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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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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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GENERALIZATIONS OF THE SUZUKI AND KANNAN FIXED POINT THEOREMS IN G-CONE METRIC SPACES 被引量:1
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作者 Mohammad Sadegh Asgari Zohreh Abbasbigi 《Analysis in Theory and Applications》 2012年第3期248-262,共15页
In this paper we develop the Banach contraction principle and Kannan fixed point theorem on generalized cone metric spaces. We prove a version of Suzuki and Kannan type generalizations of fixed point theorems in gener... In this paper we develop the Banach contraction principle and Kannan fixed point theorem on generalized cone metric spaces. We prove a version of Suzuki and Kannan type generalizations of fixed point theorems in generalized cone metric spaces. 展开更多
关键词 fixed point D-metric space 2-metric space generalized cone metric space Kannan mapping generalized Kannan mapping contractive mapping
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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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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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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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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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COMMON FIXED POINT THEOREMS FOR THREE MAPS IN DISCONTINUOUS G_b-METRIC SPACES
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作者 Jamal Rezaei ROSHAN Nabiollah SHOBKOLAEI +2 位作者 Shaban SEDGHI Vahid PARVANEH Stojan RADENOVI 《Acta Mathematica Scientia》 SCIE CSCD 2014年第5期1643-1654,共12页
In [Aghajani A, Abbas M, Roshan JR. Common fixed point of generalized weak contractive mappings in partially ordered Gb-metric spaces. Filomat, 2013, in press], using the concepts of G-metric and b-metric Aghajani et ... In [Aghajani A, Abbas M, Roshan JR. Common fixed point of generalized weak contractive mappings in partially ordered Gb-metric spaces. Filomat, 2013, in press], using the concepts of G-metric and b-metric Aghajani et al. defined a new type of metric which is called generalized b-metric or Gb-metric. In this paper, we prove a common fixed point theorem for three mappings in Gb-metric space which is not continuous. An example is presented to verify the effectiveness and applicability of our main result. 展开更多
关键词 common fixed point b-metric space G-metric space
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New Necessary Conditions for a Fixed-Point of Maps in Non-Metric Spaces
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作者 Ivan Raykov 《Advances in Pure Mathematics》 2022年第10期561-564,共4页
Our purpose is to introduce new necessary conditions for a fixed point of maps on non-metric spaces. We use a contraction map on a metric topological space and a lately published definition of limit of a function betw... Our purpose is to introduce new necessary conditions for a fixed point of maps on non-metric spaces. We use a contraction map on a metric topological space and a lately published definition of limit of a function between the metric topological space and the non-metric topological space. Then we show that we can create a function h on the non-metric space Y, h :Y →Y and present necessary conditions for a fixed point of this map on this map on Y. Therefore, this gives an opportunity to take a best conclusion in some sense, when non-metrizable matter is under consideration. 展开更多
关键词 Topological space Compact metric space Fixed Point Contraction Map Non-metric space
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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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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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UNIQUE COMMON FIXED POINT OF A FAMILY OF SELF-MAPS WITH SAME TYPE CONTRACTIVE CONDITION IN 2-METRIC SPACE 被引量:15
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作者 Yongjie Piao 《Analysis in Theory and Applications》 2008年第4期316-320,共5页
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
关键词 2-metric space contractive condition Cauchy sequence common fixed point
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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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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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A New Browder Fixed Point Theorem in Noncompact Hyperconvex Metric Spaces and Its Applications to Section Questions and Intersection Questions 被引量:3
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作者 WEN Kai-ting 《Chinese Quarterly Journal of Mathematics》 CSCD 2009年第1期112-116,共5页
In this paper, a new Browder fixed point theorem is established in the noncompact sub-admissible subsets of noncompact hyperconvex metric spaces. As application, a Ky Fan section theorem and an intersection theorem ar... In this paper, a new Browder fixed point theorem is established in the noncompact sub-admissible subsets of noncompact hyperconvex metric spaces. As application, a Ky Fan section theorem and an intersection theorem are obtained. 展开更多
关键词 hyperconvex metric space fixed point sub-admissible set noncompact measure SECTION INTERSECTION
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Some Fixed Point Results on a Class of Contractive Mappings in Cone Metric Spaces 被引量:4
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作者 HUANG Hua-ping XU Shao-yuan HAN Yan 《Chinese Quarterly Journal of Mathematics》 CSCD 2013年第4期539-545,共7页
In this paper, we consider a notion of contractive mappings with certain conditions in cone metric spaces and obtain some results of fixed points by using some necessary conditions. The results directly improve and ge... In this paper, we consider a notion of contractive mappings with certain conditions in cone metric spaces and obtain some results of fixed points by using some necessary conditions. The results directly improve and generalize some fixed point results in metric soaces and some previous results in cone metric spaces. 展开更多
关键词 cone metric space sequentially compact fixed point
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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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Common Fixed Point Theorems in Non-normal Cone Metric Spaces with Banach Algebras 被引量:2
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作者 HUANG Hua-ping XU Shao-yuan +1 位作者 LIU Qiu-hua MING Wei 《Chinese Quarterly Journal of Mathematics》 2016年第2期155-161,共7页
In this paper, we obtain a class of common fixed point theorems for generalized Lipschitz mappings in cone metric spaces with Banach algebras without the assumption of normality of cones. The results greatly generaliz... In this paper, we obtain a class of common fixed point theorems for generalized Lipschitz mappings in cone metric spaces with Banach algebras without the assumption of normality of cones. The results greatly generalize some results in the literature. Moreover,we give an example to support the main assertions. 展开更多
关键词 cone metric space with Banach algebra generalized Lispchitz constant weakly compatible
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B-Implicit Contractive Conditions and Unique(Common) Fixed Points on Complex Valued Metric Spaces 被引量:2
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作者 PIAO Yong-jie 《Chinese Quarterly Journal of Mathematics》 2018年第2期212-220,共9页
A class B of complex functions is introduced and several existence theorems of unique(common) fixed points for mappings satisfying a B-implicit contraction are presented.Moreover, the existence results of common fixed... A class B of complex functions is introduced and several existence theorems of unique(common) fixed points for mappings satisfying a B-implicit contraction are presented.Moreover, the existence results of common fixed points for two mappings on a nonempty set with two complex valued metrics are provided. Our outcomes generalize and improve some known results, especially, for instance, Banach contraction principle, Chatterjea-type fixed point theorem and the corresponding fixed point theorems. 展开更多
关键词 Complex valued metric space (Common) Fixed point B-implicit contraction
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