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Volume 6, Number 4 (2023)

Trigonometric generated Lp degree of approximation
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George A. Anastassiou
Annals of Communications in Mathematics 2023, Vol. 6 (4), 209-219

Abstract

In this article we continue the study of smooth Picard singular integral operators that started in [3], see there chapters 10-14. This time the foundation of our research is a trigonometric Taylor’s formula. We establish the Lp convergence of our operators to the unit operator with rates via Jackson type inequalities engaging the first Lp modulus of continuity. Of interest here is a residual appearing term. Note that our operators are not positive.

New definition of a singular integral operator
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Alexander G. Ramm
Annals of Communications in Mathematics 2023, Vol. 6 (4), 220-224

Abstract

Let D be a connected bounded domain in R^2, S be its boundary which is closed, connected, and smooth, or S=(-∞,∞). Let Φ(z) be the function defined as Φ(z)=1/(2πi) ∫S(f(s)ds)/(s-z), where f∈L^1(S) and z=x+iy. The singular integral operator Af is defined as Af: =1/(iπ) ∫S(f(s)ds)/(s-t), where t∈S. This new definition simplifies the proof of the existence of Φ(t). Necessary and sufficient conditions are given for f∈L^1(S) to be the boundary value of an analytic function in D. The Sokhotsky-Plemelj formulas are derived for f∈L^1(S). Our new definition allows one to treat singular boundary values of analytic functions.

Fuzzy soft tri-ideals over Gamma-semirings
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Marapureddy Murali Krishna Rao, Rajendra Kumar Kona and Noorbhasha Rafi
Annals of Communications in Mathematics 2023, Vol. 6 (4), 225-237

Abstract

In this paper, we introduce the notion of a fuzzy soft tri-ideal over Γ−semiring. We characterize the regular Γ−semiring in terms of fuzzy soft tri-ideals, and study some of the properties. M is a regular Γ−semiring, E be a parameters set and A ⊆ E. If (µ, A) is a fuzzy soft left tri-ideal over M, then (µ, A) is a fuzzy soft right ideal over M.

Approximation by sequences of q-Szasz-operators generated by Dunkl exponential function
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Md. Nasiruzzaman and M. Mursaleen
Annals of Communications in Mathematics 2023, Vol. 6 (4), 238-246

Abstract

The main purpose of this article is to introduce a modification of q-Dunkl generalization of Szasz-operators. We obtain approximation results via well known Ko- ´ rovkin’s type theorem. Moreover, we obtain the order of approximation, rate of convergence, functions belonging to the Lipschitz class and some direct theorems.

On m∆-open sets in micro topological spaces
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S. Ganesan
Annals of Communications in Mathematics 2023, Vol. 6 (4), 247-252

Abstract

The aim of this article, we introduced and studied m∆-open sets in micro topological spaces. We offer a new class of sets called m∆-closed sets in micro topological spaces and we study some of its basic properties. we introduce m∆-interior and m∆- closure and study some of its basic properties. We introduce m∆-continuous maps , m∆- irresolute maps and study some of its basic properties.

Schauder-Tychonoff Fixed Point Theorem on Sequentially Complete Hausdorff Strongly Convex Topological Vector Spaces
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G. Saravanakumar, K. A. Venkatesan and S. Sivaprakasam
Annals of Communications in Mathematics 2023, Vol. 6 (4), 253-259

Abstract

In this paper, we study the Schauder-Tychonoff fixed point (STFP) on a subset A of a sequentially complete Hausdorff strongly convex topological vector space (SCHSCTVS) E (over the field R) with calibration Γ have a unique STFP in Topological Vector Space (TVS).

Nano ∆ generalized-closed sets in nano topological spaces
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S. Ganesan
Annals of Communications in Mathematics 2023, Vol. 6 (4), 260-265

Abstract

In this paper, we study the schauder-tychonoff fixed point(STFP) on a subset A of a sequentially complete Hausdorff strongly convex topological vector space (SCHSCTVS) E (over the field R) with calibration Γ have a unique STFP in Topological Vector Space(TVS).

Anti fuzzy k-ideals of ordered semirings
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M. Murali Krishna Rao
Annals of Communications in Mathematics 2023, Vol. 6 (4), 266-281

Abstract

In this paper we introduce the notion of anti fuzzy ideals, anti fuzzy k−ideals of ordered semirings and we study the properties of anti fuzzy ideals, anti fuzzy k−ideals, homomorphic and anti homomorphic image and pre-image of fuzzy ideals, anti fuzzy ideals and anti fuzzy k−ideals of an ordered semiring. We characterize the ideals of an ordered semiring in terms of anti fuzzy k−ideals.

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