• Title/Summary/Keyword: Generalized metric spaces

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THE BROUWER AND SCHAUDER FIXED POINT THEOREMS FOR SPACES HAVING CERTAIN CONTRACTIBLE SUBSETS

  • Park, Sehie
    • Bulletin of the Korean Mathematical Society
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    • v.30 no.1
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    • pp.83-89
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    • 1993
  • Applications of the classical Knaster-Kuratowski-Mazurkiewicz theorem [KKM] and the fixed point theory of multifunctions defined on convex subsets of topological vector spaces have been greatly improved by adopting the concept of convex spaces due to Lassonde[L]. Recently, this concept has been extended to pseudo-convex spaces, contractible spaces, or spaces having certain families of contractible subsets by Horvath[H1-4]. In the present paper we give a far-reaching generalization of the best approximation theorem of Ky Fan[F1, 2] to pseudo-metric spaces and improved versions of the well-known fixed point theorems due to Brouwer [B] and Schauder [S] for spaces having certain families of contractible subsets. Our basic tool is a generalized Fan-Browder type fixed point theorem in our previous works [P3, 4].

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ON THE CLASS OF COMPLEX DOUGLAS-KROPINA SPACES

  • Aldea, Nicoleta;Munteanu, Gheorghe
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.1
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    • pp.251-266
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    • 2018
  • In this paper, considering the class of complex Kropina metrics we obtain the necessary and sufficient conditions that these are generalized Berwald and complex Douglas metrics, respectively. Special attention is devoted to a class of complex Douglas-Kropina spaces, in complex dimension 2. Also, some examples of complex Douglas-Kropina metrics are pointed out. Finally, the complex Douglas-Kropina metrics are characterized through the theory of projectively related complex Finsler metrics.

A HYBRID PROJECTION METHOD FOR RELAXED COCOERCIVE MAPPINGS AND STRICTLY PSEUDO-CONTRACTIVE MAPPINGS

  • Liu, Ying
    • East Asian mathematical journal
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    • v.28 no.3
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    • pp.305-320
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    • 2012
  • The purpose of this paper is to introduce a hybrid projection method for finding a common element of the set of solutions of a generalized equilibrium problem, the set of solutions of a variational inclusion problem and the set of common fixed points of a finite family of strict pseudo-contractions in Hilbert spaces.

ON THE C-PROJECTIVE VECTOR FIELDS ON RANDERS SPACES

  • Rafie-Rad, Mehdi;Shirafkan, Azadeh
    • Journal of the Korean Mathematical Society
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    • v.57 no.4
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    • pp.1005-1018
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    • 2020
  • A characterization of the C-projective vector fields on a Randers space is presented in terms of 𝚵-curvature. It is proved that the 𝚵-curvature is invariant for C-projective vector fields. The dimension of the algebra of the C-projective vector fields on an n-dimensional Randers space is at most n(n + 2). The generalized Funk metrics on the n-dimensional Euclidean unit ball 𝔹n(1) are shown to be explicit examples of the Randers metrics with a C-projective algebra of maximum dimension n(n+2). Then, it is also proved that an n-dimensional Randers space has a C-projective algebra of maximum dimension n(n + 2) if and only if it is locally Minkowskian or (up to re-scaling) locally isometric to the generalized Funk metric. A new projective invariant is also introduced.

RICCI-BOURGUIGNON SOLITONS AND FISCHER-MARSDEN CONJECTURE ON GENERALIZED SASAKIAN-SPACE-FORMS WITH 𝛽-KENMOTSU STRUCTURE

  • Sudhakar Kumar Chaubey;Young Jin Suh
    • Journal of the Korean Mathematical Society
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    • v.60 no.2
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    • pp.341-358
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    • 2023
  • Our aim is to study the properties of Fischer-Marsden conjecture and Ricci-Bourguignon solitons within the framework of generalized Sasakian-space-forms with 𝛽-Kenmotsu structure. It is proven that a (2n + 1)-dimensional generalized Sasakian-space-form with 𝛽-Kenmotsu structure satisfying the Fischer-Marsden equation is a conformal gradient soliton. Also, it is shown that a generalized Sasakian-space-form with 𝛽-Kenmotsu structure admitting a gradient Ricci-Bourguignon soliton is either ψ∖Tk × M2n+1-k or gradient 𝜂-Yamabe soliton.

SEVERAL STABILITY PROBLEMS OF A QUADRATIC FUNCTIONAL EQUATION

  • Cho, In-Goo;Koh, Hee-Jeong
    • Communications of the Korean Mathematical Society
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    • v.26 no.1
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    • pp.99-113
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    • 2011
  • In this paper, we investigate the stability using shadowing property in Abelian metric group and the generalized Hyers-Ulam-Rassias stability in Banach spaces of a quadratic functional equation, $f(x_1+x_2+x_3+x_4)+f(-x_1+x_2-x_3+x_4)+f(-x_1+x_2+x_3)+f(-x_2+x_3+x_4)+f(-x_3+x_4+x_1)+f(-x_4+x_1+x_2)=5{\sum\limits_{i=1}^4}f(x_i)$. Also, we study the stability using the alternative fixed point theory of the functional equation in Banach spaces.

GENERALIZED CONDITIONS FOR THE CONVERGENCE OF INEXACT NEWTON-LIKE METHODS ON BANACH SPACES WITH A CONVERGENCE STRUCTURE AND APPLICATIONS

  • Argyros, Ioannis-K.
    • Journal of applied mathematics & informatics
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    • v.5 no.2
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    • pp.433-448
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    • 1998
  • In this study we use inexact Newton-like methods to find solutions of nonlinear operator equations on Banach spaces with a convergence structure. Our technique involves the introduction of a generalized norm as an operator from a linear space into a par-tially ordered Banach space. In this way the metric properties of the examined problem can be analyzed more precisely. Moreover this approach allows us to derive from the same theorem on the one hand semi-local results of kantorovich-type and on the other hand 2global results based on monotonicity considerations. By imposing very general Lipschitz-like conditions on the operators involved on the other hand by choosing our operators appropriately we can find sharper error bounds on the distances involved than before. Furthermore we show that special cases of our results reduce to the corresponding ones already in the literature. Finally our results are used to solve integral equations that cannot be solved with existing methods.

SOME FIXED POINT THEOREMS VIA COMMON LIMIT RANGE PROPERTY IN NON-ARCHIMEDEAN MENGER PROBABILISTIC METRIC SPACES

  • Nashine, Hemant Kumar;Kadelburg, Zoran
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.3
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    • pp.789-807
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    • 2015
  • We propose coincidence and common fixed point results for a quadruple of self mappings satisfying common limit range property and weakly compatibility under generalized ${\Phi}$-contractive conditions i Non-Archimedean Menger PM-spaces. As examples we exhibit different types of situations where these conditions can be used. A common fixed point theorem for four finite families of self mappings is presented as an application of the proposed results. The existence and uniqueness of solutions for certain system of functional equations arising in dynamic programming are also presented as another application.

POSITIVE SOLUTIONS FOR A NONLINEAR MATRIX EQUATION USING FIXED POINT RESULTS IN EXTENDED BRANCIARI b-DISTANCE SPACES

  • Reena, Jain;Hemant Kumar, Nashine;J.K., Kim
    • Nonlinear Functional Analysis and Applications
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    • v.27 no.4
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    • pp.709-730
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    • 2022
  • We consider the nonlinear matrix equation (NMEs) of the form 𝓤 = 𝓠 + Σki=1 𝓐*iℏ(𝓤)𝓐i, where 𝓠 is n × n Hermitian positive definite matrices (HPDS), 𝓐1, 𝓐2, . . . , 𝓐m are n × n matrices, and ~ is a nonlinear self-mappings of the set of all Hermitian matrices which are continuous in the trace norm. We discuss a sufficient condition ensuring the existence of a unique positive definite solution of a given NME and demonstrate this sufficient condition for a NME 𝓤 = 𝓠 + 𝓐*1(𝓤2/900)𝓐1 + 𝓐*2(𝓤2/900)𝓐2 + 𝓐*3(𝓤2/900)𝓐3. In order to do this, we define 𝓕𝓖w-contractive conditions and derive fixed points results based on aforesaid contractive condition for a mapping in extended Branciari b-metric distance followed by two suitable examples. In addition, we introduce weak well-posed property, weak limit shadowing property and generalized Ulam-Hyers stability in the underlying space and related results.