Relevant bibliographies by topics / Mathematics. Metric spaces. Mappings (Mathematics)

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Mathematics. Metric spaces. Mappings (Mathematics)'

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Published: 4 June 2021
Last updated: 16 February 2022

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Journal articles on the topic "Mathematics. Metric spaces. Mappings (Mathematics)"

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CHO, Y. J., N. J. HUANG, and L. XIANG. "COINCIDENCE THEOREMS IN COMPLETE METRIC SPACES." Tamkang Journal of Mathematics 30, no. 1 (March 1, 1999): 1–7. http://dx.doi.org/10.5556/j.tkjm.30.1999.4191.

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The purpose of this paper is to introduce new classes of generalized contractive type set-valued mappings and weakly dissipative mappings and to prove some coincidence theorems for these mappings by using the concept of $\omega$-distances.
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Zimmerman, Scott. "Sobolev Extensions of Lipschitz Mappings into Metric Spaces." International Mathematics Research Notices 2019, no. 8 (August 21, 2017): 2241–65. http://dx.doi.org/10.1093/imrn/rnx201.

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Abstract Wenger and Young proved that the pair $(\mathbb{R}^m,\mathbb{H}^n)$ has the Lipschitz extension property for $m \leq n$ where $\mathbb{H}^n$ is the sub-Riemannian Heisenberg group. That is, for some $C>0$, any $L$-Lipschitz map from a subset of $\mathbb{R}^m$ into $\mathbb{H}^n$ can be extended to a $CL$-Lipschitz mapping on $\mathbb{R}^m$. In this article, we construct Sobolev extensions of such Lipschitz mappings with no restriction on the dimension $m$. We prove that any Lipschitz mapping from a compact subset of $\mathbb{R}^m$ into $\mathbb{H}^n$ may be extended to a Sobolev mapping on any bounded domain containing the set. More generally, we prove this result in the case of mappings into any Lipschitz $(n-1)$-connected metric space.
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Amini, A., M. Fakhar, and J. Zafarani. "KKM mappings in metric spaces." Nonlinear Analysis: Theory, Methods & Applications 60, no. 6 (March 2005): 1045–52. http://dx.doi.org/10.1016/j.na.2004.10.003.

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Ćirić, Ljubomir. "On some discontinuous fixed point mappings in convex metric spaces." Czechoslovak Mathematical Journal 43, no. 2 (1993): 319–26. http://dx.doi.org/10.21136/cmj.1993.128397.

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Aras, Cigdem Gunduz, Sadi Bayramov, and Murat Ibrahim Yazar. "Soft D-metric spaces." Boletim da Sociedade Paranaense de Matemática 38, no. 7 (October 14, 2019): 137–47. http://dx.doi.org/10.5269/bspm.v38i7.44641.

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FUKHAR-UD-DIN, HAFIZ. "Existence and approximation of fixed points in convex metric spaces." Carpathian Journal of Mathematics 30, no. 2 (2014): 175–85. http://dx.doi.org/10.37193/cjm.2014.02.11.

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A fixed point theorem for a generalized nonexpansive mapping is established in a convex metric space introduced by Takahashi [A convexity in metric spaces and nonexpansive mappings, Kodai Math. Sem. Rep., 22 (1970), 142–149]. Our theorem generalizes simultaneously the fixed point theorem of Bose and Laskar [Fixed point theorems for certain class of mappings, Jour. Math. Phy. Sci., 19 (1985), 503–509] and the well-known fixed point theorem of Goebel and Kirk [A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 35 (1972), 171–174] on a nonlinear domain. The fixed point obtained is approximated by averaging Krasnosel’skii iterations of the mapping. Our results substantially improve and extend several known results in uniformly convex Banach spaces and CAT(0) spaces.
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Chernikov, P. V. "Metric spaces and extensions of mappings." Siberian Mathematical Journal 27, no. 6 (1987): 958–62. http://dx.doi.org/10.1007/bf00970017.

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Zhou, Qingshan, Yaxiang Li, and Yuehui He. "Quasihyperbolic mappings in length metric spaces." Comptes Rendus. Mathématique 359, no. 3 (April 20, 2021): 237–47. http://dx.doi.org/10.5802/crmath.154.

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Bridges, Douglas, and Ray Mines. "Sequentially continuous linear mappings in constructive analysis." Journal of Symbolic Logic 63, no. 2 (June 1998): 579–83. http://dx.doi.org/10.2307/2586851.

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A mapping u: X → Y between metric spaces is sequentially continuous if for each sequence (xn) converging to x ∈ X, (u(xn)) converges to u(x). It is well known in classical mathematics that a sequentially continuous mapping between metric spaces is continuous; but, as all proofs of this result involve the law of excluded middle, there appears to be a constructive distinction between sequential continuity and continuity. Although this distinction is worth exploring in its own right, there is another reason why sequential continuity is interesting to the constructive mathematician: Ishihara [8] has a version of Banach's inverse mapping theorem in functional analysis that involves the sequential continuity, rather than continuity, of the linear mappings; if this result could be upgraded by deleting the word “sequential”, then we could prove constructively the standard versions of the inverse mapping theorem and the closed graph theorem.Troelstra [9] showed that in Brouwer's intuitionistic mathematics (INT) a sequentially continuous mapping on a separable metric space is continuous. On the other hand, Ishihara [6, 7] proved constructively that the continuity of sequentially continuous mappings on a separable metric space is equivalent to a certain boundedness principle for subsets of ℕ; in the same paper, he showed that the latter principle holds within the recursive constructive mathematics (RUSS) of the Markov School. Since it is not known whether that principle holds within Bishop's constructive mathematics (BISH), of which INT and RUSS are models and which can be regarded as the constructive core of mathematics, the exploration of sequential continuity within BISH holds some interest.
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Stojakovic, Mila. "Common fixed point theorems in complete metric and probabilistic metric spaces." Bulletin of the Australian Mathematical Society 36, no. 1 (August 1987): 73–88. http://dx.doi.org/10.1017/s0004972700026319.

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In this paper several common fixed point theorems for four continuous mappings in Menger and metric spaces are proved. These mappings are assumed to satisfy some generalizations of the contraction condition.
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Dissertations / Theses on the topic "Mathematics. Metric spaces. Mappings (Mathematics)"

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Niyitegeka, Jean Marie Vianney. "Generalizations of some fixed point theorems in banach and metric spaces." Thesis, Nelson Mandela Metropolitan University, 2015. http://hdl.handle.net/10948/5265.

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A fixed point of a mapping is an element in the domain of the mapping that is mapped into itself by the mapping. The study of fixed points has been a field of interests to mathematicians since the discovery of the Banach contraction theorem, i.e. if is a complete metric space and is a contraction mapping (i.e. there exists such that for all ), then has a unique fixed point. The Banach contraction theorem has found many applications in pure and applied mathematics. Due to fixed point theory being a mixture of analysis, geometry, algebra and topology, its applications to other fields such as physics, economics, game theory, chemistry, engineering and many others has become vital. The theory is nowadays a very active field of research in which many new theorems are published, some of them applied and many others generalized. Motivated by all of this, we give an exposition of some generalizations of fixed point theorems in metric fixed point theory, which is a branch of fixed point theory about results of fixed points of mappings between metric spaces, where certain properties of the mappings involved need not be preserved under equivalent metrics. For instance, the contractive property of mappings between metric spaces need not be preserved under equivalent metrics. Since metric fixed point theory is wide, we limit ourselves to fixed point theorems for self and non-self-mappings on Banach and metric spaces. We also take a look at some open problems on this topic of study. At the end of the dissertation, we suggest our own problems for future research.
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Ruth, Harry Leonard Jr. "Conformal densities and deformations of uniform loewner metric spaces." Cincinnati, Ohio : University of Cincinnati, 2008. http://www.ohiolink.edu/etd/view.cgi?ucin1210203872.

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Thesis (Ph.D.)--University of Cincinnati, 2008.
Committee/Advisors: David Herron PhD (Committee Chair), David Minda PhD (Committee Member), Nageswari Shanmugalingam PhD (Committee Member). Title from electronic thesis title page (viewed Sep.3, 2008). Keywords: conformal density; uniform spaces; Loewner; quasisymmetry; quasiconofrmal. Includes abstract. Includes bibliographical references.
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Stofile, Simfumene. "Fixed points of single-valued and multi-valued mappings with applications." Thesis, Rhodes University, 2013. http://hdl.handle.net/10962/d1002960.

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The relationship between the convergence of a sequence of self mappings of a metric space and their fixed points, known as the stability (or continuity) of fixed points has been of continuing interest and widely studied in fixed point theory. In this thesis we study the stability of common fixed points in a Hausdorff uniform space whose uniformity is generated by a family of pseudometrics, by using some general notations of convergence. These results are then extended to 2-metric spaces due to S. Gähler. In addition, a well-known theorem of T. Suzuki that generalized the Banach Contraction Principle is also extended to 2-metric spaces and applied to obtain a coincidence theorem for a pair of mappings on an arbitrary set with values in a 2-metric space. Further, we prove the existence of coincidence and fixed points of Ćirić type weakly generalized contractions in metric spaces. Subsequently, the above result is utilized to discuss applications to the convergence of modified Mann and Ishikawa iterations in a convex metric space. Finally, we obtain coincidence, fixed and stationary point results for multi-valued and hybrid pairs of mappings on a metric space.
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Medwid, Mark Edward. "Rigidity of Quasiconformal Maps on Carnot Groups." Bowling Green State University / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1497620176117104.

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Hume, David S. "Embeddings of infinite groups into Banach spaces." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:e38f58ec-484c-4088-bb44-1556bc647cde.

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In this thesis we build on the theory concerning the metric geometry of relatively hyperbolic and mapping class groups, especially with respect to the difficulty of embedding such groups into Banach spaces. In Chapter 3 (joint with Alessandro Sisto) we construct simple embeddings of closed graph manifold groups into a product of three metric trees, answering positively a conjecture of Smirnov concerning the Assouad-Nagata dimension of such spaces. Consequently, we obtain optimal embeddings of such spaces into certain Banach spaces. The ideas here have been extended to other closed three-manifolds and to higher dimensional analogues of graph manifolds. In Chapter 4 we give an explicit method of embedding relatively hyperbolic groups into certain Banach spaces, which yields optimal bounds on the compression exponent of such groups relative to their peripheral subgroups. From this we deduce that the fundamental group of every closed three-manifold has Hilbert compression exponent one. In Chapter 5 we prove that relatively hyperbolic spaces with a tree-graded quasi-isometry representative can be characterised by a relative version of Manning's bottleneck property. This applies to the Bestvina-Bromberg-Fujiwara quasi-trees of spaces, yielding an embedding of each mapping class group of a closed surface into a finite product of simplicial trees. From this we obtain explicit embeddings of mapping class groups into certain Banach spaces and deduce that these groups have finite Assouad-Nagata dimension. It also applies to relatively hyperbolic groups, proving that such groups have finite Assouad-Nagata dimension if and only if each peripheral subgroup does.
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Gonzalez, Villasanti Hugo Jose. "Stability of Input/Output Dynamical Systems on Metric Spaces: Theory and Applications." The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu155558269238935.

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Razafindrakoto, Ando Desire. "Hyperconvex metric spaces." Thesis, Stellenbosch : University of Stellenbosch, 2010. http://hdl.handle.net/10019.1/4106.

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Thesis (MSc (Mathematics))--University of Stellenbosch, 2010.
ENGLISH ABSTRACT: One of the early results that we encounter in Analysis is that every metric space admits a completion, that is a complete metric space in which it can be densely embedded. We present in this work a new construction which appears to be more general and yet has nice properties. These spaces subsequently called hyperconvex spaces allow one to extend nonexpansive mappings, that is mappings that do not increase distances, disregarding the properties of the spaces in which they are defined. In particular, theorems of Hahn-Banach type can be deduced for normed spaces and some subsidiary results such as fixed point theorems can be observed. Our main purpose is to look at the structures of this new type of “completion”. We will see in particular that the class of hyperconvex spaces is as large as that of complete metric spaces.
AFRIKAANSE OPSOMMING: Een van die eerste resultate wat in die Analise teegekom word is dat enige metriese ruimte ’n vervollediging het, oftewel dat daar ’n volledige metriese ruimte bestaan waarin die betrokke metriese ruimte dig bevat word. In hierdie werkstuk beskryf ons sogenaamde hiperkonvekse ruimtes. Dit gee ’n konstruksie wat blyk om meer algemeen te wees, maar steeds gunstige eienskappe het. Hiermee kan nie-uitbreidende, oftewel afbeeldings wat nie afstande rek nie, uitgebrei word sodanig dat die eienskappe van die ruimte waarop dit gedefinieer is nie ’n rol speel nie. In die besonder kan stellings van die Hahn- Banach-tipe afgelei word vir genormeerde ruimtes en sekere addisionele ressultate ondere vastepuntstellings kan bewys word. Ons hoofdoel is om hiperkonvekse ruimtes te ondersoek. In die besonder toon ons aan dat die klas van alle hiperkonvekse ruimtes net so groot soos die klas van alle metriese ruimtes is.
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Otafudu, Olivier Olela. "Convexity in quasi-metric spaces." Doctoral thesis, University of Cape Town, 2012. http://hdl.handle.net/11427/10950.

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Includes abstract.
Includes bibliographical references.
The principal aim of this thesis is to investigate the existence of an injective hull in the categories of T-quasi-metric spaces and of T-ultra-quasi-metric spaces with nonexpansive maps.
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Jeganathan, P. "Fixed points for nonexpansive mappings in Banach spaces." Master's thesis, University of Cape Town, 1991. http://hdl.handle.net/11427/17067.

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Sarantopoulos, I. C. "Polynomials and multilinear mappings in Banach spaces." Thesis, Brunel University, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.376057.

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Books on the topic "Mathematics. Metric spaces. Mappings (Mathematics)"

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service), SpringerLink (Online, ed. A nonlinear transfer technique for renorming. Berlin: Springer, 2009.

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1862-1943, Hilbert David, ed. Hilbert's projective metric and iterated nonlinear maps. Providence, R.I., USA: American Mathematical Society, 1988.

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Nussbaum, Roger D. Iterated nonlinear maps and Hilbert's projective metric, II. Providence, R.I., USA: American Mathematical Society, 1989.

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Universal spaces and mappings. Amsterdam: Elsevier, 2005.

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Grigorʹevich, Reshetni͡a︡k I͡U︡riĭ, ed. Quasiconformal mappings and Sobolev spaces. Dordrecht: Kluwer Academic Publishers, 1990.

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Heinonen, Juha. Lectures on Analysis on Metric Spaces. New York, NY: Springer New York, 2001.

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Ciorănescu, Ioana. Geometry of banach spaces, duality mappings, and nonlinear problems. Dordrecht: Kluwer Academic Publishers, 1990.

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Min, Chen. Decompositions of Teichmüller space by geodesic length mappings. Helsinki: Suomalainen Tiedeakatemia, 1991.

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Endre, Pap, ed. Fixed point theory in probabilistic metric spaces. Dordrecht: Kluwer Academic, 2001.

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Jana, Björn, ed. Nonlinear potential theory on metric spaces. Zürich, Switzerland: European Mathematical Society, 2011.

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Book chapters on the topic "Mathematics. Metric spaces. Mappings (Mathematics)"

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Lin, Shou, and Ziqiu Yun. "Mappings on Metric Spaces." In Atlantis Studies in Mathematics, 53–146. Paris: Atlantis Press, 2016. http://dx.doi.org/10.2991/978-94-6239-216-8_2.

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Koskela, Pekka. "Sobolev Spaces and Quasiconformal Mappings on Metric Spaces." In European Congress of Mathematics, 457–67. Basel: Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8268-2_26.

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Goud, J. Suresh, P. Rama Bhadra Murthy, Ch Achi Reddy, and K. Madhusudhan Reddy. "Common Fixed Point Theorems in 2-Metric Spaces Using Composition of Mappings via A-Contractions." In Trends in Mathematics, 103–10. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-01120-8_13.

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Nazir, Talat, and Sergei Silvestrov. "Common Fixed Point for Integral Type Contractive Mappings in Multiplicative Metric Spaces." In Springer Proceedings in Mathematics & Statistics, 723–41. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-41850-2_30.

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Auwalu, Abba, and Ali Denker. "Cone Rectangular Metric Spaces over Banach Algebras and Fixed Point Results of T-Contraction Mappings." In Springer Proceedings in Mathematics & Statistics, 107–16. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-69292-6_7.

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Nazir, Talat, and Sergei Silvestrov. "Common Fixed Point Results for Family of Generalized Multivalued F-Contraction Mappings in Ordered Metric Spaces." In Springer Proceedings in Mathematics & Statistics, 419–32. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-42105-6_20.

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Aserkar, Anushri A., and Manjusha P. Gandhi. "The Unique Common Fixed Point Theorem for Four Mappings Satisfying Common Limit in the Range Property in b-Metric Space." In Springer Proceedings in Mathematics & Statistics, 161–71. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-1153-0_14.

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Komornik, Vilmos. "Metric Spaces." In Springer Undergraduate Mathematics Series, 3–35. London: Springer London, 2017. http://dx.doi.org/10.1007/978-1-4471-7316-8_1.

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Brown, Arlen, and Carl Pearcy. "Metric spaces." In Graduate Texts in Mathematics, 96–134. New York, NY: Springer New York, 1995. http://dx.doi.org/10.1007/978-1-4612-0787-0_6.

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Conway, John B. "Metric Spaces." In Undergraduate Texts in Mathematics, 1–38. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-02368-7_1.

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Conference papers on the topic "Mathematics. Metric spaces. Mappings (Mathematics)"

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Auwalu, Abba. "A note on some fixed point theorems for generalized expansive mappings in cone metric spaces over Banach algebras." In INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2018). Author(s), 2018. http://dx.doi.org/10.1063/1.5048998.

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Marín, Josefa. "Partial quasi-metric completeness and Caristi's type mappings." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756274.

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Zhanakunova, Meerim, and Bekbolot Kanetov. "On strongly uniformly paracompact spaces and mappings." In INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2020). AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0040268.

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Goleţ, Ioan, Ciprian Hedrea, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "On Generalized Contractions in Probabilistic Metric Spaces." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3636943.

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Castro-Company, Francisco, and Pedro Tirado. "The bicompletion of intuitionistic fuzzy quasi-metric spaces." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756271.

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Castro-Company, Francisco, and Pedro Tirado. "Some classes of t-norms and fuzzy metric spaces." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756272.

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Goleţ, Ioan, and Ionuţ Goleţ. "On Fixed Point Theorems in Probabilistic Metric Spaces and Applications." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2990900.

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Bamini, S., M. Saraswathi, B. Vijayalakshmi, and A. Vadivel. "Fuzzy M-irresolute mappings and fuzzy M-connectedness in smooth topological spaces." In RECENT TRENDS IN PURE AND APPLIED MATHEMATICS. AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5135191.

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Kiosak, V., A. Savchenko, and O. Gudyreva. "On the conformal mappings of special quasi-Einstein spaces." In APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 11th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’19. AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5130793.

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Vashpanov, Y., O. Olshevska, and O. Lesechko. "Geodesic mappings of spaces with φ(Ric) vector fields." In APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 12th International On-line Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’20. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0033965.

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