Authors:Serap Bulut Pages: 331 - 338 Abstract: Abstract In this paper, we introduce a new subclass of analytic and bi-univalent functions in the open unit disk \(\mathbb {U}\) . For functions belonging to this class, we obtain initial coefficient bounds and Fekete–Szegö inequality. PubDate: 2018-06-01 DOI: 10.1007/s13370-018-0543-y Issue No:Vol. 29, No. 3-4 (2018)

Authors:Elmo Benedetto; Fabiano Feleppa Pages: 349 - 356 Abstract: Abstract The Einstein initial foundations of general relativity have to do with his great intuition and they are not clear as it is for special relativity. As has been widely emphasized, for example, in the book of Ohanian and Ruffini, the very name of the theory indicates a misconception. Despite this, the high school textbooks (at least the Italian ones) and books of scientific divulgation introduce the Einstein gravitational theory still following the initial approach leading, in our opinion, to misinterpretations. A careful student, for example, immediately asks: it is not true that the Earth rotates because I can consider it at rest thanks to general relativity theory. The relativity of motion is trivial in mathematics while it has deep meaning in physics and it is not sufficiently analyzed. Similarly, the arbitrary choice of the origin and the perfect equivalence between all coordinate systems are mathematical properties satisfied by general relativity and students can confuse it with physical equivalence between reference systems that have a deeper meaning and the Einstein theory does not verify it. Gravitational force does not exist and this is the real core of Einsteinian revolution. As happens in Newtonian physics and Special Relativity, also in general relativity the relative motions are the geodesic motions with the difference that spacetime can be curved and geodesics may not be a straight line. Similarly, in general relativity forces cause non-geodesic motion. Geodesic and non-geodesic are tensorial properties and for this reason they are absolute. PubDate: 2018-06-01 DOI: 10.1007/s13370-018-0545-9 Issue No:Vol. 29, No. 3-4 (2018)

Authors:Baby Kalita; Sunil Kumar Singh Pages: 357 - 370 Abstract: Abstract For \(1 \le p,q <\infty \) , we define the space \(W^{p,q}_{k_1,k_2}({\mathbb {R}}^n)\) by means of the S-transform where \(k_1\) and \(k_2\) are weight functions on \({{\mathbb {R}}^n}\) and \({\mathbb {R}}^n\times {\mathbb {R}}_0^n \) , respectively. It is a Banach space with respect to a sum norm defined in this paper. Latter we discuss inclusion properties and obtain the dual space of \(W^{p,q}_{k_1,k_2}({\mathbb {R}}^n)\) . Furthermore, we define the space \(\left( W^{p,q}_{k_1,k_2}\right) _{\xi }({\mathbb {R}}^n)\) where \(\xi \) is fixed and show that it is an essential Banach module over \(L^1_{k_1}({\mathbb {R}}^n)\) . PubDate: 2018-06-01 DOI: 10.1007/s13370-018-0546-8 Issue No:Vol. 29, No. 3-4 (2018)

Authors:Sujit Kumar Sardar; Krishanu Dey; Sugato Gupta Pages: 371 - 381 Abstract: Abstract In this paper we introduce the notion of Gabriel topology on semirings as well as on bisemimodules with unities. We also show that there is a lattice isomorphism between the Gabriel topologies on semirings and those on bisemimodules connected via Morita context. PubDate: 2018-06-01 DOI: 10.1007/s13370-018-0547-7 Issue No:Vol. 29, No. 3-4 (2018)

Authors:Ahmed A. Abdelhakim; R. A. Rashwan Pages: 399 - 406 Abstract: Abstract Suppose E is a Banach space with certain geometric properties and K is a nonempty closed convex subset of E. We prove that if a certain iterative sequence converges to the unique fixed point of a \(\Phi \) -pseudocontractive mapping \(T:K\rightarrow K\) under certain conditions then such an iterative process can be used to approximate the unique common fixed point of a finite family of \(\Phi \) -pseudocontractive self mappings of K. Our results extend and generalize the results in Chidume (Proc Am Math Soc 120:2641–2649, 1994; Proc Am Math Soc 9:545–551, 1998), Huang (Comput Math Appl 36:13–21, 1998), Liu (Comput Math Appl 45:623–634, 2003), Osilike (Math Anal Appl 200:259–271, 1996; Nonlinear Anal 36:1–9, 1999) and many others. PubDate: 2018-06-01 DOI: 10.1007/s13370-018-0549-5 Issue No:Vol. 29, No. 3-4 (2018)

Authors:Tanveer A. Tarray; Housial P. Singh Pages: 407 - 423 Abstract: Abstract The nitty-gritty of this paper is to estimate the mean of the number of persons possessing a rare sensitive attribute by utilizing the Poisson distribution in stratified survey sampling. It is also shown that the proposed models are more efficient than Lee et al.’s (Statistics 47:575–589, 2013) models in both the cases when the proportion of persons possessing a rare unrelated attribute is known and that when it is unknown. Properties of the proposed randomized response models have been studied alongwith recommendations. Numerical illustrations are also given in support of the present study. PubDate: 2018-06-01 DOI: 10.1007/s13370-018-0550-z Issue No:Vol. 29, No. 3-4 (2018)

Authors:Neha Choubey; Bhavna Panday; J. P. Jaiswal Pages: 435 - 449 Abstract: Abstract In this article, our main motivation is to present two-step with memory iterative methods for solving nonlinear equations. We attempted to convert the existing fourth-order without memory method into a with memory method. Further acceleration of convergence order is attained by means of different approximations of self-accelerating parameters. The parameters are calculated by Hermite interpolating polynomial and applied to accelerate the order of convergence of the without memory methods. In particular, the R-order of the proposed two-step with memory iterative method is increased without any additional calculations and it possesses high computational efficiency. At the end, the theoretical results are confirmed by considering different numerical examples. Numerical comparisons specify that the new family is efficient and give tough competition to some existing with memory iterative methods. PubDate: 2018-06-01 DOI: 10.1007/s13370-018-0552-x Issue No:Vol. 29, No. 3-4 (2018)

Authors:Rajneesh Kumar; Sachin Kaushal; M. Marin Pages: 451 - 462 Abstract: Abstract The present paper is devoted to the study of propagation of plane waves in micropolar thermodiffusion elastic half-space in the context of generalized theories of thermoelasticity. The variations of amplitude ratios for plane waves (longitudinal wave, thermal wave and mass diffusive wave) are computed analytically and depicted graphically for longitudinal wave against the angle of incidence. The impact of relaxation times, micropolarity and diffusion have been studied. Some particular cases of interest are also deduced from the present investigation. PubDate: 2018-06-01 DOI: 10.1007/s13370-018-0553-9 Issue No:Vol. 29, No. 3-4 (2018)

Authors:S. Mirvakili; S. M. Anvariyeh; B. Davvaz Pages: 463 - 475 Abstract: Abstract Davvaz and Leoreanu-Fotea (Commun Algebra 38(10):3621–3636, 2010) studied binary relations on ternary semihypergroups. A ternary relation or triadic relation is a relation in which the number of places in the relation is three. Now, in this paper, instead of binary relations we consider ternary relations and instead of ternary semihypergroups we consider ordinary semihypergroups. Then, we study ternary relations on semihypergroups. In particular, we discuss some properties of compatible ternary relations on them. PubDate: 2018-06-01 DOI: 10.1007/s13370-018-0554-8 Issue No:Vol. 29, No. 3-4 (2018)

Authors:Fatima Gogah; Amjad D. Al-Nasser Pages: 477 - 497 Abstract: Abstract We develop a ranked acceptance sampling plan by attribute for exponential distribution assuming that the life test is truncated at a pre-assigned time. Two main requirements are essential for the proposed ranked sampling plans; namely; the life times of the test units are assumed to follow the exponential distribution; and the data are selected by using a free cost sampling method, the median ranked set sampling scheme from a large lot. The main advantage of using the median rank set sampling is to reduce producer’s risk, and it is one of the ranked scheme that produces a judgment order statistics that are mutually independent and identically distributed random variables to meet the binomial theory assumptions. The distribution function characterization under the median ranked set sampling scheme is derived assuming that the set size is known; then the minimum sample size necessary to ensure the specified average life are obtained and the operating characteristic values of the sampling plans based on the ranked samples and producer’s risk are presented. A comparisons with sampling plan based on simple random sampling and an illustrative example are given. PubDate: 2018-06-01 DOI: 10.1007/s13370-018-0555-7 Issue No:Vol. 29, No. 3-4 (2018)

Authors:Hilal A. Ganie; Bilal A. Chat Pages: 499 - 507 Abstract: Abstract In this paper, we consider the Laplacian energy of digraphs. Various approaches for the Laplacian energy of a digraph have been put forward by different authors. We consider the skew Laplacian energy of a digraph as given in Cai et al. (Trans Combin 2:27–37, 2013). We obtain some upper and lower bounds for the skew Laplacian energy which are better than some previous known bounds. We also show every even positive integer is the skew Laplacian energy of some digraphs. PubDate: 2018-06-01 DOI: 10.1007/s13370-018-0556-6 Issue No:Vol. 29, No. 3-4 (2018)

Authors:Manash Jyoti Borah; Bipan Hazarika Pages: 509 - 529 Abstract: Abstract The main aim of this paper is to introduced the operations “Union”, “Intersection” and four operators namely \(\tilde{O_1},\tilde{ O_2},\tilde{ O_3},\tilde{ O_4}, \) on interval-valued hesitant fuzzy soft sets and discuss some of their properties. PubDate: 2018-06-01 DOI: 10.1007/s13370-018-0557-5 Issue No:Vol. 29, No. 3-4 (2018)

Authors:J. O. Ehigie; S. A. Okunuga Pages: 531 - 555 Abstract: Abstract We consider a new class of modified block Falkner methods for the direct numerical integration of second-order initial value problems having periodic and oscillatory solutions. We will give a new collocation formulation different from that of Ramos et al. (J Comput Appl Math. https://doi.org/10.1016/j.cam.2015.12.018, 2016) for the coefficients of a modified block Falkner-type methods, which are frequency dependent. We give an example using our new approach to derive a practical method. Furthermore, the uniform general order conditions and the investigation of the stability properties are presented. Numerical experiments are carried out to illustrate the high effectiveness of the new methods compared with some recent methods in the literature. PubDate: 2018-06-01 DOI: 10.1007/s13370-018-0558-4 Issue No:Vol. 29, No. 3-4 (2018)

Authors:H. El Boujaoui Pages: 557 - 574 Abstract: Abstract In this paper, we are interested to prove the uniform exponential decay of the energy for the finite difference fully-discretization of 1-D wave equation with an interior damping at \(\xi \) . To this end, we decompose the fully discrete system into two subsystems: a conservative system, and a non conservative one. We show under a numerical hypothesis on \(\xi \) that a uniform observability inequality holds for a conservative system, when the mesh size tends to zero using Fourier series technique. Then, we use the observability inequality to prove the uniform exponential decay of the energy for the damped system. Finally, we describe some numerical experiments to illustrate the exponential decay of the energy. PubDate: 2018-06-01 DOI: 10.1007/s13370-018-0559-3 Issue No:Vol. 29, No. 3-4 (2018)

Authors:B. Boufoussi; S. Hajji; S. Mouchtabih Pages: 575 - 589 Abstract: Abstract Using the method of Girsanov transformation, we establish the transportation inequalities, with respect to the uniform distance, for the law of the mild solution of fractional stochastic functional differential equations driven by fractional Brownian motion. The case of neutral fractional stochastic functional differential equations are also investigated. PubDate: 2018-06-01 DOI: 10.1007/s13370-018-0560-x Issue No:Vol. 29, No. 3-4 (2018)

Authors:Tapan Senapati Pages: 591 - 600 Abstract: Abstract In this paper, using t-norm T, the notion of (imaginable) T-fuzzy KU-ideals of KU-algebras are introduced and investigated their related results. Images and preimages of KU-ideals under homomorphism are investigated. Using level subsets of KU-algebras, some characterization theorems are given. The Cartesian product and T-product of T-fuzzy KU-ideals of KU-algebras are discussed. PubDate: 2018-06-01 DOI: 10.1007/s13370-018-0561-9 Issue No:Vol. 29, No. 3-4 (2018)

Authors:Akanksha; G. S. Srivastava Pages: 601 - 614 Abstract: Abstract Several authors have studied the growth properties of Dirichlet series and vector valued Dirichlet series (VVDS). Wen Ping Huang, Ju Hong Ning and Jin Tu have obtained various results by considering Dirichlet series with complex exponents. In this paper we obtainthe characterizations of order and type of vector valued Dirichlet series which generalize some well known results for growth of classical Dirichlet series. Further we have tried to study the growth properties of holomorphic vector valued Dirichlet series with complex exponents. PubDate: 2018-06-01 DOI: 10.1007/s13370-018-0563-7 Issue No:Vol. 29, No. 3-4 (2018)

Authors:H. Fettouch; S. Hamouda Pages: 625 - 639 Abstract: Abstract In this paper we investigate the n-iterated exponent of convergence of \( f^{\left( i\right) }-\varphi \) where \(f\not \equiv 0\) is a solution of linear differential equation with analytic and meromorphic coefficients in the unit disc and \(\varphi \) is a small function of f. By this investigation we can deduce the value distribution of the fixed points of \(f^{\left( i\right) }\) by taking \(\varphi \left( z\right) =z\) . This work is an extension to the unit disc and an improvement of recent results in the complex plane by Xu et al. (Adv Differ Equ 2012(114):1–16, 2012) and Tu et al. (Adv Differ Equ 2013(71):1–16, 2013). PubDate: 2018-06-01 DOI: 10.1007/s13370-018-0565-5 Issue No:Vol. 29, No. 3-4 (2018)

Authors:Kenan Kaygisiz Pages: 641 - 654 Abstract: Abstract In this paper, soft int-groups, soft normal int-groups and their basic properties are presented. Normal soft int-subgroup of a soft int-group is defined and relations concerning them are given. Then, homomorphism and isomorphism theorems are applied to the soft int-groups. PubDate: 2018-06-01 DOI: 10.1007/s13370-018-0566-4 Issue No:Vol. 29, No. 3-4 (2018)