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Vol.31 No.1

Ebrahim Tamimi(Velayat University) ; Ali Ghaffari(Semnan University) pp.1-19 https://doi.org/10.7468/jksmeb.2024.31.1.1
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Abstract

In this paper, the notions of strong Connes amenability for certain products of Banach algebras and module extension of dual Banach algebras is investigated. We characterize χ ⊗ η-strong Connes amenability of projective tensor product K⨶H via χ ⊗ η-σwc virtual diagonals, where χ ∈ K∗ and η ∈ H∗ are linear functionals on dual Banach algebras K and H, respectively. Also, we present some conditions for the existence of (χ, θ)-σwc virtual diagonals in the θ-Lau product of K ×_θ H. Finally, we characterize the notion of (χ, 0)-strong Connes amenability for module extension of dual Banach algebras K ⊕ X, where X is a normal Banach K-bimodule.

Seung Hyun Kim(yungsung University) ; Mee Kwang Kang(Dongeui University) pp.21-32 https://doi.org/10.7468/ksmeb.2024.31.1.21
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Abstract

In this paper, we introduce new types of weakly Picard operators being available to a much wider class of maps, and prove common fixed point theorems of Subrahmanyam type for two these weakly Picard operators in the collection of singlevalued and multi-valued mappings in complete metric spaces. Our results extend and generalize the corresponding fixed point theorems in the literature [3, 6].

Muhammad Bilal(University of Karachi) ; Asif R. Khan(University of Karachi) pp.33-48 https://doi.org/10.7468/jksmeb.2024.31.1.33
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Abstract

In this study, we would like to state two refined results related to Hermite Hadamard type inequality for convex functions with two distinct techniques. Hence our obtained results would be better than the results already established for the class of convex functions. Applications to trapezoidal rule and special means are also discussed.

Mahnaz Shafi Chishti(Shobhit Institute of Engineering & Technology(Deemed to be University) Meerut) ; Vipin Kumar Tyagi(Shobhit Institute of Engineering and Technology(Deemed to be University) Meerut) ; Mohammad Ibrahim Mir(University of Kashmir) pp.49-56 https://doi.org/10.7468/jksmeb.2024.31.1.49
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Abstract

For a Polynomial P(z)= SMALLSUM _{j=0}^{n} `a _{j} z ^{j} with a_j ≥ a_j−1, a_0 > 0 (j = 1, 2, ..., n), a classical result of Enestrom-Kakeya says that all the zeros of P(z) lie in |z| ≤ 1. This result was generalized by A. Joyal et al. [3] where they relaxed the non-negative condition on the coefficents. This result was further generalized by Dewan and Bidkham [9] by relaxing the monotonicity of the coefficients. In this paper, we use some techniques to obtain some more generalizations of the results [3], [8], [9].

Hyosang Kang(Daegu Gyeongbuk Institute of Scienceand Technology) ; Hyunwoo Jung(Daegu Science High School) ; Chaehwan Seol(Gwangju Science Academy) ; Namho Hong(Daegu Science High School) ; Hyunjin Lim(Daegu Science High School) ; Seokhyun Um(Daegu Science High School) pp.57-81 https://doi.org/10.7468/jksmeb.2024.31.1.57
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Abstract

We introduce a new degree reduction method for homogeneous symmetric polynomials on binary variables that generalizes the conventional degree reduction methods on monomials introduced by Freedman and Ishikawa. We also design an degree reduction algorithm for general polynomials on binary variables, simulated on the graph coloring problem for random graphs, and compared the results with the conventional methods. The simulated results show that our new method produces reduced quadratic polynomials that contains less variables than the reduced quadratic polynomials produced by the conventional methods.

Amrish Handa(Govt. P. G. Arts and Science College) ; Dinesh Verma(Govt. Madhav Science College Ujjain) pp.83-102 https://doi.org/10.7468/jksmeb.2024.31.1.83
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Abstract

In this paper, first we establish a unique common fixed point theorem satisfying new contractive condition on partially ordered non-Archimedean fuzzy metric spaces and give an example to support our result. By using the result established in the first section of the manuscript, we formulate a unique common coupled fixed point theorem and also give an example to validate our result. In the end, we study the existence of solution of integral equation to verify our hypothesis. These results generalize, improve and fuzzify several well-known results in the existing literature.

Om Prakash Chauhan(Jabalpur Engineering College) ; Vishal Joshi(Jabalpur Engineering College) ; Saurabh Singh(Jabalpur Engineering College) pp.103-117 https://doi.org/10.7468/jksmeb.2024.31.1.103
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Abstract

In this article, we utilize the concepts of hybrid rational Geraghty type generalized F-contraction and to prove some fixed point results for such mappings are in the perspective of partially ordered b-metric like space. Some innovative examples are also presented which substantiate the validity of obtained results. The example is also authenticated with the help of graphical representations.

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics