In this paper, we prove that a family of self-maps {Ti,j}i,j∈N in 2-metric space has a unique common fixed point if （i） {Ti,j}i,j∈N satisfies the same type contractive condition for each j ∈ N; （ii） Tm,μ .Tn,v...In this paper, we prove that a family of self-maps {Ti,j}i,j∈N in 2-metric space has a unique common fixed point if （i） {Ti,j}i,j∈N satisfies the same type contractive condition for each j ∈ N; （ii） Tm,μ .Tn,v = Tn,v.Tm.μ for all m,n,μ,v ∈ N with μ≠v. Our main result generalizes and improves many known unique common fixed point theorems in 2-metric spaces.展开更多
In this paper, some new unique common fixed points for four mappings satisfying Ф-contractive conditions on non-complete 2-metric spaces are obtained, in which the mappings do not satisfy continuity and commutation. ...In this paper, some new unique common fixed points for four mappings satisfying Ф-contractive conditions on non-complete 2-metric spaces are obtained, in which the mappings do not satisfy continuity and commutation. The main results generalize and improve many well-known and corresponding conclusions in the literatures.展开更多
The aim of this article is to prove a fixed point theorem in 2-Banach spaces and show its applications to the Ulam stability of functional equations. The obtained stability re- sults concern both some single variable ...The aim of this article is to prove a fixed point theorem in 2-Banach spaces and show its applications to the Ulam stability of functional equations. The obtained stability re- sults concern both some single variable equations and the most important functional equation in several variables, namely, the Cauchy equation. Moreover, a few corollaries corresponding to some known hyperstability outcomes are presented.展开更多
In this paper, we will introduce a class of 5-dimensional functions Φ and prove that a family of self-mappings {Ti,j} iεN in 2-metric space have an unique common fixed point if 1) {Ti,j} iεN satisfies Φj-contracti...In this paper, we will introduce a class of 5-dimensional functions Φ and prove that a family of self-mappings {Ti,j} iεN in 2-metric space have an unique common fixed point if 1) {Ti,j} iεN satisfies Φj-contractive condition, where ΦjεΦ, for each jεN;2) Tm,μ n,v for all m,n,μ,vεN with μ ≠ v . Our main result generalizes and unifies many known unique common fixed point theorems in 2-metric spaces.展开更多
In this work,syngas methanation over Ni-W/TiO2-SiO2catalyst was studied in a fluidized-bed reactor(FBR)and its performance was compared with a fixed-bed reactor(FIXBR).The effects of main operating variables including...In this work,syngas methanation over Ni-W/TiO2-SiO2catalyst was studied in a fluidized-bed reactor(FBR)and its performance was compared with a fixed-bed reactor(FIXBR).The effects of main operating variables including feedstock gases space velocity,coke content,bed temperature and sulfur-tolerant stability of 100 h life were investigated.The structure of the catalysts was characterized by XRD,N2adsorptiondesorption and TEM.It is found that under same space velocity from 5000 h 1to 25000 h 1FBR gave a higher CH4yield,lower coke content,and lower bed temperature than those obtained in FIXBR.Ni-W/TiO2-SiO2catalyst possessed excellent sulfur-tolerant stability on the feedstock gases less than 500 ppm H2S in FBR.The carbon deposits formed on the spent catalyst were in the form of carbon fibers in FBR,while in the form of dense accumulation distribution appearance in FIXBR.展开更多
In this paper, we introduce a class Ψ of real functions defined on the set of non-negative real numbers, and obtain a new unique common fixed point theorem for four mappings satisfying Ψ-contractive condition on a n...In this paper, we introduce a class Ψ of real functions defined on the set of non-negative real numbers, and obtain a new unique common fixed point theorem for four mappings satisfying Ψ-contractive condition on a non-complete 2-metric space and give the versions of the corresponding result for two and three mappings.展开更多
In this paper, we introduce a new class Γ, which is weak than a known class Ψ, of real continuous functions defined on [0, +∞), and use another method to prove the known unique common fixed point theorem for four m...In this paper, we introduce a new class Γ, which is weak than a known class Ψ, of real continuous functions defined on [0, +∞), and use another method to prove the known unique common fixed point theorem for four mappings with γ-contractive condition instead of Ψ-contractive condition on 2-metric spaces.展开更多
In this paper, we give existence theorems of common fixed points for two mappings with a weakly C*-contractive condition on partially ordered 2-metric spaces and give a sufficient condition under which there exists a ...In this paper, we give existence theorems of common fixed points for two mappings with a weakly C*-contractive condition on partially ordered 2-metric spaces and give a sufficient condition under which there exists a unique common fixed point.展开更多
In this paper, we introduce a new class U of 3-dimensional real functions, use U and a 2-dimensional real function ? to construct a new implicit-linear contractive condition and obtain some existence theorems of commo...In this paper, we introduce a new class U of 3-dimensional real functions, use U and a 2-dimensional real function ? to construct a new implicit-linear contractive condition and obtain some existence theorems of common fixed points for two mappings on partially ordered 2-metric spaces and give a sufficient condition under which there exists a unique common fixed point. The obtained results goodly generalize and improve the corresponding conclusions in references.展开更多
In this work,we apply the Brzdȩk and Ciepliński's fixed point theorem to investigate new stability results for the generalized Cauchy functional equation of the form f(ax+by)=af(x)+bf(y),where a,b∈N and f is a m...In this work,we apply the Brzdȩk and Ciepliński's fixed point theorem to investigate new stability results for the generalized Cauchy functional equation of the form f(ax+by)=af(x)+bf(y),where a,b∈N and f is a mapping from a commutative group(G,+)to a 2-Banach space(Y,||·,·||).Our results are generalizations of main results of Brzdȩk and Ciepliński[J Brzdȩk,K Ciepliński.On a fixed point theorem in 2-normed spaces and some of its applications.Acta Mathematica Scientia,2018,38B(2):377-390].展开更多
Purpose: This is a retrospective, comparative, head-to-head, not commissioned study about the efficacy of bimato-prost 0.03%, brimonidine 0.2%, brinzolamide 1%, dorzolamide 2%, and travoprost 0.004%/timolol 0.5%-fixed...Purpose: This is a retrospective, comparative, head-to-head, not commissioned study about the efficacy of bimato-prost 0.03%, brimonidine 0.2%, brinzolamide 1%, dorzolamide 2%, and travoprost 0.004%/timolol 0.5%-fixed combinations in patients affected by na?ve open-angle glaucoma and IOP > 25 mmHg. Patients and Methods: Files from 70 patients (35 M, 35 F, mean age 69.52 y, S.D. 11.56, range: 37-87y) in our Glaucoma Service were retrospectively analyzed as long as 12 months. Every subgroup, including 14 age- and sex-matched patients, was allocated to 1 of the 5 groups of the fixed combinations monotherapy. Data recorded after 3 months follow-up were statistically analyzed by descriptive and ANOVA statistics as percentage of IOP reduction from baseline. Results: All the fixed combinations were effective in lowering IOP. The mean percentage reduction was: brimonidine/timolol 43.57%, dorzolamide/timolol 37.67%, bimatoprost/timolol 35.60%, travoprost/timolol 33.25% and brinzolamide/timolol 23.0%. The brimonidine/timolol fixed combination showed to be statistically significant more effective only than brinzolamide/timolol fixed combination (p = 0.001). Setting the α error to 5%, the power of the study is 26%, phi: 0.842. Discussion: In all this cohort of patients the target IOP was successfully achieved. All the fixed combinations used in this study had a very good profile of efficacy. Brimonidine, dorzolamide, bimatoprost and travoprost/timolol fixed combinations statistically significantly reduced the percentage of IOP from baseline (p = 0.001) more than brinzolamide/timolol fixed combination.展开更多
In this paper,we introduce the notion of generalized cyclic contraction pairs in b2-metric spaces and establish some fixed point theorems for such pairs.Then,we give an example to illustrate our results.
Adsorption and desorption characteristics of 2,4-dichlorophenoxybutyric acid (2,4-DB) from aqueous solution on bamboo activated carbon (BAC) were studied in a fixed bed adsorber. The adsorption equilibrium capacity of...Adsorption and desorption characteristics of 2,4-dichlorophenoxybutyric acid (2,4-DB) from aqueous solution on bamboo activated carbon (BAC) were studied in a fixed bed adsorber. The adsorption equilibrium capacity of 2,4-DB on BAC increased with decreasing initial pH of the solution and with a maximum adsorption capacity of 1.61 mol/kg. The adsorption rate of 2,4-DB on BAC could be best fitted by the pseudo first-order model. The adsorption model based on the linear driving force approximation (LDFA) was used for simulating the adsorption behavior of the 2,4-DB in a fixed bed. More than 95% desorption of 2,4-DB was obtained using distilled water.展开更多
文摘In this paper, we prove that a family of self-maps {Ti,j}i,j∈N in 2-metric space has a unique common fixed point if （i） {Ti,j}i,j∈N satisfies the same type contractive condition for each j ∈ N; （ii） Tm,μ .Tn,v = Tn,v.Tm.μ for all m,n,μ,v ∈ N with μ≠v. Our main result generalizes and improves many known unique common fixed point theorems in 2-metric spaces.
文摘In this paper, some new unique common fixed points for four mappings satisfying Ф-contractive conditions on non-complete 2-metric spaces are obtained, in which the mappings do not satisfy continuity and commutation. The main results generalize and improve many well-known and corresponding conclusions in the literatures.
文摘The aim of this article is to prove a fixed point theorem in 2-Banach spaces and show its applications to the Ulam stability of functional equations. The obtained stability re- sults concern both some single variable equations and the most important functional equation in several variables, namely, the Cauchy equation. Moreover, a few corollaries corresponding to some known hyperstability outcomes are presented.
文摘In this paper, we will introduce a class of 5-dimensional functions Φ and prove that a family of self-mappings {Ti,j} iεN in 2-metric space have an unique common fixed point if 1) {Ti,j} iεN satisfies Φj-contractive condition, where ΦjεΦ, for each jεN;2) Tm,μ n,v for all m,n,μ,vεN with μ ≠ v . Our main result generalizes and unifies many known unique common fixed point theorems in 2-metric spaces.
文摘In this work,syngas methanation over Ni-W/TiO2-SiO2catalyst was studied in a fluidized-bed reactor(FBR)and its performance was compared with a fixed-bed reactor(FIXBR).The effects of main operating variables including feedstock gases space velocity,coke content,bed temperature and sulfur-tolerant stability of 100 h life were investigated.The structure of the catalysts was characterized by XRD,N2adsorptiondesorption and TEM.It is found that under same space velocity from 5000 h 1to 25000 h 1FBR gave a higher CH4yield,lower coke content,and lower bed temperature than those obtained in FIXBR.Ni-W/TiO2-SiO2catalyst possessed excellent sulfur-tolerant stability on the feedstock gases less than 500 ppm H2S in FBR.The carbon deposits formed on the spent catalyst were in the form of carbon fibers in FBR,while in the form of dense accumulation distribution appearance in FIXBR.
文摘In this paper, we introduce a class Ψ of real functions defined on the set of non-negative real numbers, and obtain a new unique common fixed point theorem for four mappings satisfying Ψ-contractive condition on a non-complete 2-metric space and give the versions of the corresponding result for two and three mappings.
文摘In this paper, we introduce a new class Γ, which is weak than a known class Ψ, of real continuous functions defined on [0, +∞), and use another method to prove the known unique common fixed point theorem for four mappings with γ-contractive condition instead of Ψ-contractive condition on 2-metric spaces.
文摘In this paper, we give existence theorems of common fixed points for two mappings with a weakly C*-contractive condition on partially ordered 2-metric spaces and give a sufficient condition under which there exists a unique common fixed point.
文摘In this paper, we introduce a new class U of 3-dimensional real functions, use U and a 2-dimensional real function ? to construct a new implicit-linear contractive condition and obtain some existence theorems of common fixed points for two mappings on partially ordered 2-metric spaces and give a sufficient condition under which there exists a unique common fixed point. The obtained results goodly generalize and improve the corresponding conclusions in references.
基金This work was supported by Research Professional Development Project under the Science Achievement Scholarship of Thailand(SAST)and Thammasat University Research Fund,Contract No.TUGG 33/2562The second author would like to thank the Thailand Research Fund and Office of the Higher Education Commission under grant no.MRG6180283 for financial support during the preparation of this manuscript.
文摘In this work,we apply the Brzdȩk and Ciepliński's fixed point theorem to investigate new stability results for the generalized Cauchy functional equation of the form f(ax+by)=af(x)+bf(y),where a,b∈N and f is a mapping from a commutative group(G,+)to a 2-Banach space(Y,||·,·||).Our results are generalizations of main results of Brzdȩk and Ciepliński[J Brzdȩk,K Ciepliński.On a fixed point theorem in 2-normed spaces and some of its applications.Acta Mathematica Scientia,2018,38B(2):377-390].
文摘Purpose: This is a retrospective, comparative, head-to-head, not commissioned study about the efficacy of bimato-prost 0.03%, brimonidine 0.2%, brinzolamide 1%, dorzolamide 2%, and travoprost 0.004%/timolol 0.5%-fixed combinations in patients affected by na?ve open-angle glaucoma and IOP > 25 mmHg. Patients and Methods: Files from 70 patients (35 M, 35 F, mean age 69.52 y, S.D. 11.56, range: 37-87y) in our Glaucoma Service were retrospectively analyzed as long as 12 months. Every subgroup, including 14 age- and sex-matched patients, was allocated to 1 of the 5 groups of the fixed combinations monotherapy. Data recorded after 3 months follow-up were statistically analyzed by descriptive and ANOVA statistics as percentage of IOP reduction from baseline. Results: All the fixed combinations were effective in lowering IOP. The mean percentage reduction was: brimonidine/timolol 43.57%, dorzolamide/timolol 37.67%, bimatoprost/timolol 35.60%, travoprost/timolol 33.25% and brinzolamide/timolol 23.0%. The brimonidine/timolol fixed combination showed to be statistically significant more effective only than brinzolamide/timolol fixed combination (p = 0.001). Setting the α error to 5%, the power of the study is 26%, phi: 0.842. Discussion: In all this cohort of patients the target IOP was successfully achieved. All the fixed combinations used in this study had a very good profile of efficacy. Brimonidine, dorzolamide, bimatoprost and travoprost/timolol fixed combinations statistically significantly reduced the percentage of IOP from baseline (p = 0.001) more than brinzolamide/timolol fixed combination.
文摘In this paper,we introduce the notion of generalized cyclic contraction pairs in b2-metric spaces and establish some fixed point theorems for such pairs.Then,we give an example to illustrate our results.
文摘Adsorption and desorption characteristics of 2,4-dichlorophenoxybutyric acid (2,4-DB) from aqueous solution on bamboo activated carbon (BAC) were studied in a fixed bed adsorber. The adsorption equilibrium capacity of 2,4-DB on BAC increased with decreasing initial pH of the solution and with a maximum adsorption capacity of 1.61 mol/kg. The adsorption rate of 2,4-DB on BAC could be best fitted by the pseudo first-order model. The adsorption model based on the linear driving force approximation (LDFA) was used for simulating the adsorption behavior of the 2,4-DB in a fixed bed. More than 95% desorption of 2,4-DB was obtained using distilled water.
