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Rough weighted 𝓘-limit points and weighted 𝓘-cluster points in θ-metric space

  • Sanjoy Ghosal EMAIL logo und Avishek Ghosh
Veröffentlicht/Copyright: 23. Mai 2020
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Mathematica Slovaca
Aus der Zeitschrift Mathematica Slovaca Band 70 Heft 3

Abstract

In 2018, Das et al. [Characterization of rough weighted statistical statistical limit set, Math. Slovaca 68(4) (2018), 881–896] (or, Ghosal et al. [Effects on rough 𝓘-lacunary statistical convergence to induce the weighted sequence, Filomat 32(10) (2018), 3557–3568]) established the result: The diameter of rough weighted statistical limit set (or, rough weighted 𝓘-lacunary limit set) of a sequence x = {xn}n∈ℕ is 2rlim infn∈Atn if the weighted sequence {tn}n∈ℕ is statistically bounded (or, self weighted 𝓘-lacunary statistically bounded), where A = {k ∈ ℕ : tk < M} and M is a positive real number such that natural density (or, self weighted 𝓘-lacunary density) of A is 1 respectively. Generally this set has no smaller bound other than 2rlim infn∈Atn. We concentrate on investigation that whether in a θ-metric space above mentioned result is satisfied for rough weighted 𝓘-limit set or not? Answer is no. In this paper we establish infinite as well as unbounded θ-metric space (which has not been done so far) by utilizing some non-trivial examples. In addition we introduce and investigate some problems concerning the sets of rough weighted 𝓘-limit points and weighted 𝓘-cluster points in θ-metric space and formalize how these sets could deviate from the existing basic results.

MSC 2010: Primary 40A35; Secondary 40G15
Keywords: θ-metric space; rough weighted 𝓘-convergence; rough weighted 𝓘-limit set; weighted 𝓘-boundedness; weighted 𝓘-cluster point

The research of the second author is supported by Jadavpur University, Kolkata-700032, West Bengal, India

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  1. Communicated by Tomasz Natkaniec

Acknowledgement

We are thankful to the Editor and Referees for their careful reading of the paper and several valuable suggestions which improved the quality and presentation of the paper.

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Received: 2019-04-03
Accepted: 2019-10-22
Published Online: 2020-05-23
Published in Print: 2020-06-25

© 2020 Mathematical Institute Slovak Academy of Sciences

Artikel in diesem Heft

  1. Regular papers
  2. Recurrences for the genus polynomials of linear sequences of graphs
  3. The existence of states on EQ-algebras
  4. On sidon sequences of farey sequences, square roots and reciprocals
  5. Repdigits as sums of three balancing numbers
  6. Lipschitz one sets modulo sets of measure zero
  7. Refinement of fejér inequality for convex and co-ordinated convex functions
  8. An extension of q-starlike and q-convex error functions endowed with the trigonometric polynomials
  9. Coefficients problems for families of holomorphic functions related to hyperbola
  10. Triebel-Lizorkin capacity and hausdorff measure in metric spaces
  11. The method of upper and lower solutions for integral boundary value problem of semilinear fractional differential equations with non-instantaneous impulses
  12. On a system of three difference equations of higher order solved in terms of Lucas and Fibonacci numbers
  13. Density of summable subsequences of a sequence and its applications
  14. Rough weighted 𝓘-limit points and weighted 𝓘-cluster points in θ-metric space
  15. A note on cosine series with coefficients of generalized bounded variation
  16. Some geometric properties of the non-Newtonian sequence spaces lp(N)
  17. On sequence spaces defined by the domain of a regular tribonacci matrix
  18. Jointly separating maps between vector-valued function spaces
  19. Some fixed point theorems for multi-valued mappings in graphical metric spaces
  20. Monotone transformations on the cone of all positive semidefinite real matrices
  21. Locally defined operators in the space of Ck,ω-functions
  22. Some properties of D-weak operator topology
  23. Estimating the distribution of a stochastic sum of IID random variables
  24. An internal characterization of complete regularity
https://doi.org/10.1515/ms-2017-0380
Schlagwörter für diesen Artikel
θ-metric space; rough weighted 𝓘-convergence; rough weighted 𝓘-limit set; weighted 𝓘-boundedness; weighted 𝓘-cluster point

Artikel in diesem Heft

  1. Regular papers
  2. Recurrences for the genus polynomials of linear sequences of graphs
  3. The existence of states on EQ-algebras
  4. On sidon sequences of farey sequences, square roots and reciprocals
  5. Repdigits as sums of three balancing numbers
  6. Lipschitz one sets modulo sets of measure zero
  7. Refinement of fejér inequality for convex and co-ordinated convex functions
  8. An extension of q-starlike and q-convex error functions endowed with the trigonometric polynomials
  9. Coefficients problems for families of holomorphic functions related to hyperbola
  10. Triebel-Lizorkin capacity and hausdorff measure in metric spaces
  11. The method of upper and lower solutions for integral boundary value problem of semilinear fractional differential equations with non-instantaneous impulses
  12. On a system of three difference equations of higher order solved in terms of Lucas and Fibonacci numbers
  13. Density of summable subsequences of a sequence and its applications
  14. Rough weighted 𝓘-limit points and weighted 𝓘-cluster points in θ-metric space
  15. A note on cosine series with coefficients of generalized bounded variation
  16. Some geometric properties of the non-Newtonian sequence spaces lp(N)
  17. On sequence spaces defined by the domain of a regular tribonacci matrix
  18. Jointly separating maps between vector-valued function spaces
  19. Some fixed point theorems for multi-valued mappings in graphical metric spaces
  20. Monotone transformations on the cone of all positive semidefinite real matrices
  21. Locally defined operators in the space of Ck,ω-functions
  22. Some properties of D-weak operator topology
  23. Estimating the distribution of a stochastic sum of IID random variables
  24. An internal characterization of complete regularity
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