International Journal Of Nonlinear Analysis And Applications
Volume:8 Issue: 1, Summer - Autumn 2017

In this paper, we solve the quadratic α-functional equations
2f(x) 2f(y) = f(x y) α−2f(α(x−y)), (0.1)
where α is a fixed non-Archimedean number with α−2 6= 3. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the functional equation (0.1) in non-Archimedean Banach spaces.

In this paper, newly defined level operators and modal-like operators over extensional generalized intuitionistic fuzzy sets (GIFSB) are proposed. Some of the basic properties of the new operators are discussed.

In the present article we discuss approximation properties of genuine Lupa¸s-Beta operators of integral type. We establish quantitative asymptotic formulae and a direct estimate in terms of Ditzian-Totik modulus of continuity. Finally we mention results on the weighted modulus of continuity for the genuine operators.

In this paper, the problem of stability for certain subclasses of harmonic univalent functions is investigated. Some lower bounds for the radius of stability of these subclasses are found.

In this paper we introduce the concept of geometrically quasiconvex functions on the co-ordinates and establish some Hermite-Hadamard type integral inequalities for functions defined on rectangles in the plane. Some inequalities for product of two geometrically quasiconvex functions on the co-ordinates are considered.

Many time-varying phenomena of various fields in science and engineering can be modeled as a stochastic differential equations, so investigation of conditions for existence of solution and obtain the analytical and numerical solutions of them are important. In this paper, the Adomian decomposition method for solution of the stochastic differential equations are improved. Uniqueness and convergence of their adapted solutions are reviewed. The efficiency of the method is demonstrated through the two numerical experiments.

In this paper, we develop a quadratic spline collocation method for integrating the nonlinear partial differential equations PDEs of a plug flow reactor model. The method is proposed in order to be used for the operation of control design and/or numerical simulations. We first present the Crank-Nicolson method to temporally discretize the state variable. Then, we develop and analyze the proposed spline collocation method for the spatial discretization. The design of the collocation method is interpreted as one order error convergent. This scheme is applied on some test examples, the numerical results illustrate the efficiency of the method and confirm the theoretical behavior of the rates of convergence.

In this paper, we study the linear fractional transportation problem with uncertain parameters. After recalling some definitions, concepts and theorems in uncertainty theory we present three approaches for solving this problem. First we consider the expected value of the objective function together with the expectation of satisfying constraints. Optimizing the expected value of the objective function with considering chance constrained method for the restrictions is our second approach. In the third approach we add the objective function to the constraints and solve again the problem by chance constrained method. A numerical example is solved by three approaches and their solutions are compared.

In this paper, author proves the algorithms for the existence as well as the approximation of solutions to a couple of periodic boundary value problems of nonlinear first order ordinary integro-differential equations using operator theoretic techniques in a partially ordered metric space. The main results rely on the Dhage iteration method embodied in the recent hybrid fixed point theorems of Dhage in a partially ordered normed linear space. The approximation of the solutions are obtained under weaker mixed partial continuity and partial Lipschitz conditions. Our hypotheses and abstract results are also illustrated by some numerical examples.

Recently, Takahashi has introduced the James and von Neumann-Jordan type constants. In this paper, we present some sufficient conditions for uniform normal structure and therefore the fixed point property of a Banach space in terms of the James and von Neumann-Jordan type constants and the Ptolemy constant. Our main results of the paper significantly generalize and improve many known results in the recent literature.

In this paper, we investigate the convergence of a sequence of minimizing trajectories in infinite horizon optimization problems. The convergence is considered in the sense of ideals and their particular case called the statistical convergence. The optimality is defined as a total cost over the infinite horizon.

In this paper, we define the concept of probabilistic like Menger (probabilistic like quasi Menger) space (briefly, PLM-space (PLqM-space)). We present some coupled fixed point and fixed point results for certain contraction type maps in partially order PLM-spaces (PLqM-spaces).

A non-contradictible axiomatic theory is constructed under the local reversibility of the metric triangle inequality. The obtained notion includes the metric spaces as particular cases and the generated metric topology is T1-separated and generally, non-Hausdorff.

This paper concerns equilibrium problems in real metric linear spaces. Considering a modified notion of upper sign property for bifunctions, we obtain the relationship between the solution sets of the local Minty equilibrium problem and the equilibrium problem, where the technical conditions on f used in the literature are relaxed. The KKM technique is used to generalize and unify some existence results for the relaxed µ-quasimonotone equilibrium problems in the literature.

In this paper we have studied the effect of free convection on the heat transfer and flow through variable porous medium which is bounded by two vertical parallel porous plates. In this study it is assume that free stream velocity oscillates with time about a constant mean. Periodic temperature is considered in the moving plate. Effect of different parameters on mean flow velocity, Transient velocity, Concentration profile and transient temperature studied in detail.

For the Fr´echet algebras (A,(pk)) and (B,(qk)) and n ∈N, n ≥ 2, a linear map T : A → B is called almost n-multiplicative, with respect to (pk) and (qk), if there exists ε ≥ 0 such that.
qk(Ta1a2···an −Ta1Ta2···Tan) ≤ εpk(a1)pk(a2)···pk(an),
for each k ∈ N and a1,a2,...,an ∈ A. The linear map T is called weakly almost n-multiplicative, if there exists ε ≥ 0 such that for every k ∈N there exists n(k) ∈N with
qk(Ta1a2···an −Ta1Ta2···Tan) ≤ εpn(k)(a1)pn(k)(a2)···pn(k)(an),
for each k ∈N and a1,a2,...,an ∈ A. The linear map T is called n-multiplicative if
Ta1a2···an = Ta1Ta2···Tan,
for every a1,a2,...,an ∈ A.
In this paper, we investigate automatic continuity of (weakly) almost n-multiplicative maps between certain classes of Fr´echet algebras, including Banach algebras. We show that if (A,(pk)) is a Fr´echet algebra and T : A → C is a weakly almost n-multiplicative linear functional, then either T is n-multiplicative, or it is continuous. Moreover, if (A,(pk)) and (B,(qk)) are Fr´echet algebras and T : A → B is a continuous linear map, then under certain conditions T is weakly almost nmultiplicative for each n ≥ 2. In particular, every continuous linear functional on A is weakly almost n-multiplicative for each n ≥ 2.

The purpose of this paper is to investigate the real quadratic number fields Q(√d) which contain the specific form of the continued fractions expansions of integral basis element where d ≡ 2,3(mod4) is a square free positive integer. Besides, the present paper deals with determining the fundamental unit
d =td ud√d/2i1
and nd and md Yokoi’s d-invariants by reference to continued fraction expansion of integral basis element where `(d) is a period length. Moreover, we mention class number for such fields. Also, we give some numerical results concluded in the tables.

Partial metric spaces were introduced by Matthews in 1994 as a part of the study of denotational semantics of data flow networks. In 2014 Asadi and et al. [New Extension of p-Metric Spaces with Some fixed point Results on M-metric paces, J. Ineq. Appl. 2014 (2014): 18] extend the Partial metric spaces to M-metric spaces. In this work, we introduce the class of F(ψ,ϕ)-contractions and investigate the existence and uniqueness of fixed points for the new classC in the setting of M-metric spaces. The theorems that we prove generalize many previously obtained results. We also give some examples showing that our theorems are indeed proper extensions.

Hermite-Hadamard inequality is one of the fundamental applications of convex functions in Theory of Inequality. In this paper, Hermite-Hadamard inequalities for B-convex and B−1-convex functions are proven.

In this paper, we define new subclass of analytic functions related with bounded positive real part, and coefficients estimates, duality and neighborhood are considered.

In this work we use the Noor iteration process for total asymptotically nonexpansive mapping to establish the strong and ∆-convergence theorems in the framework of CAT(0) spaces. By doing this, some of the results existing in the current literature generalize, unify and extend.

In this paper, we present some refinements of the famous Young type inequality. As application of our result, we obtain some matrix inequalities for the Hilbert-Schmidt norm and the trace norm. The results obtained in this paper can be viewed as refinement of the derived results by H. Kai [Young type inequalities for matrices, J. East China Norm. Univ. 4 (2012) 12–17].

In this paper, we propose an inexact alternating direction method with square quadratic proximal (SQP) regularization for the structured variational inequalities. The predictor is obtained via solving SQP system approximately under significantly relaxed accuracy criterion and the new iterate is computed directly by an explicit formula derived from the original SQP method. Under appropriate conditions, the global convergence of the proposed method is proved. We show the O(1/t) convergence rate for the inexact SQP alternating direction method. We also reported some numerical results to illustrate the efficiency of the proposed method.

Online social networks like Instagram are places for communication. Also, these media produce rich metadata which are useful for further analysis in many fields including health and cognitive science. Many researchers are using these metadata like hashtags, images, etc. to detect patterns of user activities. However, there are several serious ambiguities like how much reliable are these information. In this paper, we attempt to answer two main questions. Firstly, are image hashtags directly related to image concepts? Can image concepts being predicted using machine learning models? The results of our analysis based on 105000 images on Instagram show that user hashtags are hardly related to image concepts (only 10%of test cases). Second contribution of this paper is showing the suggested pre-trained model predicate image concepts much better (more than 50% of test cases) than user hashtags. Therefore, it is strongly recommended to social media researchers not to rely only on the user hashtags as a label of images or as a signal of information for their study. Alternatively, they can use machine learning methods line deep convolutional neural network model to describe images to extract more related contents. As a proof of concept, some results on food images are studied. We use few similarity measurements to compare result of human and deep convolutional neural network. These analysis is important because food is an important society health field.

This paper deals with the Periodic boundary value problems for Controlled nonlinear impulsive evolution equations. By using the theory of semigroup and fixed point methods, some conditions ensuring the existence and uniqueness. Finally, two examples are provided to demonstrate the effectiveness of the proposed results.

In this paper, we present some fixed and coincidence point theorems for hybrid rational Geraghty contractive mappings in partially ordered b-metric spaces. Also, we derive certain coincidence point results for such contractions. An illustrative example is provided here to highlight our findings.

In this note, we give some estimate of the generalized quadrature formula of Gauss-Jacobi
aη(b,a) Z a (x−a)p (a η (b,a)−x)q f (x)dx
in the cases where f and |f|λ for λ > 1, are s-preinvex functions in the second sense.

In this brief note, using the technique of measures of noncompactness, we give some extensions of Darbo fixed point theorem. Also we prove an existence result for a quadratic integral equation of Hammerstein type on an unbounded interval in two variables which includes several classes of nonlinear integral equations of Hammerstein type. Furthermore, an example is presented to show the efficiency of our result.

In this paper we present new iterative algorithms in convex metric spaces. We show that these iterative schemes are convergent to the fixed point of a single-valued contraction operator. Then we make the comparison of their rate of convergence. Additionally, numerical examples for these iteration processes are given.

Let (X,d) be a compact metric space and let K be a nonempty compact subset of X. Let α ∈ (0,1] and let Lip(X,K,dα) denote the Banach algebra of all continuous complex-valued functions f on X for which
p(K,dα)(f) = sup{|f(x)−f(y)| dα(x,y) : x,y ∈ K,x 6= y}