Pub Date : 2018-12-31DOI: 10.30538/PSRP-OMA2018.0015
Muhammad Akmal, Muhammad Saqib Khan, Shahzad Ahmad Maitla
The aim of this paper is to present a viscosity approximation method for asymptotically nonexpansive mappings in Banach spaces. The strong convergence of the viscosity rules is proved with some assumptions. This paper extend and improve results presented in [1, 2, 3, 4]. Mathematics Subject Classification: 47J25, 47N20, 34G20, 65J15.
{"title":"Viscosity Methods for Approximating Solutions of Variational Inequalities for Asymptotically Nonexpansive Mappings","authors":"Muhammad Akmal, Muhammad Saqib Khan, Shahzad Ahmad Maitla","doi":"10.30538/PSRP-OMA2018.0015","DOIUrl":"https://doi.org/10.30538/PSRP-OMA2018.0015","url":null,"abstract":"The aim of this paper is to present a viscosity approximation method for asymptotically nonexpansive mappings in Banach spaces. The strong convergence of the viscosity rules is proved with some assumptions. This paper extend and improve results presented in [1, 2, 3, 4]. Mathematics Subject Classification: 47J25, 47N20, 34G20, 65J15.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42826807","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}
Pub Date : 2018-12-31DOI: 10.30538/psrp-oma2018.0019
Fanfan Li, Z. Han
In this paper, we use Riccati transformation technique to establish some new oscillation criteria for the second order nonlinear dynamic equation with damping on time scales (r(t)(x(t))) − p(t)(x(t)) + q(t)f(x(t)) = 0. Our results not only generalize some existing results, but also can be applied to the oscillation problems that are not covered in literature. Finally, we give some examples to illustrate our main results. Mathematics Subject Classification: 26E70, 34C10.
{"title":"Oscillation Behavior of Second Order Nonlinear Dynamic Equation with Damping on Time Scales","authors":"Fanfan Li, Z. Han","doi":"10.30538/psrp-oma2018.0019","DOIUrl":"https://doi.org/10.30538/psrp-oma2018.0019","url":null,"abstract":"In this paper, we use Riccati transformation technique to establish some new oscillation criteria for the second order nonlinear dynamic equation with damping on time scales (r(t)(x(t))) − p(t)(x(t)) + q(t)f(x(t)) = 0. Our results not only generalize some existing results, but also can be applied to the oscillation problems that are not covered in literature. Finally, we give some examples to illustrate our main results. Mathematics Subject Classification: 26E70, 34C10.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44919510","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}
Pub Date : 2018-06-30DOI: 10.30538/PSRP-OMA2018.0012
Saba Noreen, Atif Mahmood
A line graph has many useful applications in physical chemistry. Topological indices are numerical parameters associated to a structure and, in combination, determine properties of the concerned material. In this paper, we compute the closed form of Zagreb polynomilas of all generalized class of carbon nanocones and compute important degree-based topological indices. AMS Mathematics Subject Classification : 05C05, 05C07, 05C35.
{"title":"Zagreb Polynomials and Redefined Zagreb indices for the Line Graph of Carbon Nanocones","authors":"Saba Noreen, Atif Mahmood","doi":"10.30538/PSRP-OMA2018.0012","DOIUrl":"https://doi.org/10.30538/PSRP-OMA2018.0012","url":null,"abstract":"A line graph has many useful applications in physical chemistry. Topological indices are numerical parameters associated to a structure and, in combination, determine properties of the concerned material. In this paper, we compute the closed form of Zagreb polynomilas of all generalized class of carbon nanocones and compute important degree-based topological indices. AMS Mathematics Subject Classification : 05C05, 05C07, 05C35.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42010385","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}
Pub Date : 2018-06-30DOI: 10.30538/PSRP-OMA2018.0010
H. Kadakal, M. Kadakal, I. Işcan, Giresun University-Giresun-TÜRKİYE Arts
In this paper, a new identity for functions defined on an open invex subset of set of real numbers is established, and by using the this identity and the Hölder and Power mean integral inequalities we present new type integral inequalities for functions whose powers of third derivatives in absolute value are preinvex and prequasiinvex functions. AMS Mathematics Subject Classification : 26A51, 26D10, 26D15.
{"title":"New Type Integral Inequalities for Three Times Differentiable Preinvex and Prequasiinvex Functions","authors":"H. Kadakal, M. Kadakal, I. Işcan, Giresun University-Giresun-TÜRKİYE Arts","doi":"10.30538/PSRP-OMA2018.0010","DOIUrl":"https://doi.org/10.30538/PSRP-OMA2018.0010","url":null,"abstract":"In this paper, a new identity for functions defined on an open invex subset of set of real numbers is established, and by using the this identity and the Hölder and Power mean integral inequalities we present new type integral inequalities for functions whose powers of third derivatives in absolute value are preinvex and prequasiinvex functions. AMS Mathematics Subject Classification : 26A51, 26D10, 26D15.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44848875","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}
Pub Date : 2018-06-30DOI: 10.30538/psrp-oma2018.0009
S. Turhan, I. Işcan, Giresun University-Giresun-TÜRKİYE Arts
In this paper, we gave the new general identity for differentiable function. As a result of this identity some new and general fractional integral inequalities for differentiable harmonically convex functions are obtained. AMS Mathematics Subject Classification: 26D15, 26A51, 26D10, 26A15.
{"title":"Some New Hermite-Hadamard-Fejér Type Inequalities for Harmonically Convex Functions","authors":"S. Turhan, I. Işcan, Giresun University-Giresun-TÜRKİYE Arts","doi":"10.30538/psrp-oma2018.0009","DOIUrl":"https://doi.org/10.30538/psrp-oma2018.0009","url":null,"abstract":"In this paper, we gave the new general identity for differentiable function. As a result of this identity some new and general fractional integral inequalities for differentiable harmonically convex functions are obtained. AMS Mathematics Subject Classification: 26D15, 26A51, 26D10, 26A15.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48930475","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}
Pub Date : 2018-06-30DOI: 10.30538/PSRP-OMA2018.0007
M. Saqib, Zain Majeed, M. Quraish, W. Nazeer
In this paper, we establish a two step third-order iteration method for solving nonlinear equations. The efficiency index of the method is 1.442 which is greater than Newton-Raphson method. It is important to note that our method is performing very well in comparison to fixed point method and the method discussed by Kang et al. (Abstract and applied analysis; volume 2013, Article ID 487060). AMS Mathematics Subject Classification: 47H05, 47H09, 47H10.
{"title":"A New Third-Order Iteration Method for Solving Nonlinear Equations","authors":"M. Saqib, Zain Majeed, M. Quraish, W. Nazeer","doi":"10.30538/PSRP-OMA2018.0007","DOIUrl":"https://doi.org/10.30538/PSRP-OMA2018.0007","url":null,"abstract":"In this paper, we establish a two step third-order iteration method for solving nonlinear equations. The efficiency index of the method is 1.442 which is greater than Newton-Raphson method. It is important to note that our method is performing very well in comparison to fixed point method and the method discussed by Kang et al. (Abstract and applied analysis; volume 2013, Article ID 487060). AMS Mathematics Subject Classification: 47H05, 47H09, 47H10.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69237895","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}
Pub Date : 2018-06-30DOI: 10.30538/psrp-oma2018.0008
Samina Kausar, M. Asif, Mubeen Munir
In this article we present non-convex hybrid iteration algorithm corollaryresponding to Karakaya iterative scheme [1] as done by Guan et al. in [2] corollaryresponding to Mann iterative scheme [3]. We also prove some strong convergence results about common fixed points for a uniformly closed asymptotic family of countable quasi-Lipschitz mappings in Hilbert spaces. AMS Mathematics Subject Classification: 47H05; 47H09; 47H10.
{"title":"Non-convex hybrid Method corresponding to Karakaya Iterative Process","authors":"Samina Kausar, M. Asif, Mubeen Munir","doi":"10.30538/psrp-oma2018.0008","DOIUrl":"https://doi.org/10.30538/psrp-oma2018.0008","url":null,"abstract":"In this article we present non-convex hybrid iteration algorithm corollaryresponding to Karakaya iterative scheme [1] as done by Guan et al. in [2] corollaryresponding to Mann iterative scheme [3]. We also prove some strong convergence results about common fixed points for a uniformly closed asymptotic family of countable quasi-Lipschitz mappings in Hilbert spaces. AMS Mathematics Subject Classification: 47H05; 47H09; 47H10.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47495280","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}
Pub Date : 2018-06-30DOI: 10.30538/PSRP-OMA2018.0011
Allia Naseem
Unsteady free convection flow of Casson fluid over an unbounded upright plate subject to time dependent velocity Uof(t) with constant wall temperature has been carried out. By introducing dimensionless variables, the general solutions are obtained by Laplace transform method. The solution corresponding to Newtonian fluid for γ → ∞ is obtained as a limiting case. Exact solutions corresponding to (i) f(t) = fH(t), (ii) f(t) = fta, a > 0 (iii) f(t) = fH(t)cos(ωt) are also discussed as special cases of our general solutions. Expressions for shear stress in terms of skin friction and the rate of heat transfer in the form of Nusselt number are also presented. Velocity and temperature profiles for different parameters are discussed graphically. AMS Mathematics Subject Classification: 26D15, 26A51, 26D10, 26A15.
{"title":"General solution of Casson fluid past a vertical plate subject to the time dependent velocity with constant wall temperature","authors":"Allia Naseem","doi":"10.30538/PSRP-OMA2018.0011","DOIUrl":"https://doi.org/10.30538/PSRP-OMA2018.0011","url":null,"abstract":"Unsteady free convection flow of Casson fluid over an unbounded upright plate subject to time dependent velocity Uof(t) with constant wall temperature has been carried out. By introducing dimensionless variables, the general solutions are obtained by Laplace transform method. The solution corresponding to Newtonian fluid for γ → ∞ is obtained as a limiting case. Exact solutions corresponding to (i) f(t) = fH(t), (ii) f(t) = fta, a > 0 (iii) f(t) = fH(t)cos(ωt) are also discussed as special cases of our general solutions. Expressions for shear stress in terms of skin friction and the rate of heat transfer in the form of Nusselt number are also presented. Velocity and temperature profiles for different parameters are discussed graphically. AMS Mathematics Subject Classification: 26D15, 26A51, 26D10, 26A15.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41475699","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}
Pub Date : 2018-02-19DOI: 10.5269/BSPM.V38I1.34767
Zouaoui Bekri, S. Benaicha
In this paper, we study the existence of nontrivial solution for the fourth-order three- point boundary value problem having the following form u(4) (t) + f (t, u(t)) = 0, 0 < t < 1, u(0) = α(η), u'(0) = u''(0) = 0, u(1) = βu(η), where η ∈ (0, 1), α, β ∈ R, f ∈ C ([0, 1] × R, R). We give sufficient conditions that allow us to obtain the existence of a nontrivial solution. And by using the Leray-Schauder nonlinear alternative we prove the existence of at least one solution of the posed problem. As an application, we also given some examples to illustrate the results obtained.
{"title":"Existence of solution for a nonlinear fifth-order three-point boundary value problem","authors":"Zouaoui Bekri, S. Benaicha","doi":"10.5269/BSPM.V38I1.34767","DOIUrl":"https://doi.org/10.5269/BSPM.V38I1.34767","url":null,"abstract":"In this paper, we study the existence of nontrivial solution for the fourth-order three- point boundary value problem having the following form u(4) (t) + f (t, u(t)) = 0, 0 < t < 1, u(0) = α(η), u'(0) = u''(0) = 0, u(1) = βu(η), where η ∈ (0, 1), α, β ∈ R, f ∈ C ([0, 1] × R, R). We give sufficient conditions that allow us to obtain the existence of a nontrivial solution. And by using the Leray-Schauder nonlinear alternative we prove the existence of at least one solution of the posed problem. As an application, we also given some examples to illustrate the results obtained.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.5269/BSPM.V38I1.34767","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43550746","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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