increasing right-dense continuous function; p, q, e : [t0,∞)픛 → ℝ, r : (t0,∞)픛 x [a, b]픛1 → ℝ, τ : (t0,∞)픛 → (t0,∞)픛, and g : (t0,∞)픛 x [a, b]픛1 → (t0,∞)픛 are right-dense continuous functions; ξ : [a, b]픛1 → ℝ is strictly increasing. Some interval oscillation criteria are established in both the cases of delayed and advanced arguments. As a special case, the work in this paper unifies and improves many existing results in the literature for equations with a finite number of nonlinear terms. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present a new hybrid block iterative scheme by the generalized f - projection method for finding a common element of the fixed point set for a countable family of uniformly quasi-Φ-asymptotically nonexpansive mappings and the set of solutions of the system of generalized mixed equilibrium problems in a strictly convex and uniformly smooth Banach space with the Kadec-Klee property. Furthermore, we prove that our new iterative scheme converges strongly to a common element of the aforementioned sets. The results presented in this paper improve and extend important recent results in the literature. [ABSTRACT FROM AUTHOR]

Existence of nonoscillatory solutions for the second-order dynamic equation (A0xΔ)Δ(t) + ∑i∈[1,n]ℕ Ai(t)x(αi(t)) = 0 for t ∈ [t0,∞)핋 is investigated in this paper. The results involve nonoscillation criteria in terms of relevant dynamic and generalized characteristic inequalities, comparison theorems, and explicit nonoscillation and oscillation conditions. This allows to obtain most known nonoscillation results for second-order delay differential equations in the case A0(t) ≡ 1 for t ∈ [t0,∞)ℝ and for second-order nondelay difference equations (αi(t) = t + 1 for t ∈ [t0,∞)ℕ). Moreover, the general results imply new nonoscillation tests for delay differential equations with arbitrary A0 and for second-order delay difference equations. Known nonoscillation results for quantum scales can also be deduced. [ABSTRACT FROM AUTHOR]

We focus our study on a discussion of duality relationships of a minimax fractional programming problem with its two types of second-order dual models under the second-order generalized convexity type assumptions. Results obtained in this paper naturally unify and extend some previously known results on minimax fractional programming in the literature. [ABSTRACT FROM AUTHOR]

This paper gives sufficient and necessary conditions for the classification of Sturm-Liouville differential equations with complex coefficients given by Brown et al. These conditions involve weighted Sobolev subspaces and the asymptotic behavior of elements in themaximal domain. The results of the present paper generalize the corresponding results for formally symmetric Sturm-Liouville differential equations to non-self-adjoint cases. [ABSTRACT FROM AUTHOR]

The sequence space ℓ(p) was introduced byMaddox (1967). Quite recently, the domain of the generalized difference matrix B(r,s) in the sequence space ℓ(p) has been investigated by Kirişçi and Başar (2010). In the present paper, the sequence space ℓ(B,p) of nonabsolute type has been studied which is the domain of the generalized difference matrix B(r,s) sequence space ℓ(p). Furthermore, the alpha-, beta-, and gamma-duals of the space ℓ(B,p) have been determined, and the Schauder basis has been given. The classes of matrix transformations from the space ℓ(B,p) to the spaces ℓ8,c and c0 have been characterized. Additionally, the characterizations of some other matrix transformations from the space ℓ(B,p) to the Euler, Riesz, difference, and so forth sequence spaces have been obtained by means of a given lemma. The last section of the paper has been devoted to conclusion. [ABSTRACT FROM AUTHOR]

A further generalization of an economic growth model is the main topic of this paper. The paper specifically analyzes the effects on the asymptotic dynamics of the Solow model when two time delays are inserted: the time employed in order that the capital is used for production and the necessary time so that the capital is depreciated. The existence of a unique nontrivial positive steady state of the generalized model is proved and sufficient conditions for the asymptotic stability are established. Moreover, the existence of a Hopf bifurcation is proved and, by using the normal form theory and center manifold argument, the explicit formulas which determine the stability, direction, and period of bifurcating periodic solutions are obtained. Finally, numerical simulations are performed for supporting the analytical results. [ABSTRACT FROM AUTHOR]

Here we show that the main results in the papers by Yalcinkaya (2008), Yalcinkaya and Cinar (2010), and Yalcinkaya, Cinar, and Simsek (2008), as well as a conjecture from the last mentioned paper, follow from a slight modification of a result by G. Papaschinopoulos and C. J. Schinas. We also give some generalizations of these results. [ABSTRACT FROM AUTHOR]

The distribution of zeros and poles of best rational approximants is well understood for the functions f(x) = |x|a, a > 0. If f ε C[-1, 1] is not holomorphic on [-1, 1], the distribution of the zeros of best rational approximants is governed by the equilibrium measure of [-1, 1] under the additional assumption that the rational approximants are restricted to a bounded degree of the denominator. This phenomenon was discovered first for polynomial approximation. In this paper, we investigate the asymptotic distribution of zeros, respectively, a-values, and poles of best real rational approximants of degree at most n to a function f ε C[-1, 1] that is realvalued, but not holomorphic on [-1, 1]. Generalizations to the lower half of the Walsh table are indicated. [ABSTRACT FROM AUTHOR]

The objective of the present paper is to determine the generalized Hyers-Ulam stability of the mixed additive-cubic functional equation in n-Banach spaces by the direct method. In addition, we show under some suitable conditions that an approximately mixed additive-cubic function can be approximated by a mixed additive and cubic mapping. [ABSTRACT FROM AUTHOR]

The generalized coupled Sylvester systems play a fundamental role in wide applications in several areas, such as stability theory, control theory, perturbation analysis, and some other fields of pure and applied mathematics. The iterative method is an important way to solve the generalized coupled Sylvester systems. In this paper, an iterative algorithm is constructed to solve the minimum Frobenius norm residual problem: ... min over generalized reflexive matrix X. For any initial generalized reflexive matrix X1, by the iterative algorithm, the generalized reflexive solution X* can be obtained within finite iterative steps in the absence of round-off errors, and the unique least-norm generalized reflexive solution X* can also be derived when an appropriate initial iterative matrix is chosen. Furthermore, the unique optimal approximate solution ... to a given matrix X0 in Frobenius norm can be derived by finding the least-norm generalized reflexive solution ...* of a new corresponding minimum Frobenius norm residual problem: min ... with ... Finally, several numerical examples are given to illustrate that our iterative algorithm is effective [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce new types of asymptotically (g,φ)-contractions which generalize the Binayak S. Choudhury type contraction on fuzzy metric spaces and prove some fixed-point theorems for single- and multivalued mappings on fuzzy metric spaces. Hence, our results can be viewed as a generalization and improvement of many recent results. [ABSTRACT FROM AUTHOR]

This paper deals with approximating properties of the q-generalization of the Sza´sz-Mirakjan operators in the case q < 1. Quantitative estimates of the convergence in the polynomial-weighted spaces and the Voronovskaja's theorem are given. In particular, it is proved that the rate of approximation by the q-Sza´sz-Mirakjan operators (q < 1 ) is of order q-n versus 1/n for the classical Sza´sz-Mirakjan operators. [ABSTRACT FROM AUTHOR]

This paper presents some efficient spectral algorithms for solving linear sixth-order two-point boundary value problems in one dimension based on the application of the Galerkin method. The proposed algorithms are extended to solve the two-dimensional sixth-order differential equations. A family of symmetric generalized Jacobi polynomials is introduced and used as basic functions. The algorithms lead to linear systems with specially structured matrices that can be efficiently inverted. The various matrix systems resulting from the proposed algorithms are carefully investigated, especially their condition numbers and their complexities. These algorithms are extensions to some of the algorithms proposed by Doha and Abd-Elhameed (2002) and Doha and Bhrawy (2008) for second- and fourth-order elliptic equations, respectively. Three numerical results are presented to demonstrate the efficiency and the applicability of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This paper is concerned with oscillation of second-order nonlinear dynamic equations of the form (r(t)((y(t)+p(t)y(τ(t)))Δ)y)Δ + f1(t,y(δ1(t))) + f2(t,y(δ2(t))) = 0 on time scales. By using a generalized Riccati technique and integral averaging techniques, we establish new oscillation criteria which handle some cases not covered by known criteria. [ABSTRACT FROM AUTHOR]

We introduce a new twice power type contractive condition for three mappings in G-metric spaces, and several new common fixed point theorems are established in complete G-metric space. An example is provided to support our result. The results obtained in this paper differ from other comparable results already known. [ABSTRACT FROM AUTHOR]

In recent years, the definition of relatively nonexpansive multivalued mapping and the definition of weak relatively nonexpansive multivalued mapping have been presented and studied by many authors. In this paper, we give some results about weak relatively nonexpansive multivalued mappings and give two examples which are weak relatively nonexpansive multivalued mappings but not relatively nonexpansive multivalued mappings in Banach space l2 and Lp[0,1](1 < p < +∞). [ABSTRACT FROM AUTHOR]

We consider the existence of positive solutions for a class of nonlinear integral boundary value problems for fractional differential equations. By using some fixed point theorems, the existence and multiplicity results of positive solutions are obtained. The results obtained in this paper improve and generalize some well-known results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present some coincidence and common fixed point results for generalized weakly G-contractive mappings in the setup of partially ordered G-metric space. We also provide an example to illustrate the results presented herein. As an application of our results, periodic points of weakly G-contractive mappings are obtained. [ABSTRACT FROM AUTHOR]

This paper is concerned with a new sequence of linear positive operators which generalize Szasz operators including Boas-Buck-type polynomials. We establish a convergence theorem for these operators and give the quantitative estimation of the approximation process by using a classical approach and the second modulus of continuity. Some explicit examples of our operators involving Laguerre polynomials, Charlier polynomials, and Gould-Hopper polynomials are given. Moreover, a Voronovskaya-type result is obtained for the operators containing Gould-Hopper polynomials. [ABSTRACT FROM AUTHOR]

The paper is concerned with the variational formulation of the oligopolistic market equilibrium problem in presence of both production and demand excesses. In particular, we generalize a previous model in which the authors, instead, considered only the problem with production excesses, by allowing also the presence of demand excesses. First we examine the equilibrium conditions in terms of the well-known dynamic Cournot-Nash principle. Next, the equilibrium conditions will be expressed in terms of Lagrange multipliers by means of the infinite dimensional duality theory. Then, we show the equivalence between the two conditions that are both expressed by an appropriate evolutionary variational inequality. Moreover, thanks to the variational formulation, some existence and regularity results for equilibrium solutions are proved. At last, a numerical example, which illustrates the features of the problem, is provided. [ABSTRACT FROM AUTHOR]

Badora (2002) proved the following stability result. Let e and d be nonnegative real numbers, then for every mapping f of a ring R onto a Banach algebra B satisfying ||f(x + y) - f(x) - f(y)|| = e and ||f(x ·y)-f(x)f(y)|| = d for all x, y ∈ R, there exists a unique ring homomorphism h :R ? B such that ||f(x) - h(x)|| = e, x ∈ R. Moreover, b · (f(x) - h(x)) = 0, (f(x) - h(x)) · b = 0, for all x ∈ R and all b from the algebra generated by h(R). In this paper, we generalize Badora's stability result above on ring homomorphisms for Riesz algebras with extended norms. [ABSTRACT FROM AUTHOR]

A new concept of the c-distance in cone metric space has been introduced recently in 2011. The aim of this paper is to extend and generalize some fixed point results in literature for c-distance in cone metric spaces by replacing the constants in contractive conditions with functions. Some supporting examples are given. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present the fixed points and endpoints of set-valued contractions concerning with the stronger Meir-Keeler cone-type mappings in cone metric spcaes. Our results generalize the recent results of Kadelburg and Radenovi'c, 2011; Wardowski, 2009. [ABSTRACT FROM AUTHOR]

Fusion frames are generalizations of frames in Hilbert spaces which were introduced by Casazza et al. (2008). In the present paper, we study the relations between fusion frames and subfusion frame operators. Specially, we introduce new construction of subfusion frames and derive new results. [ABSTRACT FROM AUTHOR]

This paper is concerned with a class of fractional differential inclusions whose multivalued term depends on lower-order fractional derivative with fractional nonseparated boundary conditions. The cases of convex-valued and non-convex-valued right-hand sides are considered. Some existence results are obtained by using standard fixed point theorems. A possible generalization for the inclusion problem with integral boundary conditions is also discussed. Examples are given to illustrate the results. [ABSTRACT FROM AUTHOR]

We introduce a new general system of generalized nonlinear mixed composite-type equilibria and propose a new iterative scheme for finding a common element of the set of solutions of a generalized equilibrium problem, the set of solutions of a general system of generalized nonlinear mixed composite-type equilibria, and the set of fixed points of a countable family of strict pseudocontraction mappings. Furthermore, we prove the strong convergence theorem of the purposed iterative scheme in a real Hilbert space. As applications, we apply our results to solve a certain minimization problem related to a strongly positive bounded linear operator. Finally, we also give a numerical example which supports our results. The results obtained in this paper extend the recent ones announced by many others. [ABSTRACT FROM AUTHOR]

Recently, Abbas et al. (2012) obtained some unique common fixed-point results for a pair of mappings satisfying (E.A) property under certain generalized strict contractive conditions in the framework of a generalized metric space. In this paper, we present common coincidence and common fixed points of two pairs of mappings when only one pair satisfies (E.A) property in the setup of generalized metric spaces. We present some examples to support our results. We also study well-posedness of common fixed-point problem. [ABSTRACT FROM AUTHOR]

The aim of this paper is to define and study a class of Bazilevic functions using the generalized Salagean operator. Some properties of this class are investigated: inclusion relation, some convolution properties, coefficient bounds, and other interesting results. [ABSTRACT FROM AUTHOR]

By using the weakly commutative and weakly compatible conditions of self-mapping pairs, we prove some new common fixed point theorems for six self-mappings in the framework of generalized metric spaces. An example is provided to support our result. The results presented in this paper generalize the well-known comparable results in the literature due to Abbas, Nazir, Saadati, Mustafa, and Sims. [ABSTRACT FROM AUTHOR]

In 1999 Molodtsov introduced the concept of soft set theory as a general mathematical tool for dealing with uncertainty. Alkhazaleh et al. in 2011 introduced the definition of a soft multiset as a generalization of Molodtsov's soft set. In this paper we give the definition of fuzzy soft multiset as a combination of soft multiset and fuzzy set and study its properties and operations. We give examples for these concepts. Basic properties of the operations are also given. An application of this theory in decision-making problems is shown. [ABSTRACT FROM AUTHOR]

We introduce a new iterative algorithm for finding a common element of the set of solutions of a system of generalized mixed equilibrium problems, zero set of the sum of a maximal monotone operators and inverse-strongly monotone mappings, and the set of common fixed points of an infinite family of nonexpansive mappings with infinite real number. Furthermore, we prove under some mild conditions that the proposed iterative algorithm converges strongly to a common element of the above four sets, which is a solution of the optimization problem related to a strongly positive bounded linear operator. The results presented in the paper improve and extend the recent ones announced by many others. [ABSTRACT FROM AUTHOR]