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In this paper, three modified Polak-Ribière-Polyak (PRP) conjugate gradient methods for unconstrained optimization are proposed. They are based on the two-term PRP method proposed by Cheng (Numer. Funct. Anal. Optim. 28:1217-1230, 2007), the three-term PRP method proposed by Zhang et al. (IMA J. Numer. Anal. 26:629-640, 2006), and the descent PRP method proposed by Yu et al. (Optim. Methods Softw. 23:275-293, 2008). These modified methods possess the sufficient descent property without any line searches. Moreover, if the exact line search is used, they reduce to the classical PRP method. Under standard assumptions, we show that these three methods converge globally with a Wolfe line search. We also report some numerical results to show the efficiency of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, we introduce new implicit and explicit iterative methods for finding a common fixed point set of an infinite family of strict pseudo-contractions by the sunny nonexpansive retractions in a real q-uniformly and uniformly convex Banach space which admits a weakly sequentially continuous generalized duality mapping. Then we prove the strong convergence under mild conditions of the purposed iterative scheme to a common fixed point of an infinite family of strict pseudo-contractions which is a solution of some variational inequalities. Furthermore, we apply our results to study some strong convergence theorems in Lp and ℓp spaces with 1 < p <∞. Our results mainly improve and extend the results announced by Ceng et al. (Comput. Math. Appl. 61:2447-2455, 2011) and many authors from Hilbert spaces to Banach spaces. Finally, we give some numerical examples for support our main theorem in the end of the paper. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and analyze a general iterative algorithm for finding a common solution of a finite family of mixed equilibrium problems, a general system of generalized equilibria and a fixed point problem of nonexpansive mappings in a real Hilbert space. Under some appropriate conditions, we derive the strong convergence of the sequence generated by the proposed algorithm to a common solution, which also solves some optimization problem. The result presented in this paper improves and extends some corresponding ones in the earlier and recent literature. [ABSTRACT FROM AUTHOR]

In this paper, the stability of a class of time-delay Takagi-Sugeno (T-S) fuzzy Markovian jumping partial differential equations (PDEs) with p-Laplace and probabilistic time-varying delays is investigated, and the robust exponential stability criterion is obtained by way of some variational methods in Sobolev space W1,p(Ω), the Lyapunov functional method and the linear matrix inequalities technique. Moreover, a numerical example shows the effectiveness of the proposed methods due to the large allowable variation range of time delay. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and analyze a multistep Mann-type extragradient iterative algorithm by combining Korpelevich's extragradient method, viscosity approximation method, hybrid steepest-descent method, Mann's iteration method, and the projection method. It is proven that under appropriate assumptions, the proposed algorithm converges strongly to a common element of the fixed point set of infinitely many nonexpansive mappings and a strict pseudocontraction, the solution set of finitely many generalized mixed equilibrium problems (GMEPs), the solution set of finitely many variational inclusions and the solution set of a variational inequality problem (VIP), which is just a unique solution of a system of hierarchical variational inequalities (SHVI) in a real Hilbert space. The results obtained in this paper improve and extend the corresponding results announced by many others. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Navier-Stokes equations and temperature equation arising from the evolution process of the atmosphere. Under certain assumptions imposed on the initial data, we show the L¹-stability of weak solutions for the atmospheric equations. Some ideas and delicate estimates are introduced to prove these results. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence of solutions for a variational-like inequality and a generalized variational-like inequality in the relaxed η-α pseudomonotone and strictly η-quasimonotone cases in Banach spaces by using the KKM technique. The results presented in this paper improve and extend some corresponding results of several authors. [ABSTRACT FROM AUTHOR]

In this paper, we present some inequalities involving k-gamma and k-beta functions via some classical inequalities, like Chebyshev's inequality for synchronous (asynchronous) mappings, Grüss', and Ostrowski's inequality. Also, we give applications of k-beta function in probability distributions. Most of the inequalities produced in this paper are the k-analogs of existing results. If k = 1,we have the classical one. [ABSTRACT FROM AUTHOR]

In this paper, we show the regularity theory on an A-harmonic system and an A-Dirac system. By the method of the removability theorem, we explain how an A-harmonic system arises from an A-Dirac system and establish that an A-harmonic system is in fact the real part of the corresponding A-Dirac system. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce the concepts of total asymptotically demicontractive mappings and total asymptotically hemicontractive mappings. Under suitable conditions some strong convergence theorems for these two kinds of mappings to converge to their fixed points in CAT(0) space are proved. The results presented in the paper extend and improve some recent results announced in the current literature. [ABSTRACT FROM AUTHOR]

In this paper, we identify the unknown source which depends only on spatial variable for a fractional diffusion equation using the Fourier method. Not alike the previous literature, we propose to choose the regularization parameter by an a posteriori rule, with which we can obtain error estimate of Hölder type between the exact solution and the regularized approximation. Numerical simulations show that the proposed scheme is effective and stable. [ABSTRACT FROM AUTHOR]

In this paper, by using a nonlinear scalarization technique, we obtain sufficient conditions for Hölder continuity of the solution mapping for a parametric generalized vector quasi-equilibrium problem with set-valued mappings. The results are different from the recent ones in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we will define Hardy spaces Hp(ℂn) associated with twisted convolution operators and give the atomic decomposition of Hp(ℂn), where 2n/2n+1 < p ≤ 1. Then we consider the boundedness of the Weyl multiplier on Hp(ℂn). [ABSTRACT FROM AUTHOR]

The augmented Zagreb index of a graph G is defined as where $E(G)$ is the edge set, and $d_{u}$, $d_{v}$ are the degrees of vertices u and v in G, respectively. This new molecular structure descriptor, introduced by Furtula et al. (J. Math. Chem. 48:370-380, 2010), has proven to be a valuable predictive index in the study of the heat of formation in heptanes and octanes. In this paper, the n-vertex unicyclic graphs with the minimal and the second minimal AZI indices and the n-vertex bicyclic graphs with the minimal AZI index are determined. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and analyze a multi-step hybrid extragradient algorithm by combining Korpelevich's extragradient method, the viscosity approximation method, the hybrid steepest-descent method, Mann's iteration method and the gradient-projection method (GPM) with regularization in the setting of infinite-dimensional Hilbert spaces. It is proven that, under appropriate assumptions, the proposed algorithm converges strongly to a solution of the convex minimization problem (CMP) with constraints of several problems: finitely many generalized mixed equilibrium problems (GMEPs), finitely many variational inclusions, and the fixed point problem of a strictly pseudocontractive mapping. In the meantime, we also prove the strong convergence of the proposed algorithm to the unique solution of a hierarchical variational inequality problem (over the fixed point set of a strictly pseudocontractive mapping) with constraints of finitely many GMEPs, finitely many variational inclusions and the CMP. The results presented in this paper improve and extend the corresponding results announced by many others. [ABSTRACT FROM AUTHOR]

In this paper, using the concept of the common (E.A) property, we prove a common fixed point theorem for a class of twice power type weakly compatible mappings in generalized metric space. Our results do not rely on any commuting or continuity condition of the mappings. We also state some examples to illustrate our new results in symmetric and nonsymmetric generalized metric spaces. It should be pointed out that this is the first time to use common (E.A) properties to discuss common fixed point problems of contractive mappings for twice power type in generalized metric spaces. [ABSTRACT FROM AUTHOR]

The paper studies a linear errors-in-variables model with first order autoregressive processes. The Huber-Dutter (HD) estimators of unknown parameters are given, and the asymptotic normality of the HD estimators is investigated. Finally, a simple example is given to illustrate our estimation method. [ABSTRACT FROM AUTHOR]

In this paper, we first introduce the concepts of generalized (ψ, f )λ-expansive mappings and generalized (φ, g, h)λ-weakly expansive mappings designed for three mappings. Then we establish some common fixed point results for such two new types of mappings in partial b-metric spaces. These results generalize and extend the main results of Karapınar et al. (J. Inequal. Appl. 2014:22, 2014), Nashine et al. (Fixed Point Theory Appl. 2013:203, 2013) and many comparable results from the current literature. Moreover, some examples and an application to a system of integral equations are given here to illustrate the usability of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we study the blow-up singularity of a semilinear parabolic equation with nonlinear memory both in the reaction term and the boundary condition. We firstly establish the local solvability for a large class of semilinear parabolic equations with various nonlocal reaction terms. Secondly, we give a complete classification for the existence of a blow-up solution and a global solution. Next, we show that under some hypotheses the blow-up can only occur on the boundary of the domain. [ABSTRACT FROM AUTHOR]

In this paper, multi-valued version of SCC, SKC, KSC, and CSC conditions in Ptolemy metric space are presented. Then the existence of a fixed point for these mappings in a Ptolemy metric space are proved. Finally, some examples are presented. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new notion to generalize a Mizoguchi-Takahashi type contraction. Then, using this notion, we obtain a fixed point theorem for multivalued maps. Our results generalize some results by Minak and Altun, Kamran and those contained therein. [ABSTRACT FROM AUTHOR]

In this paper, we obtain an inequality for the normalized Casorati curvature of slant submanifolds in quaternionic space forms by using T Oprea's optimization method. [ABSTRACT FROM AUTHOR]

In the present paper, we propose several kinds of adaptively relaxed iterative algorithms with a new step size for solving the split feasibility problem in real Hilbert spaces. The proposed algorithms never terminate, while the known algorithms existing in the literature may terminate. Several weak and strong convergence theorems of the proposed algorithms have been established. Some numerical experiments are also included to illustrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

In this paper we give the direct approximation theorem, the inverse theorem, and the equivalence theorem for Szász-Durrmeyer-Bézier operators in the space Lp[0,∞) (1 ≤ p≤∞) with Ditzian-Totik modulus. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce the q-analog of the Stancu variant of Szász-Baskakov operators. We establish the moments of the operators by using the q-derivatives and then prove the basic convergence theorem. Next, the Voronovskaja type theorem and some direct results for the above operators are discussed. Also, the rate of convergence and weighted approximation by these operators in terms of modulus of continuity are studied. Then we obtain a point-wise estimate using the Lipschitz type maximal function. Lastly, we study the A-statistical convergence of these operators and also, in order to obtain a better approximation, we study a King type modification of the above operators. [ABSTRACT FROM AUTHOR]

In this paper, we study an operator version of the modified Browder-Tikhonov regularization method for finding a common solution for a system of ill-posed operator equations involving m-accretive operators Ai, i = 0, ... ,N, in a reflexive Banach space. The convergence rates of the regularized solutions are estimated not only in the infinite-dimensional space, but also in connection with its finite-dimensional approximations without the weakly sequential continuity of the dual mapping. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new concept of quasi-b-metric-like spaces as a generalization of b-metric-like spaces and quasi-metric-like spaces. Some fixed point theorems are investigated in quasi-b-metric-like spaces. Moreover, an example is given to support one of our results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate some identities of q-extensions of special polynomials which are derived from the fermonic q-integral on ℤp and the bosonic q-integral on ℤp. [ABSTRACT FROM AUTHOR]

Let X be a non-empty set. We say that an element x ∈ X is a φ-fixed point of T, where φ : X →[0,∞) and T : X →X, if x is a fixed point of T and φ(x) = 0. In this paper, we establish some existence results of φ-fixed points for various classes of operators in the case, where X is endowed with a metric d. The obtained results are used to deduce some fixed point theorems in the case where X is endowed with a partial metric p. [ABSTRACT FROM AUTHOR]

In this paper, we obtain sufficient conditions for the lower semicontinuity of an approximate solution mapping for a parametric generalized vector equilibrium problem involving set-valued mappings. By using a scalarization method, we obtain the lower semicontinuity of an approximate solution mapping for such a problem without the assumptions of monotonicity and compactness. [ABSTRACT FROM AUTHOR]

This paper deals with the oscillation of second order neutral difference equations of the form Δ(an(Δ(xn + pnxτ (n)))α) + qnxβσ(n) = 0. The oscillation of all solutions of this equation is established via comparison theorems. Examples are provided to illustrate the main results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of the rank game and propose a mathematical model for it. By a discrete fixed point theorem, we give the existence results of rank equilibria. [ABSTRACT FROM AUTHOR]

In this paper, we prove that the double inequality Mp(a, b) < U(a, b) < Mq(a, b) holds for all a, b > 0 with a ≠ b if and only if p ≤ 2 log 2/(2 logπ - log 2) = 0.8684 ⋯ and q ≥ 4/3, where U(a, b) and Mr (a, b) are the Yang and rth power means of a and b, respectively. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a mixed general type of variational relation problems, and establish the existence theorem of solutions of mixed general types of variational relation problems. Moreover, we study the stability of a solution set of mixed general types of variational relation problems. We prove that most of mixed general types of variational relation problems (in the sense of Baire category) are essential and, for any mixed general type of variational relation problems, there exists at least one essential connected component of its solution set. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the unique continuation properties for multi-dimensional heat equations with inverse square potential in a bounded convex domain Ω of Rd. We establish observation estimates for solutions of equations. Our result shows that the value of the solutions can be determined uniquely by their value on an open subset ω of Ω at any given positive time L. [ABSTRACT FROM AUTHOR]

In high-dimensional models, the penalized method becomes an effective measure to select variables. We propose an adaptive bridge method and show its oracle property. The effectiveness of the proposed method is demonstrated by numerical results. [ABSTRACT FROM AUTHOR]

In this paper, inspired by Jitsupa et al. (J. Comput. Appl. Math. 318:293-306, 2017), we propose a general iterative scheme for finding a solution of a split monotone variational inclusion with the constraints of a variational inequality and a fixed point problem of a finite family of strict pseudo-contractions in real Hilbert spaces. Under very mild conditions, we prove a strong convergence theorem for this iterative scheme. Our result improves and extends the corresponding ones announced by some others in the earlier and recent literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a hybrid extragradient viscosity iterative algorithm for finding a common element of the set of solutions of a general mixed equilibrium problem, the set of solutions of a general system of variational inequalities, the set of solutions of a split feasibility problem (SFP), and the set of common fixed points of finitely many nonexpansive mappings and a strict pseudocontraction in a real Hilbert space. The iterative algorithm is based on Korpelevich's extragradient method, viscosity approximation method, Mann's iteration method, hybrid steepest-descent method and gradient-projection method (GPM) with regularization. We derive the strong convergence of the iterative algorithm to a common element of these sets, which also solves some hierarchical variational inequality. [ABSTRACT FROM AUTHOR]

In this paper, we present a fuzzy semi-infinite optimization problem. Moreover, we will deduce the Fritz-John and Kuhn-Tucker necessary conditions of this problem. Finally, a numerical example is given to illustrate the results. [ABSTRACT FROM AUTHOR]

We introduce and study a new general split feasibility problem (GSFP) in a Hilbert space. This problem generalizes the split feasibility problem (SFP). The GSFP extends the SFP with a nonlinear continuous operator. We apply the preconditioning methods to increase the efficiency of the CQ algorithm, two general preconditioning CQ algorithms for solving the GSFP are presented. We also propose a new inexact method to approximate the preconditioner. The convergence theorems are established under the projections with respect to special norms. Some numerical results illustrate the efficiency of the proposed methods. [ABSTRACT FROM AUTHOR]

Let ω1, ω2 be slowly increasing weight functions, and let ω3 be any weight function on ℝn. Assume that m(ξ ,η) is a bounded, measurable function on ℝn × ℝn. We define Bm(f , g)(x) = ∫ℝn ∫ ℝn ˆf (ξ )ˆg(η)m(ξ ,η)e2π/(ξ+η,x) dξ dη for all f , g ∈ Cc∞ (ℝn). We say that m(ξ ,η) is a bilinear multiplier on ℝn of type (W(p1, q1,ω1; p2, q2,ω2; p3, q3,ω3)) if Bm is a bounded operator from W(Lp1 , Lω1q1)×W(Lp2 , Lω2q2) to W(Lp3 , Lω3q3 ), where 1 ≤ p1 ≤ q1 <∞, 1 ≤ p2 ≤ q2 <∞, 1 < p3, q3≤∞. We denote by BM(W(p1, q1,ω1; p2, q2,ω2; p3, q3,ω3)) the vector space of bilinear multipliers of type (W(p1, q1,ω1; p2, q2,ω2; p3, q3,ω3)). In the first section of this work, we investigate some properties of this space and we give some examples of these bilinear multipliers. In the second section, by using variable exponent Wiener amalgam spaces, we define the bilinear multipliers of type (W(p1(x), q1,ω1; p2(x), q2,ω2; p3(x), q3,ω3)) from W(Lq1p1(x), Lω1q1)×W(Lp2(x), Lω2q2) to W(Lp3(x), Lω3q3), where p*1, p*2, p*3 <∞, p1(x) ≤ q1, p2(x) ≤ q2, 1 ≤ q3≤∞for all p1(x), p2(x), p3(x) ∈ P(ℝn). We denote by BM(W(p1(x), q1,ω1; p2(x), q2,ω2; p3(x), q3,ω3)) the vector space of bilinear multipliers of type (W(p1(x), q1,ω1; p2(x), q2,ω2; p3(x), q3,ω3)). Similarly, we discuss some properties of this space. [ABSTRACT FROM AUTHOR]

New modified Schurer-type q-Bernstein Kantorovich operators are introduced. The local theorem and statistical Korovkin-type approximation properties of these operators are investigated. Furthermore, the rate of approximation is examined in terms of the modulus of continuity and the elements of Lipschitz class functions. [ABSTRACT FROM AUTHOR]

According to the notion of the Lp-mixed geominimal surface area of multiple convex bodies which were introduced by Ye et al., we define the concept of the Lp-dual mixed geominimal surface area for multiple star bodies, and we establish several inequalities related to this concept. [ABSTRACT FROM AUTHOR]

We present the best possible parameters p1, p2, p3, p4, q1, q2, q3, q4 ϵ [0,1] such that the double inequalities Gp1 (a, b) < SHA(a, b) < Gq1 (a, b), Qp2 (a, b) < SCA(a, b) < Qq2 (a, b), Hp3 (a, b) < SAH(a, b) < Hq3 (a, b), Cp4 (a, b) < SAC(a, b) < Cq4 (a, b) hold for all a, b > 0with a ≠ b, where SHA, SCA, SAH, SAC are the Neuman means, and Gp, Qp, Hp, Cp are the one-parameter means. [ABSTRACT FROM AUTHOR]

Criteria for nonsquare points of the Lorentz spaces of maximal functions Γp,w are presented under an arbitrary (also degenerated) nonnegative weight function w. The criteria for nonsquareness of Lorentz spaces Γp,w and of their subspaces (Γp,w)a of all order continuous elements, proved directly in (Kolwicz and Panfil in Indag. Math. 24:254-263, 2013), are deduced. [ABSTRACT FROM AUTHOR]

Let L = -Δ+ V be a Schrödinger operator on ℝd, d ≥ 3, where the nonnegative potential V belongs to the reverse Hölder class RHq for q ≥ d/2. Suppose that b belongs to a new BMO space which is larger than the classical BMO space. We obtain the Lp boundedness of higher order commutators Tbm defined by Tb0 = T, Tbm = [Tbm-1, b], m = 1,2, ... , and T is any of the Riesz transforms or their conjugates associated to the Schrödinger operator -Δ+ V. The range of p is related to the index q. Moreover, we prove that Tbm is bounded from the Hardy space HL¹ (ℝd) into the space Lweak¹(ℝd) when T is the Riesz transform associated to the Schrödinger operator. [ABSTRACT FROM AUTHOR]

We obtain some new characterizations for the Bloch space on the open unit disk in the complex plane ℂ and the open unit ball of ℂn. [ABSTRACT FROM AUTHOR]

We introduce and investigate the notion of an operator P-class function. We show that every nonnegative operator convex function is of operator P-class, but the converse is not true in general. We present some Jensen type operator inequalities involving P-class functions and some Hermite-Hadamard inequalities for operator P-class functions. [ABSTRACT FROM AUTHOR]

We obtain inequalities for sums of adapted random fields in p-uniformly smooth Banach spaces, and we extend Kolmogorov and Marcinkiewicz-Zygmund strong laws for blockwise α-martingale difference fields. [ABSTRACT FROM AUTHOR]

First, we will see that if T is a contraction of the k-quasi-∗-class A operator, then the nonnegative operator D = T∗k(∣T²∣ - ∣T∗∣²)Tk is a contraction whose power sequence {Dn}n=1∞ converges strongly to a projection P and TT∗kP = 0. Second, it will be proved that if T is a contraction of the k-quasi-∗-class A operator, then either T has a non-trivial invariant subspace or T is a proper contraction. Finally it will be proved that if T belongs to the k-quasi-∗-class A and is a contraction, then T has a Wold-type decomposition and T has the PF property. [ABSTRACT FROM AUTHOR]