Authors:B. Fadli; D. Zeglami; S. Kabbaj Pages: 1 - 22 Abstract: Let G be a locally compact abelian Hausdorff group, let \(\sigma \) be a continuous involution on G, and let \(\mu ,\nu \) be regular, compactly supported, complex-valued Borel measures on G. We determine the continuous solutions \(f,g:G\rightarrow {\mathbb {C}}\) of each of the two functional equations $$\begin{aligned}&\int _{G}f(x+y+t)d\mu (t)+\int _{G}f(x+\sigma (y)+t)d\nu (t)=f(x)g(y),\quad x,y\in G,\\&\int _{G}f(x+y+t)d\mu (t)+\int _{G}f(x+\sigma (y)+t)d\nu (t)=g(x)f(y),\quad x,y\in G, \end{aligned}$$ in terms of characters and additive functions. These equations provides a common generalization of many functional equations such as d’Alembert’s, Cauchy’s, Gajda’s, Kannappan’s, Van Vleck’s, or Wilson’s equations. So, several functional equations will be solved. PubDate: 2018-03-01 DOI: 10.1007/s13370-017-0521-9 Issue No:Vol. 29, No. 1-2 (2018)

Authors:Virendra Kumar Pages: 23 - 27 Abstract: In the present paper the Euler transform of the V-function is obtained. The main result provides useful extension and unification of a number of (known or new) results for various special cases of the V-function. For the sake of illustration, some special cases of the main result are mentioned. PubDate: 2018-03-01 DOI: 10.1007/s13370-017-0522-8 Issue No:Vol. 29, No. 1-2 (2018)

Authors:Athoumane Niang; Adama Thiandoum Pages: 29 - 32 Abstract: The aim of this work is to prove that Hopf conjecture is true on the class of metrics g on \(M={\mathbb {S}}^2\times {\mathbb {S}}^2\) conformal to the standard metric \(g_0\) induced by \({\mathbb {R}}^6\) on M. PubDate: 2018-03-01 DOI: 10.1007/s13370-017-0523-7 Issue No:Vol. 29, No. 1-2 (2018)

Authors:O. S. Fard; J. Soolaki; R. Almeida Pages: 33 - 46 Abstract: The theory of the calculus of variations for fuzzy systems was recently initiated in Farhadinia (Inf Sci 181:1348–1357, 2011), with the proof of the fuzzy Euler–Lagrange equation. Using fuzzy Euler–Lagrange equation, we obtain here a Noether–like theorem for fuzzy variational problems. PubDate: 2018-03-01 DOI: 10.1007/s13370-017-0524-6 Issue No:Vol. 29, No. 1-2 (2018)

Authors:Niovi Kehayopulu Pages: 65 - 71 Abstract: The concept of a \(\Gamma \) -semigroup has been introduced by Mridul Kanti Sen in the Int. Symp., New Delhi, 1981. It is well known that the Green’s relations play an essential role in studying the structure of semigroups. In the present paper we deal with an application of \(\Gamma \) -semigroups techniques to the Green’s Theorem in an attempt to show the way we pass from semigroups to \(\Gamma \) -semigroups. PubDate: 2018-03-01 DOI: 10.1007/s13370-017-0526-4 Issue No:Vol. 29, No. 1-2 (2018)

Authors:Wenchang Chu; Xiaoyuan Wang Pages: 73 - 79 Abstract: As extensions of Vandermonde determinant, we establish a general determinant evaluation formula by means of the Laplace expansion formula. Several interesting determinant identities are consequently derived by computing divided differences. PubDate: 2018-03-01 DOI: 10.1007/s13370-017-0527-3 Issue No:Vol. 29, No. 1-2 (2018)

Authors:Paltu Sarkar; Sukhendu Kar Pages: 81 - 96 Abstract: In this paper, our main objective is to introduce and investigate the interval-valued (in short, (i-v)) prime fuzzy hyperideal in semihypergroups in detail. We notice that every (i-v) semiprime fuzzy hyperideal may not be an (i-v) prime fuzzy hyperideal and we produce a counter example to illustrate this result. Moreover, we define (i-v) fuzzy hyper radical of an (i-v) fuzzy hyperideal of a semihypergroup. Finally, we study some interesting properties regarding this radical. PubDate: 2018-03-01 DOI: 10.1007/s13370-017-0528-2 Issue No:Vol. 29, No. 1-2 (2018)

Authors:Mahmood Bakhshi; Mahdi Izanlou Pages: 97 - 114 Abstract: Based on Pawlak’s rough set theory, we study and investigate the roughness in non-commutative residuated lattices, which are generalizations of non-commutative fuzzy structures such as MV-algebras and BL-algebras. We give many theorems and examples to describe the rough approximations. Also, to investigate the properties of roughness of subsets (and of course filters) more closely, we consider some different kinds of filters such as Boolean filters and prime filters. Especially, we prove that with respect to some certain filters, the obtained approximations form a Boolean algebra or a pseudo MTL-algebra. PubDate: 2018-03-01 DOI: 10.1007/s13370-017-0529-1 Issue No:Vol. 29, No. 1-2 (2018)

Authors:Bashir Ali; G. C. Ugwunnadi Pages: 115 - 136 Abstract: A new strong convergence theorem for approximation of common fixed points of family of uniformly asymptotically regular asymptotically nonexpansive mappings, which is also a unique solution of some variational inequality problem is proved in the framework of a real Banach space. The Theorem presented here extend, generalize and unify many recently announced results. PubDate: 2018-03-01 DOI: 10.1007/s13370-017-0530-8 Issue No:Vol. 29, No. 1-2 (2018)

Authors:Artem Ostapenko; Galina Bulanchuk Pages: 137 - 147 Abstract: In this work, we studied the calculation of the drag coefficient using the lattice Boltzmann method with variable lattice speed of sound. The modified method of calculation the drag coefficient that includes the kinematic viscosity dependence was proposed. Calculations were based on the variable lattice speed of sound values that depend on the kinematic viscosity and the computational grid resolution. Shown the influence of the Reynolds number on the flow pattern and on the drag coefficient. The relation between the lattice Mach number and the computational grid resolution have been shown. The influence of the lattice Mach number on the accuracy of the numerical results was studied in detail. Shown that proposed method is more efficient because the researcher can set the kinematic viscosity of the fluid and the computational grid resolution at the same time. Therefore there is an opportunity to control the accuracy of the numerical results and the modeling time. PubDate: 2018-03-01 DOI: 10.1007/s13370-017-0531-7 Issue No:Vol. 29, No. 1-2 (2018)

Authors:Nacira Agram; Elin Engen Røse Pages: 149 - 174 Abstract: We study methods for solving stochastic control problems of systems offorward–backward mean-field equations with delay, in finite and infinite time horizon.Necessary and sufficient maximum principles under partial information are given. The results are applied to solve a mean-field recursive utility optimal problem. PubDate: 2018-03-01 DOI: 10.1007/s13370-017-0532-6 Issue No:Vol. 29, No. 1-2 (2018)

Authors:Mina Dinarvand Pages: 175 - 193 Abstract: The purpose of this paper is to give some fixed point results for mappings involving generalized \((\psi ,\varphi )\) -contractions via rational expressions in the setup of partially ordered b-metric spaces. Our main results extend, generalize and enrich several well known comparable results in the recent literature. Moreover, some examples and an application to integral equation are given here to illustrate the usability of the obtained results. PubDate: 2018-03-01 DOI: 10.1007/s13370-017-0533-5 Issue No:Vol. 29, No. 1-2 (2018)

Authors:Fahad Sikander; Alveera Mehdi; Tanveer Fatima Pages: 195 - 202 Abstract: In this paper we generalize the concept of commutator socle regular abelian \(p\hbox {-groups}\) for the QTAG-modules. In fact this is an extension of the study of socle regular, strong socle regular and projection-invariant QTAG-modules (Sikander et al., New Trends Math Sci 2(2):129–133, 2014; Sci Ser A Math Sci 25:47–53, 2014; J Egypt Math Soc, 2015. Here we investigate commutator socle regular modules, study their crucial properties and establish their relationship with the above mentioned modules. PubDate: 2018-03-01 DOI: 10.1007/s13370-017-0534-4 Issue No:Vol. 29, No. 1-2 (2018)

Authors:Nanjundan Magesh; Serap Bulut Pages: 203 - 209 Abstract: In this paper, we obtain initial coefficient bounds for functions belong to a subclass of analytic bi-univalent functions related to pseudo-starlike functions by using the Chebyshev polynomials and also we find Fekete-Szegö inequalities for this class. PubDate: 2018-03-01 DOI: 10.1007/s13370-017-0535-3 Issue No:Vol. 29, No. 1-2 (2018)

Authors:Mohammad M. Al-Gharabli Pages: 211 - 221 Abstract: In this paper, we consider a porous thermoelastic system with a micro-heat dissipation and a nonlinear frictional damping. We establish an explicit and general decay rate result, using some properties of the convex functions and the multiplier method. Our result is obtained without imposing any restrictive growth assumption on the damping term. PubDate: 2018-03-01 DOI: 10.1007/s13370-017-0536-2 Issue No:Vol. 29, No. 1-2 (2018)

Authors:Naokant Deo; Minakshi Dhamija Pages: 223 - 232 Abstract: In the present paper, we study modified Szász–Durrmeyer positive linear operators involving Charlier polynomials, one of the discrete orthogonal polynomials which are generalization of Szász Durrmeyer operators. Also, King type modification of these operators is given. We obtain uniform convergence of our operators with the help of Korovkin theorem, asymptotic formula and the order of approximation by using classical modulus of continuity. PubDate: 2018-03-01 DOI: 10.1007/s13370-017-0537-1 Issue No:Vol. 29, No. 1-2 (2018)

Authors:Brahim Boufoussi; Salah Hajji; El Hassan Lakhel Pages: 233 - 247 Abstract: In this paper we consider a class of impulsive neutral stochastic functional differential equations with variable delays driven simultaneously by a fractional Brownian motion and a Poisson point processes in a Hilbert space. We prove an existence and uniqueness result and we establish some conditions ensuring the exponential decay to zero in mean square for the mild solution by means of the Banach fixed point theory. Finally, an illustrative example is given to demonstrate the effectiveness of the obtained result. PubDate: 2018-03-01 DOI: 10.1007/s13370-017-0538-0 Issue No:Vol. 29, No. 1-2 (2018)

Authors:P. Hemavathi; P. Muralikrishna; K. Palanivel Pages: 249 - 262 Abstract: This paper deals the notion of interval valued instuitionistic fuzzy subalgebras of \(\beta \) -algebra and investigate some of the related results. PubDate: 2018-03-01 DOI: 10.1007/s13370-017-0539-z Issue No:Vol. 29, No. 1-2 (2018)

Authors:Luc Paquet Abstract: In a preceding paper (MSIA, 2012), we have studied the radiative heating of a glass plate. We have proved existence and uniqueness of the solution. Here, we want to study the semi-discrete problem and to prove a priori error estimates. Previously, in that purpose, we have to study the regularity of the solution to the exact problem and of its time derivative. A very important property, Proposition 13, is remarked concerning our elliptic projection, the milestone in deriving the a priori error estimates. A numerical test corroborating our theoretical a priori bounds is given. PubDate: 2018-01-24 DOI: 10.1007/s13370-018-0542-z

Authors:Rasoul Soleimani Abstract: In this paper, we introduce the notion of a central B-automorphism of a finite B-algebra. Also some properties of a finite B-algebra and B-automorphism algebra are investigated. PubDate: 2017-12-19 DOI: 10.1007/s13370-017-0540-6