This thematic series originates from the International Conference on the Theory, Methods and Applications of Nonlinear Equations which was held in December 2012 in Kingsville, TX-USA and was organized by the Department of Mathematics at the Texas A&M University-Kingsville.
Edited by: Ravi Agarwal, Shusen Ding, Billur Kaymakcalan, Dumitru Motreanu and Anthony To Ming Lau
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In this paper, we study the existence and uniqueness of solutions for the boundary value problem of fractional difference equations
The goal of this paper is to introduce and study some properties of some sequence spaces that are defined using the φ-function and the generalized three parametric real matrix A. Also, we define A-statistical con...
In this paper, the separability properties of elliptic convolution operator equations are investigated. It is obtained that the corresponding convolution-elliptic operator is positive and also is a generator o...
We first prove a norm inequality for the composition of the Dirac operator and Green’s operator. Then, we estimate for the Lipschitz and BMO norms of the composite operator in terms of the ...
We consider the number of the weak solutions for some fourth order elliptic boundary value problem with bounded nonlinear term decaying at the origin. We get a theorem, which shows the existence of the bounded...
The purpose of the paper is to extend the notion of dissipativity of maps on infinite-dimensional simplex. We study the fixed points of dissipative quadratic stochastic operators on infinite-dimensional simple...
The purpose of this paper is to study Mann iterative schemes. Strong convergence of a modified Mann iterative scheme is obtained in a reflexive Banach space.
In this paper, we study the boundary value problem of a class of nonlinear fractional q-difference equations with parameter involving the Riemann-Liouville fractional derivative. By means of a fixed point theorem...
The purpose of this paper is to establish the general theory of the direct methods to functionals I defined on the Grassmann algebra employing the classical approaches. In this paper, various notions of convexity...
We first introduce the concept of b-metric-like space which generalizes the notions of partial metric space, metric-like space and b-metric space. Then we establish the existence and uniqueness of fixed points in...
We obtain fixed point theorems for cyclic self-maps on complete metric spaces involving Meir-Keeler and weaker Meir-Keeler functions, respectively. In this way, we extend several well-known fixed point theorem...
In this paper, we focus on the generalized 3D magnetohydrodynamic equations. Two logarithmically blow-up criteria of smooth solutions are established.
An equilibrium problem based on a projection algorithm is investigated. A strong convergence theorem for solutions of the equilibrium problems is established in a nonuniformly smooth Banach space.
It is well-known that Mann’s algorithm fails to converge for Lipschitzian pseudocontractions and strong convergence of Ishikawa’s algorithm for Lipschitzian pseudocontractions have not been achieved without co...
Very recently, a notion of cone b-metric was introduced as a generalization of b-metric, and some related fixed point results were obtained. In this paper, we investigate the answer to the question whether the gi...
In this paper, we consider p-Laplacian multipoint boundary value problems on time scales. By using a generalization of the Leggett-Williams fixed point theorem due to Bai and Ge, we prove that a boundary value pr...
During the last three decades, the problem of evaluation of the determinants of the Laplacians on Riemann manifolds has received considerable attention from many authors. The functional determinant for the k-dime...
In this paper, we give some new and interesting identities involving harmonic and hyperharmonic numbers which are derived from the transfer formula for the associated sequences.
This paper investigates the existence and potential uniqueness of equilibrium points and some stability, instability and oscillatory properties of a discrete nonlinear epidemic model, which generalises previou...
In this paper, a functional boundary value problem of fractional differential equations is studied. Based on Mawhin’s coincidence degree theory, some existence theorems are obtained in the case of nonresonance...
In this paper we develop the spectral theory for discrete symplectic systems with general jointly varying endpoints. This theory includes a characterization of the eigenvalues, construction of the M-lambda functi...
By means of two fundamental fractional integral identities, we derive two classes of new Hermite-Hadamard type inequalities involving Riemann-Liouville fractional integrals for once and twice differentiable
Saadati et al. (Math. Comput. Model. 52:797-801, 2010) introduced the concept of Ω-distance in generalized metric spaces and studied some nice fixed point theorems. Very recently, Jleli and Samet (Fixed Point The...
We study strong convergence of an Ishikawa-type algorithm of two asymptotically nonexpansive type maps to their common fixed point on a
A fixed point problem of a generalized asymptotically quasi-Ï•-nonexpansive mapping and an equilibrium problem are investigated. A strong convergence theorem for solutions of the fixed point problem and the equili...
The Harary index is defined as the sum of reciprocals of distances between all pairs of vertices of a connected graph. In this paper, expressions for the Harary indices of the join, corona product, Cartesian p...
The main purpose of this paper is to define and investigate the Kirchhoff matrix, a new Kirchhoff index, the Kirchhoff energy and the Kirchhoff Estrada index of a graph. In addition, we establish upper and low...
The Retraction Note to this article has been published in Journal of Inequalities and Applications 2014 2014:424
Very recently, Caballero, Harjani and Sadarangani (Fixed Point Theory Appl. 2012:231, 2012) observed some best proximity point results for Geraghty contractions by using the P-property. In this paper, we introduc...
We provide the existence of a positive solution for the quasilinear elliptic equation
In this paper, we extend Hartley and Hartley-Hilbert transformations (HT and HHT, respectively) to a certain space of tempered distributions. We then establish a certain convolution theorem for the HHT. The convo...
The stationary and instationary Stokes equations with operator coefficients in abstract function spaces are studied. The problems are considered in the whole space, and equations include small parameters. The ...
In this paper, we study a periodic p-Laplacian equation with nonlocal terms and Neumann boundary conditions. We establish the existence of time periodic solutions of the p-Laplacian-Neumann problem by the theory ...
In this paper, we propose and analyze some iterative algorithms by hybrid viscosity approximation methods for solving a general system of variational inequalities and a common fixed point problem of an infinit...
The purpose of this paper is to present a new modified Halpern-Mann type iterative scheme by using the generalized f-projection operator for finding a common element in the set of zeroes of a system of maximal mo...
We introduce a new nonlinear mapping generated by a finite family of nonexpansive mappings. Weak and strong convergence theorems are also established in the setting of a Banach space.
In this paper, we present some coupled coincidence point results for mixed g-monotone mappings in partially ordered complete metric spaces involving altering distance functions. Moreover, we present an example to...
In this paper, Hermite-Hadamard type inequalities involving Hadamard fractional integrals for the functions satisfying monotonicity, convexity and s-e-condition are studied. Three classes of left-type Hadamard fr...
In this paper, we investigate the existence results for a class of abstract fractional neutral integro-differential evolution systems involving the Caputo derivative in Banach spaces. The main techniques rely ...
The purpose of this paper is to introduce and analyze a weakly convergent theorem by using the regularized method and the relaxed extragradient method for finding a common element of the solution set Γ of the ...
In this paper, we study the existence of positive solutions for a nonlinear fractional boundary value problem on the half-line. Based on the monotone iterative technique, we obtain the existence of positive so...
In the present paper, an iterative algorithm for solving mixed equilibrium problems and fixed points problems has been constructed. It is shown that under some mild conditions, the sequence generated by the pr...
In this paper, we generalized the notion of proximal contractions of the first and second kinds by using Geraghty’s theorem and establish best proximity point theorems for proximal contractions. Our results im...
The purpose of this paper is by using Maingé’s approach to study the existence and approximation problem of solutions for a class of hierarchical variational inclusion problems in the setting of Hilbert spaces...
In this paper, we obtain some fixed point results for multi-valued mappings in partial metric spaces. Our results unify, generalize and complement various known comparable results from the current literature. ...