• 제목/요약/키워드: Generalized metric spaces

검색결과 110건 처리시간 0.023초

FIXED POINT THEOREMS IN MENGER SPACES USING AN IMPLICIT RELATION

  • Chauhan, Sunny;Khan, M. Alamgir;Pant, B.D.
    • 호남수학학술지
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    • 제35권4호
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    • pp.551-564
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    • 2013
  • In 2008, Al-Thaga and Shahzad [Generalized I-nonexpansive selfmaps and invariant approximations, Acta Math. Sinica, 24(5) (2008), 867-876] introduced the notion of occasionally weakly compatible mappings in metric spaces. In this paper, we prove some common fixed point theorems for families of occasionally weakly compatible mappings in Menger spaces using an implicit relation. We also give an illustrative example to support our main result.

WEAK CONVERGENCE THEOREMS FOR GENERALIZED MIXED EQUILIBRIUM PROBLEMS, MONOTONE MAPPINGS AND PSEUDOCONTRACTIVE MAPPINGS

  • JUNG, JONG SOO
    • 대한수학회지
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    • 제52권6호
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    • pp.1179-1194
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    • 2015
  • In this paper, we introduce a new iterative algorithm for finding a common element of the set of solutions of a generalized mixed equilibrium problem related to a continuous monotone mapping, the set of solutions of a variational inequality problem for a continuous monotone mapping, and the set of fixed points of a continuous pseudocontractive mapping in Hilbert spaces. Weak convergence for the proposed iterative algorithm is proved. Our results improve and extend some recent results in the literature.

EXISTENCE OF COINCIDENCE POINT UNDER GENERALIZED GERAGHTY-TYPE CONTRACTION WITH APPLICATION

  • Handa, Amrish
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제27권3호
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    • pp.109-124
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    • 2020
  • We establish coincidence point theorem for S-non-decreasing mappings under Geraghty-type contraction on partially ordered metric spaces. With the help of obtain result, we derive two dimensional results for generalized compatible pair of mappings F, G : X2 → X. As an application, we obtain the solution of integral equation and also give an example to show the usefulness of our results. Our results improve, sharpen, enrich and generalize various known results.

FIXED POINTS SOLUTIONS OF GENERALIZED EQUILIBRIUM PROBLEMS AND VARIATIONAL INEQUALITY PROBLEMS

  • Shehu, Yekini;Collins, C. Obiora
    • Journal of applied mathematics & informatics
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    • 제28권5_6호
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    • pp.1263-1275
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    • 2010
  • In this paper, we introduce a new iterative scheme for finding a common element of the set of common fixed points of infinite family of nonexpansive mappings and the set of solutions to a generalized equilibrium problem and the set of solutions to a variational inequality problem in a real Hilbert space. Then strong convergence of the scheme to a common element of the three sets is proved. As applications, three new strong convergence theorems are obtained. Our theorems extend important recent results.

COMMON FIXED POINTS OF A LIMIT WEAK COMPATIBLE PAIR OF A MULTIVALUED MAPPING AND A SINGLE VALUED MAPPING IN D-METRIC SPACES

  • Singh, Bijendra;Jain, Shobha;jain, Shishir
    • East Asian mathematical journal
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    • 제22권1호
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    • pp.35-51
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    • 2006
  • This paper deals with a general contraction. Two fixed-point theorems for a limit weak-compatible pair of a multi-valued map and a self map on a D-metric space have been established. These results improve significantly, the main results of Dhage, Jennifer and Kang [5] by reducing its assumption and generalizing its contraction simultaneously. At the same time some results of Singh, Jain and Jain [12] are generalized from a self map to a pair of a set-valued and a self map. Theorems of Veerapandi and Rao [16] get generalized and improved by these results. All the results of this paper are new.

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UTILIZING GENERALIZED MEIR-KEELER CONTRACTION IN PERIODIC BOUNDARY VALUE PROBLEMS

  • Handa, Amrish
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제28권4호
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    • pp.297-314
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    • 2021
  • This manuscript is divided into three segments. In the first segment, we formulate a unique common fixed point theorem satisfying generalized Meir-Keeler contraction on partially ordered metric spaces and also give an example to demonstrate the usability of our result. In the second segment of the article, some common coupled fixed point results are derived from our main results. In the last segment, we investigate the solution of some periodic boundary value problems. Our results generalize, extend and improve several well-known results of the existing literature.

DIMENSIONALLY INVARIANT SPACES

  • Baek, In Soo
    • 충청수학회지
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    • 제22권2호
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    • pp.245-250
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    • 2009
  • We consider a code function from the unit interval which has a generalized dyadic expansion into a coding space which has an associated ultra metric. The code function is not a bi-Lipschitz map but a dimension-preserving map in the sense that the Hausdorff and packing dimensions of any subset in the unit interval and its image under the code function coincide respectively.

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COMMON FIXED POINT THEOREMS FOR GENERALIZED 𝜓∫𝜑-WEAKLY CONTRACTIVE MAPPINGS IN G-METRIC SPACES

  • Kim, Jong Kyu;Kumar, Manoj;Bhardwaj, Preeti;Imdad, Mohammad
    • Nonlinear Functional Analysis and Applications
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    • 제26권3호
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    • pp.565-580
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    • 2021
  • In this paper, first of all we prove a fixed point theorem for 𝜓∫𝜑-weakly contractive mapping. Next, we prove some common fixed point theorems for a pair of weakly compatible self maps along with E.A. property and (CLR) property. An example is also given to support our results.