In this research article, we deal with a new kind of mixed exponential fuzzy vector variational inequalities in ordered Euclidean spaces. By using KKM-technique and Nadler’s fixed point theorem, we prove some existence theorems of solutions to mixed exponential vector variational inequality problems in fuzzy environment.
{"title":"On the existence problem of solutions to a class of fuzzy mixed exponential vector variational inequalities","authors":"Shih-sen Chang, Salahuddin, C. Wen, Xiongrui Wang","doi":"10.22436/JNSA.011.07.04","DOIUrl":"https://doi.org/10.22436/JNSA.011.07.04","url":null,"abstract":"In this research article, we deal with a new kind of mixed exponential fuzzy vector variational inequalities in ordered Euclidean spaces. By using KKM-technique and Nadler’s fixed point theorem, we prove some existence theorems of solutions to mixed exponential vector variational inequality problems in fuzzy environment.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"35 1","pages":"916-926"},"PeriodicalIF":0.0,"publicationDate":"2018-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73598251","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Belfakih Keltouma, E. Elhoucien, T. Rassias, R. Ahmed
In this paper, we prove the superstability theorems of the functional equations μ(y)f(xσ(y)z0)± f(xyz0) = 2f(x)f(y), x,y ∈ S, μ(y)f(σ(y)xz0)± f(xyz0) = 2f(x)f(y), x,y ∈ S, where S is a semigroup, σ is an involutive morphism of S, and μ : S −→ C is a bounded multiplicative function such that μ(xσ(x)) = 1 for all x ∈ S, and z0 is in the center of S.
{"title":"Superstability of Kannappan's and Van vleck's functional equations","authors":"Belfakih Keltouma, E. Elhoucien, T. Rassias, R. Ahmed","doi":"10.22436/JNSA.011.07.03","DOIUrl":"https://doi.org/10.22436/JNSA.011.07.03","url":null,"abstract":"In this paper, we prove the superstability theorems of the functional equations μ(y)f(xσ(y)z0)± f(xyz0) = 2f(x)f(y), x,y ∈ S, μ(y)f(σ(y)xz0)± f(xyz0) = 2f(x)f(y), x,y ∈ S, where S is a semigroup, σ is an involutive morphism of S, and μ : S −→ C is a bounded multiplicative function such that μ(xσ(x)) = 1 for all x ∈ S, and z0 is in the center of S.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"19 1","pages":"894-915"},"PeriodicalIF":0.0,"publicationDate":"2018-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81952764","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Peter Saveliev generalized Lomonosov’s invariant subspace theorem to the case of linear relations. In particular, he proved that if S and T are linear relations defined on a Banach space X and having finite dimensional multivalued parts and if T right commutes with S, that is, ST ⊂ TS, and if S is compact then T has a nontrivial weakly invariant subspace. However, the case of left commutativity remained open. In this paper, we develop some operator representation techniques for linear relations and use them to solve the left commutativity case mentioned above under the assumption that ST(0) = S(0) and TS(0) = T(0).
Peter Saveliev将Lomonosov不变子空间定理推广到线性关系。特别地，他证明了如果S和T是定义在巴拿赫空间X上具有有限维多值部分的线性关系，如果T与S右交换，即ST∧TS，如果S是紧的，则T有一个非平凡的弱不变子空间。然而，左交换性的情况仍然没有解决。本文发展了一些线性关系的算子表示技术，并在ST(0) = S(0)和TS(0) = T(0)的假设下，用它们解决了上述左交换性情况。
{"title":"Weakly invariant subspaces for multivalued linear operators on Banach spaces","authors":"G. Wanjala","doi":"10.22436/JNSA.011.07.01","DOIUrl":"https://doi.org/10.22436/JNSA.011.07.01","url":null,"abstract":"Peter Saveliev generalized Lomonosov’s invariant subspace theorem to the case of linear relations. In particular, he proved that if S and T are linear relations defined on a Banach space X and having finite dimensional multivalued parts and if T right commutes with S, that is, ST ⊂ TS, and if S is compact then T has a nontrivial weakly invariant subspace. However, the case of left commutativity remained open. In this paper, we develop some operator representation techniques for linear relations and use them to solve the left commutativity case mentioned above under the assumption that ST(0) = S(0) and TS(0) = T(0).","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"87 1","pages":"877-884"},"PeriodicalIF":0.0,"publicationDate":"2018-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83437952","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, Adomain decomposition method is reintroduced with double Laplace transform methods to obtain closed form solutions of linear and nonlinear singular one dimensional pseudo thermo-elasticity coupled system. The nonlinear terms can be easily handled by the use of Adomian polynomials. Furthermore, we illustrate our proposed methods by one example.
{"title":"A note on double Laplace decomposition method for solving singular one dimensional pseudo thermo-elasticity coupled system","authors":"H. Eltayeb, Imed Bachar","doi":"10.22436/JNSA.011.06.12","DOIUrl":"https://doi.org/10.22436/JNSA.011.06.12","url":null,"abstract":"In this paper, Adomain decomposition method is reintroduced with double Laplace transform methods to obtain closed form solutions of linear and nonlinear singular one dimensional pseudo thermo-elasticity coupled system. The nonlinear terms can be easily handled by the use of Adomian polynomials. Furthermore, we illustrate our proposed methods by one example.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"1 1","pages":"864-876"},"PeriodicalIF":0.0,"publicationDate":"2018-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85915131","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the article, we prove that the symmetric function Fn (x1, x2, · · · , xn; r) = ∑ 16i1
本文证明了对称函数Fn (x1, x2，···，xn;r) =∑16i1
{"title":"Schur convexity properties for a class of symmetric functions with applications","authors":"Wei-Mao Qian, Y. Chu","doi":"10.22436/JNSA.011.06.10","DOIUrl":"https://doi.org/10.22436/JNSA.011.06.10","url":null,"abstract":"In the article, we prove that the symmetric function Fn (x1, x2, · · · , xn; r) = ∑ 16i1<i2<···<ir6n r ∏ j=1 ( 1 + xij 1 − xij )1/r is Schur convex, Schur multiplicatively convex and Schur harmonic convex on [0, 1)n, and establish several new analytic inequalities by use of the theory of majorization, where r ∈ {1, 2, · · · ,n} and i1, i2, · · · in are integers.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"12 1","pages":"841-849"},"PeriodicalIF":0.0,"publicationDate":"2018-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84971495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Generalized results of majorization inequality are obtained by using newly Green functions defined in [N. Mahmood, R. P. Agarwal, S. I. Butt, J. Pecari ˇ c, J. Inequal. Appl., ´ 2017 (2017), 17 pages] and Lidstone’s polynomial. We find new upper bounds of Gruss and Ostrowski type. We give further results of majorization inequality by making linear functionals constructed on ¨ convex functions. Some applications are given.
利用[N]中定义的新Green函数，得到了多数化不等式的推广结果。马茂德，r.p. Agarwal, S. I. Butt, J. Pecari, c, J.不等式。达成。， ' 2017(2017)， 17页]和Lidstone的多项式。我们找到了新的Gruss型和Ostrowski型的上界。通过构造在凸函数上构造的线性泛函，给出了多数化不等式的进一步结果。给出了一些应用。
{"title":"Generalized results of Majorization inequality via Lidstone's polynomial and newly Green function","authors":"N. Latif, J. Pečarić, N. Siddique","doi":"10.22436/jnsa.011.06.08","DOIUrl":"https://doi.org/10.22436/jnsa.011.06.08","url":null,"abstract":"Generalized results of majorization inequality are obtained by using newly Green functions defined in [N. Mahmood, R. P. Agarwal, S. I. Butt, J. Pecari ˇ c, J. Inequal. Appl., ´ 2017 (2017), 17 pages] and Lidstone’s polynomial. We find new upper bounds of Gruss and Ostrowski type. We give further results of majorization inequality by making linear functionals constructed on ¨ convex functions. Some applications are given.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"50 1","pages":"812-831"},"PeriodicalIF":0.0,"publicationDate":"2018-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86454656","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we study the analytic continuation Tq(s) and Tq(s,w) of the q-Tangent numbers Tn,q and q-Tangent polynomials Tn,q(x) introduced by authors. The new concept of dynamics of the zeros of analytic continued q-tangent polynomials is investigated observing an interesting phenomenon of ‘scattering’ of the zeros of Tq(s,w). Finally, we study linear differential equations arising from the generating functions of q-tangent polynomials giving explicit identities for the q-tangent polynomials.
{"title":"Dynamics of the zeros of analytic continued polynomials and differential equations associated with q-tangent polynomials","authors":"C. Ryoo, Kyung-Won Hwang, Do Jin Kim, N. Jung","doi":"10.22436/JNSA.011.06.06","DOIUrl":"https://doi.org/10.22436/JNSA.011.06.06","url":null,"abstract":"In this paper, we study the analytic continuation Tq(s) and Tq(s,w) of the q-Tangent numbers Tn,q and q-Tangent polynomials Tn,q(x) introduced by authors. The new concept of dynamics of the zeros of analytic continued q-tangent polynomials is investigated observing an interesting phenomenon of ‘scattering’ of the zeros of Tq(s,w). Finally, we study linear differential equations arising from the generating functions of q-tangent polynomials giving explicit identities for the q-tangent polynomials.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"73 1","pages":"785-797"},"PeriodicalIF":0.0,"publicationDate":"2018-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86175898","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, a stochastic process, which is a class of nonhomogeneous diffusion process from the perspective of the corresponding nonlinear stochastic differential equation is studied. The parameter included in the drift term are estimated by sequential maximum likelihood methodology. The sequential estimators are proved to be closed, unbiased, strongly consistent, normally distributed, and optimal in the mean square sense.
{"title":"Asymptotic behavior of parametric estimation for a class of nonlinear diffusion process","authors":"Chengliang Zhu","doi":"10.22436/jnsa.011.06.05","DOIUrl":"https://doi.org/10.22436/jnsa.011.06.05","url":null,"abstract":"In this paper, a stochastic process, which is a class of nonhomogeneous diffusion process from the perspective of the corresponding nonlinear stochastic differential equation is studied. The parameter included in the drift term are estimated by sequential maximum likelihood methodology. The sequential estimators are proved to be closed, unbiased, strongly consistent, normally distributed, and optimal in the mean square sense.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"1 1","pages":"778-784"},"PeriodicalIF":0.0,"publicationDate":"2018-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90039920","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we prove and develop a conjecture on the generalized double Papenfuss-Bach inequality proposed by Sun and Zhu [Z. Sun, L. Zhu, J. Appl. Math., 2011 (2011), 9 pages]. In the last section we pose a conjecture on a general form of Papenfuss-Bach-type inequality.
{"title":"Sharp generalized Papenfuss-Bach-type inequality","authors":"Ling Zhu","doi":"10.22436/JNSA.011.06.04","DOIUrl":"https://doi.org/10.22436/JNSA.011.06.04","url":null,"abstract":"In this paper, we prove and develop a conjecture on the generalized double Papenfuss-Bach inequality proposed by Sun and Zhu [Z. Sun, L. Zhu, J. Appl. Math., 2011 (2011), 9 pages]. In the last section we pose a conjecture on a general form of Papenfuss-Bach-type inequality.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"400 1","pages":"770-777"},"PeriodicalIF":0.0,"publicationDate":"2018-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80075226","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The notion of Aleksandrov body in the classical Brunn-Minkowski theory is extended to that of Orlicz-Aleksandrov body in the Orlicz Brunn-Minkowski theory. The analogs of the Brunn-Minkowski type inequality and the first variations of volume are established via Orlicz-Aleksandrov body. We also make some considerations for the polar of Orlicz combination.
{"title":"On Brunn-Minkowski type inequality","authors":"Lewen Ji, Zhenbing Zeng, Jingjing Zhong","doi":"10.22436/jnsa.011.06.03","DOIUrl":"https://doi.org/10.22436/jnsa.011.06.03","url":null,"abstract":"The notion of Aleksandrov body in the classical Brunn-Minkowski theory is extended to that of Orlicz-Aleksandrov body in the Orlicz Brunn-Minkowski theory. The analogs of the Brunn-Minkowski type inequality and the first variations of volume are established via Orlicz-Aleksandrov body. We also make some considerations for the polar of Orlicz combination.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"36 1","pages":"762-769"},"PeriodicalIF":0.0,"publicationDate":"2018-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75776476","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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