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Rock Mass Quality Rating Based on the Multi-Criteria Grey Metric Space
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作者 Miloš Gligoric Zoran Gligoric +3 位作者 Saša Jovanovic Suzana Lutovac Dragan Pamucar Ivan Jankovic 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第9期2635-2664,共30页
Assessment of rock mass quality significantly impacts the design and construction of underground and open-pit mines from the point of stability and economy.This study develops the novel Gromov-Hausdorff distance for r... Assessment of rock mass quality significantly impacts the design and construction of underground and open-pit mines from the point of stability and economy.This study develops the novel Gromov-Hausdorff distance for rock quality(GHDQR)methodology for rock mass quality rating based on multi-criteria grey metric space.It usually presents the quality of surrounding rock by classes(metric spaces)with specified properties and adequate interval-grey numbers.Measuring the distance between surrounding rock sample characteristics and existing classes represents the core of this study.The Gromov-Hausdorff distance is an especially useful discriminant function,i.e.,a classifier to calculate these distances,and assess the quality of the surrounding rock.The efficiency of the developed methodology is analyzed using the Mean Absolute Percentage Error(MAPE)technique.Seven existing methods,such as the Gaussian cloud method,Discriminant method,Mutation series method,Artificial neural network(ANN),Support vector machine(SVM),Grey wolf optimizer and Support vector classification method(GWO-SVC)and Rock mass rating method(RMR)are used for comparison with the proposed GHDQR method.The share of the highly accurate category of 85.71%clearly indicates compliance with actual values obtained by the compared methods.The results of comparisons showed that the model enables objective,efficient,and reliable assessment of rock mass quality. 展开更多
关键词 Rock mass rating MULTI-CRITERIA class metric space interval-grey numbers
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OBSTACLE PROBLEMS ON RCD(K,N)METRIC MEASURE SPACES
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作者 林锶坍 《Acta Mathematica Scientia》 SCIE CSCD 2023年第5期1925-1944,共20页
In this paper,we solve the obstacle problems on metric measure spaces with generalized Ricci lower bounds.We show the existence and Lipschitz continuity of the solutions,and then we establish some regularities of the ... In this paper,we solve the obstacle problems on metric measure spaces with generalized Ricci lower bounds.We show the existence and Lipschitz continuity of the solutions,and then we establish some regularities of the free boundaries. 展开更多
关键词 obstacle problem metric measure space Riemannian curvature-dimension condition
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Generalization of Inequalities in Metric Spaces with Applications
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作者 Eltigani I. Hassan 《Journal of Applied Mathematics and Physics》 2023年第10期2923-2931,共9页
In this paper, which serves as a continuation of earlier work, we generalize the idea of inequalities in metric spaces and use them to demonstrate that the incomplete metric space can be used to obtain a Banach space.
关键词 metric spaces Banach space INEQUALITIES
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Fixed points on complete metric spaces
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作者 朱顺荣 《Journal of Southeast University(English Edition)》 EI CAS 2004年第2期256-260,共5页
Two new fixed point theorems on two complete metric spaces are proved by using the concept of w -distance. One of the results is: let (X,d) and (Y,ρ) be two complete metric spaces,let p 1 be a w -distance o... Two new fixed point theorems on two complete metric spaces are proved by using the concept of w -distance. One of the results is: let (X,d) and (Y,ρ) be two complete metric spaces,let p 1 be a w -distance on X and p 2 be a w -distance on Y . If T is a continuous mapping of X into Y and S is a mapping of Y into X ,satisfying the inequalities: p 1(STx,STx′)≤c max {p 1(x,x′),p 1(x,STx),p 1(x′,STx′),p 1(x,STx′)/2,p 2(Tx,Tx′)} and p 2(TSy,TSy′)≤c max {p 2(y,y′),p 2(y,TSy),p 2(y′,TSy′),p 2(y,TSy′)/2,p 1(Sy,Sy′)} for all x,x′ in X and y,y′ in Y ,where 0≤ c<1. We have proved that ST has a unique fixed point z in X and TS has a unique fixed point w in Y . The two theorems have improved the fixed point theorems of Fisher and Namdeo,et al. 展开更多
关键词 fixed point complete metric space w-distance
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Common Fixed Point Theorems for Commuting Maps on a Complete Metric Space
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作者 朱顺荣 《Journal of Southeast University(English Edition)》 EI CAS 2001年第1期82-84,共3页
The concept of w distance on a metric space is introduced and three common fixed points theorems for commuting maps on a complete metric space are proved. These results extended fixed point theorems of Jungck a... The concept of w distance on a metric space is introduced and three common fixed points theorems for commuting maps on a complete metric space are proved. These results extended fixed point theorems of Jungck and Ciric. 展开更多
关键词 DISTANCE fixed point complete metric space
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《Metric Linear Spaces》的两点注记
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作者 王见勇 《常熟高专学报》 2002年第2期13-16,共4页
指出StefanRolewicz先生的名著《MetricLinearSpaces》中的三个定理的证明错误 。
关键词 度量线性空间 σ-有限测度空间 连续嵌入 实心F*-空间 最大不友好 凹性模
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GENERALIZED H-KKM TYPE THEOREMS IN H-METRIC SPACES WITH APPLICATIONS 被引量:23
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作者 DING Xie-ping(丁协平) +1 位作者 XIA Fu-quan(夏福全) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第10期1140-1148,共9页
The new notions of H-metric spaces and generalized H-KKM mappings were introduced. Some generalized H-KKM type theorems for generalized H-K-KM mappings with finitely metrically compactly closed values and finitely met... The new notions of H-metric spaces and generalized H-KKM mappings were introduced. Some generalized H-KKM type theorems for generalized H-K-KM mappings with finitely metrically compactly closed values and finitely metrically compactly open values were established in H-metric spaces. These theorems generalize recent results of Khamsi and Yuan. As applications, some Ky Fan type matching theorems for finitely metrically compactly open covers and finitely metrically compactly closed covers, fixed point theorems and minimax inequality are obtained in H-metric spaces. These results generalize a number of known results in recent literature. 展开更多
关键词 hyperconvex space H-metric space finitely metrically compactly closed (open) set generalized H-KKM mapping admissible set
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New Common Fixed Point Results for Four Maps on Cone Metric Spaces 被引量:12
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作者 Yan Han Shaoyuan Xu 《Applied Mathematics》 2011年第9期1114-1118,共5页
In this paper, some new existence and uniqueness of common fixed points for four mappings are obtained, which do not satisfy continuity and commutation on non-normal cone metric spaces. These results improve and gener... In this paper, some new existence and uniqueness of common fixed points for four mappings are obtained, which do not satisfy continuity and commutation on non-normal cone metric spaces. These results improve and generalize several well-known comparable results in the literature. 展开更多
关键词 COMMON Fixed Point CONE metric space Non-Normal CONE
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FIXED POINT THEOREMS FOR MAPPINGS SATISFYING IMPLICIT RELATION ON TWO COMPLETE AND COMPACT METRIC SPACES 被引量:3
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作者 Abdlkrim Aliouche Brian Fisher 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第9期1217-1222,共6页
First, the implicit relations were given. A common fixed point theorem was proved for two mappings satisfying implicit relation functions. A further fixed point theorem was proved for mappings satisfying implicit rela... First, the implicit relations were given. A common fixed point theorem was proved for two mappings satisfying implicit relation functions. A further fixed point theorem was proved for mappings satisfying implicit relation functions on two compact metric spaces. 展开更多
关键词 complete metric space compact metric space fixed Points implicit relation
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SOME NEW EXTENSIONS OF EDELSTEIN-SUZUKI-TYPE FIXED POINT THEOREM TO G-METRIC AND G-CONE METRIC SPACES 被引量:3
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作者 Fridoun MORADLOU Peyman SALIMI Pasquale VETRO 《Acta Mathematica Scientia》 SCIE CSCD 2013年第4期1049-1058,共10页
In this paper, we prove some fixed point theorems for generalized contractions in the setting of G-metric spaces. Our results extend a result of Edelstein [M. Edelstein, On fixed and periodic points under contractive ... In this paper, we prove some fixed point theorems for generalized contractions in the setting of G-metric spaces. Our results extend a result of Edelstein [M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc., 37 (1962), 74-79] and a result of Suzuki [T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 (2009), 5313-5317]. We prove, also, a fixed point theorem in the setting of G-cone metric spaces. 展开更多
关键词 G-metric spaces G-cone metric spaces fixed point Edelstein's theorem Suzuki's theorem
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COMMON FIXED POINT OF GENERALIZED WEAKLY CONTRACTIVE MAPS IN PARTIAL METRIC SPACES 被引量:5
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作者 Vesna COJBAIC RAJIC Stojan RADENOVIC Sunny CHAUHAN 《Acta Mathematica Scientia》 SCIE CSCD 2014年第4期1345-1356,共12页
In this paper, using the context of complete partial metric spaces, some common fixed point results of maps that satisfy the generalized (ψ, Ф)-weak contractive conditions are obtained. Our results generalize, ext... In this paper, using the context of complete partial metric spaces, some common fixed point results of maps that satisfy the generalized (ψ, Ф)-weak contractive conditions are obtained. Our results generalize, extend, unify, enrich and complement many existing results in the literature. Example are given showing the validaty of our results. 展开更多
关键词 Common fixed point lower semi-continuous function weak (ψ Ф)-contraction partial metric space
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A NEW PERTURBATION THEOREM FOR MOORE-PENROSE METRIC GENERALIZED INVERSE OF BOUNDED LINEAR OPERATORS IN BANACH SPACES 被引量:3
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作者 王紫 王玉文 《Acta Mathematica Scientia》 SCIE CSCD 2017年第6期1619-1631,共13页
In this paper, we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is "the generalized Neumann lemma"... In this paper, we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is "the generalized Neumann lemma" which is quite different from the method in [12] where "the generalized Banach lemma" was used. By the method of the perturba- tion analysis of bounded linear operators, we obtain an explicit perturbation theorem and three inequalities about error estimates for the Moore-Penrose metric generalized inverse of bounded linear operator under the generalized Neumann lemma and the concept of stable perturbations in Banach spaces. 展开更多
关键词 Banach space bounded linear operator metric projection generalized inverse perturbation analysis Moore-Penrose quasi-additive
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Some New Theorems of Lipschitz Type Mappings in Cone Metric Spaces 被引量:5
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作者 HAN Yan XU Wang-bin XU Shao-yuan 《Chinese Quarterly Journal of Mathematics》 CSCD 2013年第2期224-233,共10页
In this paper, some new existence and uniqueness of common fixed points for three mappings of Lipschitz type are obtained. The conditions are greatly weaker than the classic conditions in cone metric spaces. These res... In this paper, some new existence and uniqueness of common fixed points for three mappings of Lipschitz type are obtained. The conditions are greatly weaker than the classic conditions in cone metric spaces. These results improve and generalize several wellknown comparable results in the literature. Moreover, our results are supported by some examples. 展开更多
关键词 cone metric space lipschitz type mapping common fixed point
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SPATIAL GRADIENT ANALYSIS OF URBAN GREEN SPACES COMBINED WITH LANDSCAPE METRICS IN JINAN CITY OF CHINA 被引量:6
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作者 KONG Fan-hua Nobukazu NAKAGOSHI +1 位作者 YIN Hai-wei Akira KIKUCHI 《Chinese Geographical Science》 SCIE CSCD 2005年第3期254-261,共8页
Urban green spaces have been arisen growing concern responded to the social and environmental costs of urban sprawl. A wide range of planning and policies has been and/or will be designed to protect urban green spaces... Urban green spaces have been arisen growing concern responded to the social and environmental costs of urban sprawl. A wide range of planning and policies has been and/or will be designed to protect urban green spaces and optimize their spatial pattern. A better design or planning of urban green space can make a major contribution to quality of environment and urban life, and furthermore can decide whether we can have a sustainable development in the urban area. Information about the status quo of urban green spaces can help planners design more effectively. However, how to quantify and capture such information will be the essential question we face. In this paper, to quantify the urban green space, a new method comprising gradient analysis, landscape metrics and GIS was developed through a case of Jinan City. The results demonstrate: 1) the gradient analysis is a valid and reliable instrument to quantify the urban green space spatial pattern precisely; 2) using moving window, explicit landscape metrics were spatially realized. Compared with quantifying metrics in the entire landscape, it would be better to link pattern with process and establish an important basis for analyzing the ecological and socioeconomic functions of green spaces. 展开更多
关键词 urban green space spatial pattern gradient analysis landscape metrics GIS Jinan City
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FIXED POINTS ON TWO COMPLETE AND COMPACT METRIC SPACES 被引量:2
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作者 M. Telci (Department of Mathematics, Faculty of Arts and Science, Trakya University, 22030 Ediren, Turkey) (Communicated by CHIEN Wei_zang) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第5期564-568,共5页
By using functions, some related fixed point theorems on two metric spaces are established. These results generalize some theorems of Fisher.
关键词 fixed point complete metric space compact metric space
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Common Fixed Point Theorems in Intuitionistic Fuzzy Metric Spaces 被引量:3
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作者 Saurabh Manro Sanjay Kumar Shivdeep Singh 《Applied Mathematics》 2010年第6期510-514,共5页
In this paper, we introduce the concept of – chainable intuitionistic fuzzy metric space akin to the notion of – chainable fuzzy metric space introduced by Cho, and Jung [1] and prove a common fixed point theorem fo... In this paper, we introduce the concept of – chainable intuitionistic fuzzy metric space akin to the notion of – chainable fuzzy metric space introduced by Cho, and Jung [1] and prove a common fixed point theorem for weakly compatible mappings in this newly defined space. 展开更多
关键词 Chainable Intuitionistic FUZZY metric space WEAKLY Compatible MAPS
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CONVERGENCE OF ISHIKAWA TYPE ITERATIVE SEQUENCE WITH ERRORS FOR QUASI-CONTRACTIVE MAPPINGS IN CONVEX METRIC SPACES 被引量:3
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作者 TIAN You-xian(田有先) +1 位作者 ZHANG Shi-sheng(张石生) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2002年第9期1001-1008,共8页
Some convergence theorems of Ishikawa type iterative sequence with errors for nonlinear general quasi-contractive mapping in convex metric spaces are proved. The results not only extend and improve the corresponding r... Some convergence theorems of Ishikawa type iterative sequence with errors for nonlinear general quasi-contractive mapping in convex metric spaces are proved. The results not only extend and improve the corresponding results of L. B. Ciric, Q. H. Liu, H. E. Rhoades and H. K. Xu, et al., but also give an affirmative answer to the open question of Rhoades-Naimpally- Singh in convex metric spaces. 展开更多
关键词 convex metric space fixed point generalized Ishikawa (Mann) iterative sequence with errors general quasi-contractive mapping
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Some New Fixed Point Theorems in Probabilistic Metric Spaces 被引量:14
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作者 朱传喜 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1995年第2期179-185,共7页
In this paper, we introduce the concept of the Z-M-PN space and obtain somenew fixed point theorems in probabilistic metric spaces Meanwhile,some famous fixedpoint theorems are generalized in probabilistic metric spac... In this paper, we introduce the concept of the Z-M-PN space and obtain somenew fixed point theorems in probabilistic metric spaces Meanwhile,some famous fixedpoint theorems are generalized in probabilistic metric spaces, such a.s fixed point theorem of Schauder, Guo's theorem and fixed point theorem of Petryshyn are generalized in Menger PN-space. And fixed point theorem of Altman is also generalized in the Z-M-PN space. 展开更多
关键词 topological degree. probabilistic metric spaces. operator.compact continuous operator. Z-M-PN space
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Fixed Point Results by Altering Distances in Fuzzy Metric Spaces 被引量:2
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作者 Ibtisam Masmali Sumitra Dalal Nasir Rehman 《Advances in Pure Mathematics》 2015年第6期377-382,共6页
We establish fixed point theorems in complete fuzzy metric space by using notion of altering distance, initiated by Khan et al. [Bull. Austral. Math. Soc. 30 (1984), 1-9]. Also, we find an affirmative answer in fuzzy ... We establish fixed point theorems in complete fuzzy metric space by using notion of altering distance, initiated by Khan et al. [Bull. Austral. Math. Soc. 30 (1984), 1-9]. Also, we find an affirmative answer in fuzzy metric space to the problem of Sastry [TamkangJ. Math., 31(3) (2000), 243-250]. 展开更多
关键词 Fixed POINTS Fuzzy metric spaceS Altering Distance Fixed Point RESULTS
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FIXED POINT RESULTS ON METRIC-TYPE SPACES 被引量:1
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作者 Monica COSENTINO Peyman SALIMI Pasquale VETRO 《Acta Mathematica Scientia》 SCIE CSCD 2014年第4期1237-1253,共17页
In this paper we obtain fixed point and common fixed point theorems for self- mappings defined on a metric-type space, an ordered metric-type space or a normal cone metric space. Moreover, some examples and an applica... In this paper we obtain fixed point and common fixed point theorems for self- mappings defined on a metric-type space, an ordered metric-type space or a normal cone metric space. Moreover, some examples and an application to integral equations are given to illustrate the usability of the obtained results. 展开更多
关键词 metric-type space fixed point common fixed point Suzuki type mappings cone metric space integral equation
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