Some fixed point theorems for \(F\)-expansive mapping in generalized metric spaces
OMA-Vol. 5 (2021), Issue 2, pp. 17 – 30 Open Access Full-Text PDF
Mohamed Rossafi, Abdelkarim Kari
Abstract: In this paper, we present the notion of generalized \(F\)-expansive mapping in complete rectangular metric spaces and study various fixed point theorems for such mappings. The findings of this paper, generalize and improve many existing results in the literature.
The hyper order and fixed points of solutions of a class of linear differential equations
OMA-Vol. 5 (2021), Issue 2, pp. 1 – 16 Open Access Full-Text PDF
Nour el imane Khadidja CHERIET, Benharrat BELAÏDI
Abstract: In this paper, we precise the hyper order of solutions for a class of higher order linear differential equations and investigate the exponents of convergence of the fixed points of solutions and their first derivatives for the second order case. These results generalize those of Nan Li and Lianzhong Yang and of Chen and Shon.
Strongest relation, cosets and middle cosets of \(AQFSC(G)\)
EASL-Vol. 4 (2021), Issue 3, pp. 1 – 7 Open Access Full-Text PDF
R. Rasuli
Abstract: The aim of this paper is to introduce strongest relation, cosets and middle cosets of anti \(Q\)-fuzzy subgroups of \(G\) with respect to \(t\)-conorm \(C.\) We investigate equivalent characterizations of them and we construct a new group induced by them, and give the homomorphism theorem between them.
Generalized fractional Hadamard type inequalities for \(Q_s\)-class functions of the second kind
OMS-Vol. 5 (2021), Issue 1, pp. 270 – 278 Open Access Full-Text PDF
McSylvester Ejighikeme Omaba, Louis O. Omenyi
Abstract: New Hadamard type inequalities for a class of \(s\)-Godunova-Levin functions of the second kind for fractional integrals are obtained. These new estimates extend and generalize some existing results for the \(Q\)-class and \(P\)-class functions. The generalized case for the Katugampola fractional integrals are also given.
Congruence properties of indices of triangular numbers multiple of other triangular numbers
OMS-Vol. 5 (2021), Issue 1, pp. 262 – 269 Open Access Full-Text PDF
Vladimir Pletser
Abstract: For any non-square integer multiplier \(k\), there is an infinity of triangular numbers multiple of other triangular numbers. We analyze the congruence properties of indices \(\xi\) of triangular numbers multiple of triangular numbers. Remainders in congruence relations \(\xi\) modulo \(k\) come always in pairs whose sum always equal \((k-1)\), always include 0 and \((k-1)\), and only 0 and \((k-1)\) if \(k\) is prime, or an odd power of a prime, or an even square plus one or an odd square minus one or minus two. If the multiplier \(k\) is twice the triangular number of \(n\), the set of remainders includes also \(n\) and \((n^{2}-1)\) and if \(k\) has integer factors, the set of remainders include multiples of a factor following certain rules. Algebraic expressions are found for remainders in function of \(k\) and its factors, with several exceptions. This approach eliminates those \(\xi\) values not providing solutions.
Outcome of 82 cases of nasal polyposis undergoing functional endoscopic sinus surgery
TCMS-Vol. 1 (2021), Issue 2, pp. 21 – 25 Open Access Full-Text PDF
Ankush Sathiyan, Hari Mahajan Jain, Sarfaraz Alam Khan
Abstract:The aim of this paper is to study 82 cases of nasal polyposis undergoing functional endoscopic sinus surgery (FESS). Our study comprised of 82 patients presenting with the symptoms of nasal polyposis (38 male patient, 44 female patients). All managed with FESS. Parameters assessed were NOSE score and nasal endoscopy score pre- operatively which was compared with post- operative score at 6 months and 12 months. We found pre-operative NOSE score was \(65.2\pm 5.7,\) at 6 months was \(28.4\pm 4.1\) and at 12 months post-operatively was \(24.2\pm 3.6.\) We found pre-operative nasal endoscopic score was 6.02, 6 months score was 3.1 and 12 months score was 2.5. We conclude that the patients nasal endoscopy score and NOSE symptom score was improved after treatment. Functional endoscopic sinus surgery is treatment of choice in patients with chronic rhinosinusitis with nasal polyps.
