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In this paper, we formulate best proximity pair theorems for noncyclic relatively ρ-nonexpansive mappings in modular spaces in the setting of proximal ρ-admissible sets. As a companion result, we establish a best proximity pair theorem for pointwise noncyclic contractions in modular spaces. To that end, we provide some examples throughout the paper to illustrate the validity of the obtained results. Keywords: Best proximity pair, Modular spaces, Relatively ρ-nonexpansive mappings, ρ-admissible sets, ρ-normal structure, Mathematics Subject Classification: 47H09, 41A65

In this paper, we consider a fourth-order viscoelastic plate equation with infinite memory, and with partially hinged boundary conditions. We investigate the asymptotic behaviour of solutions. This present paper improves earlier results in the literature and allow an extended range of relaxation functions.

This paper is an attempt to stress the usefulness of the multi-variable special functions. In this paper, we derive certain generating relations involving 2-indices 5-variables 5-parameters Tricomi functions (2I5V5PTF) by using a Lie-algebraic method. Further, we derive certain new and known generating relations involving other forms of Tricomi and Bessel functions as applications.

In this paper, a (3+1)-dimensional wave equation is studied from the point of view of Lie’s theory in partial differential equations including conservation laws. The symmetry operators are determined to find the reduced form of the considered equation. The non-local conservation theorems and multipliers approach are performed on the (3+1)-dimensional wave equation. We obtain conservation laws by using five methods, such as direct method, Noether’s method, extended Noether’s method, Ibragimov’s method; and finally we can derive infinitely many conservation laws from a known conservation law viewed as the last method. We also derive some exact solutions using some conservation laws Anco and Bluman (2002). Keywords: Wave equation, Conservation laws, Lie symmetry, Direct method, Noether’s theorem, Boyer’s formulation, Mathematics Subject Classification: 76M60, 70H33, 35J05

In this paper, we will study the class of biharmonic maps with potential, in the particular case represented by conformal maps between equidimensional manifolds. Some examples are constructed in particular cases (Euclidean space and sphere). Keywords: Harmonic map with potential, Biharmonic map with potential, Conformal maps, Mathematics Subject Classification: 31B30, 53C25, 58E20, 58E30

A left-symmetric algebra A is said to be a derivation algebra if all its left and right multiplications are derivations of the Lie algebra associated to A . In this paper, we shall study derivation algebras over R and then classify almost all those of dimensions ≤ 4 .

This paper deals with a characterization of the stable processes on the space of symmetric matrices by means of its Laplace transform. This characterization is done using a mixture with the Wishart distribution and under some independence properties. This extends the results of reference Louati et al. (2015).

In this paper, we propose an alternative approach combining the advantages of the Kohn–Vogelius formulation and the topological sensitivity analysis method for solving geometric inverse problems. The Kohn–Vogelius formulation can rephrase the geometric inverse problem into a shape optimization one minimizing an energy-like function. The sensitivity analysis gives the leading term of the energy-like function variation with respect to the presence of a small geometry perturbation inside the computational domain. The obtained theoretical results lead to build a fast and accurate numerical reconstruction algorithm. The efficiency and accuracy of the proposed algorithm are illustrated by some numerical results.

In this paper, we give some properties of the f -biharmonic maps, in the particular case represented by conformal maps between equidimensional manifolds. We construct a new example of the f -biharmonic maps and we characterize the p -biharmonicity of some particular cases.

In the paper, the authors analytically find some explicit formulas and recursive formulas for the large and little Schroder numbers.

In this paper, we define and study subspace-diskcyclic operators. We show that subspace-diskcyclicity does not imply diskcyclicity. We establish a subspace-diskcyclic criterion and use it to find a subspace-diskcyclic operator that is not subspace-hypercyclic for any subspaces. Also, we show that the inverses of invertible subspace-diskcyclic operators do not need to be subspace-diskcyclic for any subspaces. Finally, we prove that every finite-dimensional Banach space over the complex field supports a subspace-diskcyclic operator.

The object of the present paper is to characterize Weyl semisymmetric almost Kenmotsu manifolds with its characteristic vector field ξ belonging to the ( k , μ ) ′ -nullity distribution and ( k , μ ) -nullity distribution respectively. Also we characterize almost Kenmotsu manifolds satisfying the curvature condition C ⋅ S = 0 , where C and S are the Weyl conformal curvature tensor and Ricci tensor respectively with its characteristic vector field ξ belonging to the ( k , μ ) ′ -nullity distribution. As a consequence of the main results we obtain several corollaries. Finally, we present an example to verify our results.

In this paper we obtain a characterization of little Hankel operators defined on the Bergman space of the unit disk and then extend the result to vector valued Bergman spaces. We then derive from it certain asymptotic properties of little Hankel operators.

In this paper we study the uniqueness theorems of meromorphic functions which share a small function with its derivatives, and give some results which are related to the results of P. Li.

This paper firstly shows that there does not exist a nonzero periodic solution for a nonhomogeneous Cauchy problem by using the Laplace transformation on time scales. Secondly, two new Gronwall inequalities, which play an important role in the qualitative analysis of differential and integral equations, are established. Thirdly, by employing the contraction mapping principle, existence and uniqueness results of weighted S -asymptotically ω -periodic solutions for nonlinear Cauchy problem on time scales are obtained in an asymptotically periodic function space. Finally, some examples are presented to illustrate some of the results described here.

The aim of this paper is to study the gravitational field of Schwarzschild soliton. Use of characteristic of λ -tensor is given to determine the kinds of gravitational fields. Through the cases of two and three dimension for Schwarzschild soliton, the Gaussian curvature is expressed in terms of eigen values of the characteristic equation.

In this paper, we consider a one-dimensional porous thermoelasticity system of type III with a viscoelastic damping acting on one of the equations. We establish a general decay result for the case of equal as well as different speeds of wave propagation.

In this paper we prove that there do not exist warped product GCR-lightlike submanifolds in the form M = N⊥ × λNT such that N⊥ is an anti-invariant submanifold tangent to V and NT an invariant submanifold of M ‾ , other than GCR-lightlike product in an indefinite Sasakian manifold. We also obtain characterization theorems for a GCR-lightlike submanifold to be locally a GCR-lightlike warped product.

In this paper, we define some new sequence spaces of lacunary convergent sequences derived by Nörlund-type (Riesz) mean, which shall be denoted by |N‾,pr,θ| and (N‾,pr,θ), and investigate some relations between the sequence space |N‾,pr,θ| with the spaces ∣wθ∣ and |N‾,pn|. Further, we define a new concept, named weighted lacunary statistical convergence and examine some connections between this notion with the concept of lacunary statistical convergence and weighted statistical convergence. Also, some topological properties of these new sequence spaces are investigated.

In this paper we have used a method of reducing coupled coincidence and coupled fixed point results in partially ordered metric spaces to the respective results for mappings with one variable, even obtaining (in some cases) more general theorems. Our results generalize, extend, unify and complement coupled coincidence point theorems established by Harjani et al. (2011) [18] and Razani and Parvaneh (2012) [26]. Also, by using this method several tripled coincidence and tripled common fixed point results in partially ordered metric spaces can be reduced to the coincidence and common fixed point results with one variable.

In this paper, we give a result of regularity of weak solutions for a class of nonlinear anisotropic parabolic equations with lower-order term when the right-hand side is an L m function, with m being ”small”. This work generalizes some results given in [2] and [3] .